modelos estad´ısticos dinámicos para análisis de evolución de
TRANSCRIPT
Universidad Politecnica de Madrid
Escuela Tecnica Superior de Ingenieros Industriales
Modelos Estadısticos Dinamicos
para Analisis de Evolucion de
Tasas de Accidentes:
Metodologıa y Herramientas
Computacionales
Tesis Doctoral
BAHAR DADASHOVA
Madrid 2014
Departamento de Ingenierıa Mecanica y Fabricacion
Escuela Tecnica Superior de Ingenieros Industriales
Modelos Estadısticos Dinamicos
para Analisis de Evolucion de
Tasas de Accidentes:
Metodologıa y Herramientas
Computacionales
Tesis Doctoral
BAHAR DADASHOVA
TUTORES:
Blanca Arenas Ramırez Jose Mira McWilliamsDoctor Ingeniero de Caminos, Doctor Ingeniero IndustrialCanales y Puertos
Tribunal nombrado por el Magfco. y Excmo. Sr. Rector de la UniversidadPolitecnica de Madrid, el dıa de diciembre de 2014.
Presidente: D. Francisco Aparicio Izquierdo
Secretario: D. Camino Gonzalez Fernandez
Vocal: D. Emilio Larrode Pellicer
Vocal: D. Juan de Ona Lopez
Vocal: D. Alvaro Gomez Mendez
Suplente: D. Francisco Garcıa Benıtez
Suplente: D. Alberto Lopez Rozado
Realizado el acto de defensa y lectura de la tesis el dıa de diciembre de2014 en la E.T.S. Ingenieros Industriales.
CALIFICACION:
EL PRESIDENTE
LOS VOCALES
EL SECRETARIO
Acknowledgements
I would like to express my sincere gratitude to my supervisors, Blanca Arenasand Jose Mira for all their effort and time and to Francisco Aparicio, for givingme an opportunity to be a part of University Institute of University Instituteof Automobile Research-INSIA. I would like to thank to my family for theirconstant support and understanding, and also take the opportunity to wishmy brother Sabuhi Dadashov best luck in his doctorate studies.
I would also like to thank Rosario Romero, Camino Gonzalez, EdinalvaGomes, Filip Van den Bossche and Frits Bijleveld for their help and col-laborations; and to all of my friends and collegues, particularly, to ArgyroAvgoustaki, Jessica Viqueira, Raquel de Roa, Nasima Akalou, Azadeh Nasiriand Ana Laura Badagian for their invaluable presence along this way.
I gratefully acknowledge the funding sources that made my researchpossible.
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Abstract
Road accidents are a very relevant social phenomenon and one of the maincauses of death in industrialized countries. Sophisticated econometric modelsare applied in academic work and by the administrations for a better under-standing of this very complex phenomenon. This thesis is thus devoted to theanalysis of macro models for road accidents with application to the Spanishcase. The objectives of the thesis may be divided in two blocks:
a. To achieve a better understanding of the road accident phenomenon bymeans of the application and comparison of two of the most frequentlyused macro modelings: DRAG (demand for road use, accidents andtheir gravity) and UCM (unobserved components model); the applica-tion was made to van involved accident data in Spain in the period2000-2009. The analysis has been carried out within the frequentistframework and using available state of the art software, TRIO, SASand TRAMO/SEATS.
b. Concern on the application of the models and on the relevant inputvariables to be included in the model has driven the research to tryto improve, by theoretical and practical means, the understanding onmethodological choice and model selection procedures. The theoreticaldevelopments have been applied to fatal accidents during the period2000-2011 and van-involved road accidents in 2000-2009.
This has resulted in the following contributions:
a. Insight on the models has been gained through interpretation of theeffect of the input variables on the response and prediction accuracyof both models. The behavior of van-involved road accidents has beenexplained during this process.
b1. Development of an input variable selection procedure, which is crucialfor an efficient choice of the inputs. Following the results of a) the
v
procedure uses the DRAG-like model. The estimation is carried outwithin the Bayesian framework. The procedure has been applied forthe total road accident data in Spain in the period 2000-2011. Theresults of the model selection procedure are compared and validatedthrough a dynamic regression model given that the original data has astochastic trend.
b2. A methodology for theoretical comparison between the two modelsthrough Monte Carlo simulation, computer experiment design and ANOVA.The models have a different structure and this affects the estimation ofthe effects of the input variables. The comparison is thus carried outin terms of the effect of the input variables on the response, which is ingeneral different, and should be related. Considering the results of thestudy carried out in b1) this study tries to find out how a stochastictime trend will be captured in DRAG model, since there is no specifictrend component in DRAG. Given the results of b1) the findings of thisstudy are crucial in order to see if the estimation of data with stochas-tic component through DRAG will be valid or whether the data need acertain adjustment (typically differencing) prior to the estimation. Themodel comparison methodology was applied to the UCM and DRAGmodels, considering that, as mentioned above, the UCM has a specifictrend term while DRAG does not.
b3. New algorithms were developed for carrying out the methodologicalexercises. For this purpose different softwares, R, WinBUGs and MAT-LAB were used.
These objectives and contributions have been resulted in the followingfindings:
1. The road accident phenomenon has been analyzed by means of twomacro models: The effects of the influential input variables may beestimated through the models, but it has been observed that the esti-mates vary from one model to the other, although prediction accuracyis similar, with a slight superiority of the DRAG methodology.
2. The variable selection methodology provides very practical results, asfar as the explanation of road accidents is concerned. Prediction ac-curacy and interpretability have been improved by means of a moreefficient input variable and model selection procedure.
3. Insight has been gained on the relationship between the estimates ofthe effects using the two models. A very relevant issue here is the roleof trend in both models, relevant recommendations for the analyst haveresulted from here.
The results have provided a very satisfactory insight into both modelingaspects and the understanding of both van-involved and total fatal accidentsbehavior in Spain.
Resumen
Los accidentes del trafico son un fenomeno social muy relevantes y una de lasprincipales causas de mortalidad en los paıses desarrollados. Para entendereste fenomeno complejo se aplican modelos econometricos sofisticados tantoen la literatura academica como por las administraciones publicas. Esta tesisesta dedicada al analisis de modelos macroscopicos para los accidentes deltrafico en Espana.
El objetivo de esta tesis se puede dividir en dos bloques:
a. Obtener una mejor comprension del fenomeno de accidentes de traficomediante la aplicacion y comparacion de dos modelos macroscopicosutilizados frecuentemente en este area: DRAG y UCM, con la apli-cacion a los accidentes con implicacion de furgonetas en Espana du-rante el perıodo 2000-2009. Los analisis se llevaron a cabo con enfoquefrecuencista y mediante los programas TRIO, SAS y TRAMO/SEATS.
b. La aplicacion de modelos y la seleccion de las variables mas relevantes,son temas actuales de investigacion y en esta tesis se ha desarrollado yaplicado una metodologıa que pretende mejorar, mediante herramientasteoricas y practicas, el entendimiento de seleccion y comparacion delos modelos macroscopicos. Se han desarrollado metodologıas tantopara seleccion como para comparacion de modelos. La metodologıa deseleccion de modelos se ha aplicado a los accidentes mortales ocurridosen la red viaria en el perıodo 2000-2011, y la propuesta metodologica decomparacion de modelos macroscopicos se ha aplicado a la frecuenciay la severidad de los accidentes con implicacion de furgonetas en elperıodo 2000-2009.
Como resultado de los desarrollos anteriores se resaltan las siguientes con-tribuciones:
a. Profundizacion de los modelos a traves de interpretacion de las variablesrespuesta y poder de prediccion de los modelos. El conocimiento sobre
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el comportamiento de los accidentes con implicacion de furgonetas seha ampliado en este proceso.
b1. Desarrollo de una metodologıa para seleccion de variables relevantespara la explicacion de la ocurrencia de accidentes de trafico. Teniendoen cuenta los resultados de a) la propuesta metodologica se basa enlos modelos DRAG, cuyos parametros se han estimado con enfoquebayesiano y se han aplicado a los datos de accidentes mortales entrelos anos 2000-2011 en Espana. Esta metodologıa novedosa y originalse ha comparado con modelos de regresion dinamica (DR), que sonlos modelos mas comunes para el trabajo con procesos estocasticos.Los resultados son comparables, y con la nueva propuesta se realizauna aportacion metodologica que optimiza el proceso de seleccion demodelos, con escaso coste computacional.
b2. En la tesis se ha disenado una metodologıa de comparacion teorica entrelos modelos competidores mediante la aplicacion conjunta de simulacionMonte Carlo, diseno de experimentos y analisis de la varianza ANOVA.Los modelos competidores tienen diferentes estructuras, que afectan a laestimacion de efectos de las variables explicativas. Teniendo en cuentael estudio desarrollado en b1) este desarrollo tiene el proposito de de-terminar como interpretar la componente de tendencia estocastica queun modelo UCM modela explıcitamente, a traves de un modelo DRAG,que no tiene un metodo especıfico para modelar este elemento. Los re-sultados de este estudio son importantes para ver si la serie necesita serdiferenciada antes de modelar.
b3. Se han desarrollado nuevos algoritmos para realizar los ejercicios metodologicos,implementados en diferentes programas como R, WinBUGS, y MAT-LAB.
El cumplimiento de los objetivos de la tesis a traves de los desarrollos antesenunciados se remarcan en las siguientes conclusiones:
1. El fenomeno de accidentes del trafico se ha analizado mediante dosmodelos macroscopicos. Los efectos de los factores de influencia sondiferentes dependiendo de la metodologıa aplicada. Los resultados deprediccion son similares aunque con ligera superioridad de la metodologıaDRAG.
2. La metodologıa para seleccion de variables y modelos proporciona resul-tados practicos en cuanto a la explicacion de los accidentes de trafico.
La prediccion y la interpretacion tambien se han mejorado medianteesta nueva metodologıa.
3. Se ha implementado una metodologıa para profundizar en el conocimientode la relacion entre las estimaciones de los efectos de dos modelos com-petidores como DRAG y UCM. Un aspecto muy importante en estetema es la interpretacion de la tendencia mediante dos modelos difer-entes de la que se ha obtenido informacion muy util para los investi-gadores en el campo del modelado.
Los resultados han proporcionado una ampliacion satisfactoria del conocimientoen torno al proceso de modelado y comprension de los accidentes con impli-cacion de furgonetas y accidentes mortales totales en Espana.
Dedicated to my parents and siblings.
Contents
I Accidents and their consequences during the pe-riod 2000-2011. Potential influential factors in roadaccident analysis 1
1 Introduction 31.1 Road accidents . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Methodological approach . . . . . . . . . . . . . . . . . . . . . 61.3 Main objectives and the structure of the thesis . . . . . . . . . 8
2 Data set 112.1 Dependent variables . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Fatal accidents . . . . . . . . . . . . . . . . . . . . . . 132.1.2 Van-involved road accidents . . . . . . . . . . . . . . . 13
2.2 Explanatory factors . . . . . . . . . . . . . . . . . . . . . . . . 162.2.1 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.2 Economic variables . . . . . . . . . . . . . . . . . . . . 202.2.3 Driver characteristics and surveillance . . . . . . . . . . 272.2.4 Vehicle characteristics . . . . . . . . . . . . . . . . . . 312.2.5 Road infrastructure . . . . . . . . . . . . . . . . . . . . 312.2.6 Legislative measures . . . . . . . . . . . . . . . . . . . 342.2.7 Weather conditions . . . . . . . . . . . . . . . . . . . . 372.2.8 Calendar effect . . . . . . . . . . . . . . . . . . . . . . 40
2.3 Adjusting the data: missing values . . . . . . . . . . . . . . . 402.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
II Computational Tools for the Evaluation and Anal-ysis of Road Safety. 43
3 Statistical methodology 47
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3.1 Functional form . . . . . . . . . . . . . . . . . . . . . . . . . . 473.1.1 Dynamic regression . . . . . . . . . . . . . . . . . . . . 473.1.2 Demand for Road use, Accidents and their Gravity
(DRAG) . . . . . . . . . . . . . . . . . . . . . . . . . . 493.1.3 Unobserved Components Model (UCM) . . . . . . . . . 54
3.2 Model estimation and diagnosis . . . . . . . . . . . . . . . . . 553.2.1 Maximum likelihood estimation . . . . . . . . . . . . . 553.2.2 Markov Chain Monte Carlo estimation . . . . . . . . . 573.2.3 Goodness of fit measures . . . . . . . . . . . . . . . . . 58
3.3 Elasticity estimation . . . . . . . . . . . . . . . . . . . . . . . 613.4 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . 623.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4 Explanation of van-involved road accident indicators. Model
comparison 654.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 Van-involved road accidents . . . . . . . . . . . . . . . . . . . 664.3 Independent variables . . . . . . . . . . . . . . . . . . . . . . . 714.4 Model construction and estimation . . . . . . . . . . . . . . . 734.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.5.1 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . 814.5.2 Economic factors . . . . . . . . . . . . . . . . . . . . . 814.5.3 Driver behavior surveillance . . . . . . . . . . . . . . . 834.5.4 Fleet characteristics . . . . . . . . . . . . . . . . . . . . 844.5.5 Road infrastructure . . . . . . . . . . . . . . . . . . . . 844.5.6 Legislative measures . . . . . . . . . . . . . . . . . . . 854.5.7 Calendar effect and weather conditions . . . . . . . . . 86
4.6 Prediction analysis . . . . . . . . . . . . . . . . . . . . . . . . 864.7 Summary and discussions . . . . . . . . . . . . . . . . . . . . 91
5 Analysis of fatal accidents: model selection methodology 955.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.2 Fatal accidents . . . . . . . . . . . . . . . . . . . . . . . . . . 965.3 Independent variables . . . . . . . . . . . . . . . . . . . . . . . 965.4 Model selection procedure . . . . . . . . . . . . . . . . . . . . 965.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5.1 Explanatory variable selection . . . . . . . . . . . . . . 1025.5.2 Estimation of power transformation parameter . . . . . 1035.5.3 Model selection . . . . . . . . . . . . . . . . . . . . . . 104
5.5.4 Dynamic regression model . . . . . . . . . . . . . . . . 1065.6 Prediction analysis . . . . . . . . . . . . . . . . . . . . . . . . 1105.7 Summary and discussions . . . . . . . . . . . . . . . . . . . . 112
6 Simulation experiment based model comparison methodology
with application to road accident models 1156.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1156.2 Simulation experiment methodology . . . . . . . . . . . . . . . 1176.3 Empirical study . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186.3.2 Model estimation . . . . . . . . . . . . . . . . . . . . . 119
6.4 Experimental design: estimation and results . . . . . . . . . . 1216.4.1 Experimental design . . . . . . . . . . . . . . . . . . . 1216.4.2 Generating UCM samples . . . . . . . . . . . . . . . . 1276.4.3 Estimating DRAG models using the UCM samples . . 1276.4.4 ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.4.5 Results of the experimental design-ANOVA . . . . . . 129
6.5 Summary and discussions . . . . . . . . . . . . . . . . . . . . 132
III Conclusions 135
Bibliography 142
Appendix I 157
Appendix II 162
Appendix III 174
Appendix IV 177
Appendix V 187
Appendix VI 193
Appendix VII 211
List of Figures
1.1 Road use indicators: drivers, vehicles and total distance trav-elled vs. road traffic casualities and fatal accidents in Spain1990-2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Causes of death for age groups in Spain. Year 2012 . . . . . . 5
2.1 Fatalities in accidents with vehicle type involved.(Index Year2000 = 100.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Yearly data on fatal accidents, ACCTOT , 2000-2011: all ve-hicle types included. . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Yearly data on van-involved road accident indicators, 2000-2009: 15
2.4 Exposure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 Economic factors. . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Driver characteristics. . . . . . . . . . . . . . . . . . . . . . . . 29
2.7 Vehicle characteristics. . . . . . . . . . . . . . . . . . . . . . . 32
2.8 Road infrastructure. . . . . . . . . . . . . . . . . . . . . . . . 33
2.9 Legislative measures. . . . . . . . . . . . . . . . . . . . . . . . 35
2.10 Weather conditions. . . . . . . . . . . . . . . . . . . . . . . . . 39
2.11 Calendar effect. . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Decomposition of series into trend-cycle and seasonal compo-nents with TRAMO/SEATS: . . . . . . . . . . . . . . . . . . 70
4.2 Residual analysis of road safety measures. . . . . . . . . . . . 80
4.3 Observed versus predicted values of four road safety indicators,corresponding to year 2009. . . . . . . . . . . . . . . . . . . . 89
4.4 Prediction errors corresponding to quarterly data. . . . . . . . 91
5.1 Decomposition ofACCTOT into trend-cycle and seasonal com-ponents with TRAMO/SEATS. . . . . . . . . . . . . . . . . . 98
5.2 BCT optimization, Yt. . . . . . . . . . . . . . . . . . . . . . . 104
5.3 Prediction intervals for selected models. . . . . . . . . . . . . . 111
xvii
6.1 Simulation methodology. . . . . . . . . . . . . . . . . . . . . 1186.2 Residual analysis of ACCMOR . . . . . . . . . . . . . . . . . 1206.3 Generated samples . . . . . . . . . . . . . . . . . . . . . . . . 1286.4 Interaction plot between D and F , for the DRAG parameter
ηDLAB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
List of Tables
2.1 Explanatory factors. . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 DRAG family models. . . . . . . . . . . . . . . . . . . . . . . 503.2 Elasticity estimates for different functional forms (McCarthy ,
2001). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1 Dependent variables. . . . . . . . . . . . . . . . . . . . . . . . 664.2 Summary of TRAMO/SEATS results∗. . . . . . . . . . . . . . 714.3 Explanatory variables, 2000-2009. . . . . . . . . . . . . . . . 724.4 Parameter estimates of DRAG models. . . . . . . . . . . . . . 744.5 Fit statistics of DRAG models. . . . . . . . . . . . . . . . . . 744.6 Fit statistics of UCM components. . . . . . . . . . . . . . . . 754.7 Normality test of UCM errors. . . . . . . . . . . . . . . . . . . 764.8 Exposure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.9 Economic factors. . . . . . . . . . . . . . . . . . . . . . . . . . 824.10 Driver behavior surveillance. . . . . . . . . . . . . . . . . . . . 844.11 Fleet characteristics. . . . . . . . . . . . . . . . . . . . . . . . 844.12 Road infrastructure. . . . . . . . . . . . . . . . . . . . . . . . 854.13 Legislative measures. . . . . . . . . . . . . . . . . . . . . . . . 854.14 Calendar effect and weather conditions. . . . . . . . . . . . . . 864.15 A year ahead prediction, year 2009. . . . . . . . . . . . . . . 904.16 Prediction error in percentage for DRAG and UCM. . . . . . 90
5.1 Summary of TRAMO/SEATS results, ACCTOT . . . . . . . . 975.2 Outlier detection. . . . . . . . . . . . . . . . . . . . . . . . . . 975.3 Explanatory variables, 2000-2011. . . . . . . . . . . . . . . . 995.4 Stage 1: Pseudo-R2 values of selected two-input models for
three different values of power transformation, λX . . . . . . . . 1025.5 Explanatory variables selection. . . . . . . . . . . . . . . . . . 1035.6 Selected variables and the expected signs, based on previous
empirical studies. . . . . . . . . . . . . . . . . . . . . . . . . . 105
xix
5.7 Fit statistics of selected 10 SE models. . . . . . . . . . . . . . 1055.8 Fit statistics of DR models. . . . . . . . . . . . . . . . . . . . 1075.9 Estimation results of selected models, DR2 and SE207. . . . . 1075.10 Posterior prediction intervals of selected models. . . . . . . . . 1095.11 Prediction accuracy of selected models . . . . . . . . . . . . . 110
6.1 Explanatory variables. . . . . . . . . . . . . . . . . . . . . . . 1196.2 Results of empirical study: fit statistics and parameter estimates.1216.3 Parameter estimates. . . . . . . . . . . . . . . . . . . . . . . . 1226.7 DRAG estimation. . . . . . . . . . . . . . . . . . . . . . . . . 1266.8 Significant main effects for DRAG parameters. . . . . . . . . . 1306.9 Analysis of variance: ηPARSER . . . . . . . . . . . . . . . . . . 2126.10 Analysis of variance: ηCONALC . . . . . . . . . . . . . . . . . . 2136.11 Analysis of variance: ηSUSP . . . . . . . . . . . . . . . . . . . 2146.12 Analysis of variance: ηDLAB . . . . . . . . . . . . . . . . . . . 2156.13 Analysis of variance: ηCOMTOT . . . . . . . . . . . . . . . . . . 2166.14 Analysis of variance: ρ1 . . . . . . . . . . . . . . . . . . . . . . 2176.15 Analysis of variance: ρ2 . . . . . . . . . . . . . . . . . . . . . . 2186.16 Analysis of variance: λ . . . . . . . . . . . . . . . . . . . . . . 219
Part I
Accidents and their
consequences during the period
2000-2011. Potential influential
factors in road accident analysis
1
Chapter 1
Introduction
1.1 Road accidents
During the last two decades very important policy measures have been im-plemented by the respective administrations in Spain with the purpose ofimproving the road safety. These measures have been intensified since Jan-uary 2003. In July 2006 and December 2007 two most important policy mea-sures, the Penalty Point System and the Penal Code Reform were enactedrespectively. Other preventive and corrective strategies were also conductedduring 2005-2008, in the framework of Road Safety Strategic Plan, e.g., amore intense monitoring of speed, alcohol or drug use, media coverage ofsafety items, etc. As it can be observed in Figure 1.1 1, all these factors havethus helped in the improvement of road safety measures in Spain. Between2001 and 2010, the total number of fatal accidents decreased from 4,170 to1,953 (53% decrease) and the number of road fatalities from 5,516 to 2,479(55%).
The last two decades are also characterized by the intensified road net-work use and increasing exposure, as it can be seen in the same figure. Thenumber of travelers in transport has doubled during 1997-2007 in Spain, hav-ing in turn a significant economic, social and environmental impact. It isestimated that, currently, there are 31 million vehicles circulating in Spain,driven by more than 26 million drivers in more than 165,000 km of roads(Lopez and Skowronek , 2014). These figures (except for road length) do not
1 The data for fatalities, driver census and vehicle fleet are obtained from Directory of
General Traffic while the mobility data were obtained from Ministry of Public Works and
Transport
3
Chapter 1. Introduction 4
Fig. 1.1. Road use indicators: drivers, vehicles and total distance travelled vs. road
traffic casualities and fatal accidents in Spain 1990-2011
represent exposure caused by tourists visiting the country, that estimated tobe more than 60 million during 2013 alone.
The increasing number of road users and the exposure can jeopardize theeffect of road safety measures. The injury and the loss of human life are theprimary damages inflicted by accidents. In spite of the improving road safetyindicators, as mentioned above, the consequences of road accidents such asthe number of deaths and injured victims are still very high. It is estimatedthat in 2013 the total number of deaths in Spanish roads has been 1,680. Thenumber of seriously injured as the result of traffic accidents is even higher,19,508. In general, worldwide, more than 1.2 million people die annuallyin highway-related crashes and as many as 20-50 million are injured (WorldHealth Organization , 2013). It is estimated that by 2030 road accidents willbe the 5th leading cause of death in the world (World Health Organization ,2013). In Spain, road accident-related fatalities are one of the leading causesof death, specially among the younger age groups (Figure 1.2 2). It is the
2National Institute of Statistics (INE).
5 1.1. Road accidents
Fig. 1.2. Causes of death for age groups in Spain. Year 2012
first cause of death for age groups 20-24. And for the age group 30-39, roadaccidents have been the third leading cause of death in 2012. The averageage of death as a result of road accidents is around 50 years old. This showsthat the main victims of the road accidents are the working-age group, whichbesides the human loss also has a negative impact on the economy. Moreover,road accident-related injuries cause a great problem on the health system of astate. The impact of road traffic accidents on the economy is thus inevitable.It is estimated that, on average, their total costs, including an economicvaluation of lost quality of life, are about 2.5% of the gross domestic product(GDP) (Elvik , 2000). Excluding the valuation of lost quality of life, roadaccident costs on average amount approximately to 1.3% of the GDP.
Thus, road safety remains one of the priorities and is still pending of fur-ther improvements, which is a goal followed by safety-concerned state admin-istrations and international non-governmental organizations. This problemcan be solved through different means but all should be scientifically sound.The data collected from reliable sources should be analyzed using the mostadequate scientific and statistical methodologies in order to study road safetyindicators, with the purpose of reducing road accident frequency and severity.
Chapter 1. Introduction 6
1.2 Methodological approach
Accidents are the outcome of a complex random process, whose general char-acteristics can be modelled statistically (Elvik and Vaa , 2004, Washingtonet al. , 2011). The research on road accidents has one specific goal: to im-prove the road safety, hence the main factors causing this phenomenon shouldbe clearly stated and studied. Many empirical studies have tried to explaintraffic accident data by means of different factors. These factors are referredto as explanatory factors or variables. The estimation of the effect of theselected factors and policy measures on road safety is conducted by meansof econometric models whose main task is to describe, explain and predictroad safety developments (Hakim et al. , 1991). As road safety indicators,normally the frequency (accident count) and severity (victim count) of theaccidents are assessed. In the econometric model these measures take up therole of the response, while the explanatory factors take up the role of the re-gressors (predictors). In general the accident data can be categorized as timeseries, cross sectional or panel data, with the time-series data being mostlyused.
The choice of the econometric model to be used for the estimation ofroad accident frequency and severity depends on the data available to theresearcher. Given that road accident data are usually count data, where theobservations take only non-negative, integer values, the Poisson regressionhas served as a basis for some initial research study in road safety analysis(Abdel-Aty and Radwan , 2000, Fridstrøm et al. , 1995, Hauer , 2001, 2004,Hauer et al. , 2004, Ivan et al. , 2000, Jovanis and Chang , 1986, Knuimanet al. , 1993, Lord et al. , 2005, Lord and Mannering , 2010, Miaou , 1996,Miaou et al. , 1992, Miaou and Lum , 1993, Milton and Mannering , 1998,Poch and Mannering , 1996, Shankar et al. , 1997). The Poisson process isthe continuous time analog of Bernoulli trials and was investigated by theFrench mathematician Simon Denis Poisson (1781–1840). The Bernoulli trialis an experiment with two possible outcomes: success and failure. Thus it ismore appropriate to use Poisson models for micro (disaggregated) data, suchas number of accidents in a given intersection, severity of accidents in a givenroad section, etc. The Poisson model is used when the mean and varianceof the accident frequencies are approximately equal. A relatively longer timeseries data will be Poisson distributed. However in practice the actual dataseries is not so long, thus problems such as over-dispersion, i.e. a significantlyhigher variance, may arise. For such kind of data it is more appropriate touse a negative binomial model.
7 1.2. Methodological approach
Although the Poisson distribution structure is appropriate for countdata, it is not able to take into account the autocorrelation observed in themost time series data. The autocorrelation is observed when the error termsare correlated over time. The persistence of this problem in the model couldresult in biased estimates of the coefficients thus affecting the interpreta-tion and the prediction accuracy. The error autocorrelation can happen dueto different reasons; one is the explanatory factors present in an accidentmodel, specially if there is a lagged relationship between these factors andthe dependent variable. This phenomena can be modelled through dynamicregression (DR) or transfer functions where the autocorrelated error termis assumed to follow the Box and Jenkins autoregressive integrated movingaverage (ARIMA) process (Box and Jenkins , 1970). The DR models havebeen frequently applied in road safety analysis, specially where the effect ofmacro-economic factors and policy measures on the road safety indicators hasbeen studied (Garcıa-Ferrer et al. , 2006, 2007).
A different model type, that has been used in road safety analysis is theDRAG (demand for road use, accidents and their gravity) models developedby Gaudry (1984) and Gaudry and Lassarre (2000), where the error au-tocorrelation is treated through autoregressive process. The DRAG modeltries to explain accidents for a whole region, province or a country and definethe role the external factors play in the occurrence of accidents. In generalDRAG strategy is described as i) formulation of the problem and simulationof a system of equations which is typically estimated recursively; ii) decom-posing the damage outcomes (victims) by category; iii) making extensive useof Box -Cox transformation; iv) producing correlation signs, coefficients andassociated elasticities which show the relationship between the external fac-tors on traffic accidents and their severity. The original DRAG model wasdeveloped for Quebec, Canada and consists of a five layer procedure to ex-plain the impact of several factors on monthly demand for road use and thenumber of road accident victims, during the period of 1956-1982. Later on,DRAG-inspired models were developed for other parts of the world such asNorway (Fridstrøm , 2000), Stockholm (Tegner and Loncar-Lucassi , 1997),France (Jaeger and Lassarre , 2000), Germany (Blum and Gaudry , 2000),California (McCarthy , 2000), Spain (Aparicio et al. , 2013), Algeria (Gaudryand Himouri , 2013), which altogether make up the DRAG-family (Table 3.1)(see Section 3.1.2.2).
Yet another cause of serial autocorrelation is to be found in the natureof the time series. For monthly data, which is most commonly used for acci-dent analysis, trend and seasonality contribute to serial correlation. In order
Chapter 1. Introduction 8
to take these factors into account Harvey and Durbin (1986) developed astructural descriptive model with intervention variable, where the variancepresent in the data is filtered out by incorporating trend and seasonality asunobserved components into the model. UCM was first used to estimate theimpact of the seatbelt law on road safety in Great Britain. The authors intro-duce the seatbelt law enforced by the British Government as an interventionvariable. The further development of the UCM is studied in Commandeurand Koopman (2007), Durbin and Koopman (2001). The applications ofUCM in road safety have been carried out by several authors, among themScuffham and Langley (2002) use UCM to model the traffic crashes in NewZealand; Hermans et al. (2005, 2006) have used the UCM methodology toestimate the effect of road safety measures on the monthly frequency andseverity of road traffic accidents in Belgium; Bijleveld et al. (2008, 2010)use the state-space model for measuring exposure and risk for fatal road ac-cidents; Aparicio et al. (2011), Castillo-Manzano et al. (2010, 2011) haveapplied the UCM methodology to analyze the effect of the Penalty PointSystem and the Penal Code Reform on traffic accidents in Spain.
In spite of the ever improving methodological developments and innova-tions in road safety study there still remain some issues that have not beencompletely addressed in road safety literature. Some of these issues are themethodological choice, model selection and comparison. The lack of researchin these areas has been pointed out in the most recent study by Manneringand Bhat (2014). In addition to carrying out the macro analysis of the roadsafety indicators in Spain, this thesis has been developed with the objectiveof providing some insight, both empirical and theoretical, into these topics.The main objectives of the thesis are detailed in the following section.
1.3 Main objectives and the structure of the
thesis
The main goal of this thesis is the analysis of road safety issues in Spain,since 2000. This period is mainly characterized by a major improvement inroad safety policy by the Spanish authorities, and a significant change in theeconomic situation of country. In order to analyze the impact of these andother macro factors on road accidents, as well as to propose some method-ological developments, several road safety indicators have been studied. Inthis thesis mainly two data sets, consisting of five road safety indicators, havebeen used in the applications: 1) the total figures for fatal accidents; and 2)
9 1.3. Main objectives and the structure of the thesis
figures related to frequency and severity of van-involved accidents.
The objectives of the thesis are divided into two blocks: empirical anal-ysis and two methodological developments. Both blocks provide an extensiveliterature review of existing studies on the topic. The objective of the firstblock, empirical analysis, is to achieve a better understanding of the roadaccident phenomenon by means of the application and comparison of two ofthe most frequently used macro modeling: DRAG and UCM. The researchwas carried out using monthly data indicating the frequency and severity ofvan-involved road accidents in Spain, during 2000-2009. The main contribu-tion of this research work, apart from providing interpretation and predictionfor van-accident behavior, is the model comparison exercise. It is in generalevident that the choice of statistical methodology used in road safety stud-ies will depend on the data. However, even with the same database, modelcomparison can leave much to be desired as far as the statistical evidence isconcerned. This thesis thus tries to provide an insight on the topic of com-parison of two different types of models: explanatory and descriptive models.
Following the findings in the first block and considering some drawbacksof the model selection and comparison process, the second block objectiveswere proposing two methodological developments: 1) model selection method-ology and; 2) simulation-based model comparison methodology.
The first methodological development was carried out using data on fatalaccidents in Spain during 2000-2011. The main objective of the research workwas proposing a model selection procedure, i.e. selection of variables and pa-rameter estimation. Following the results of the previous research work, forthis exercise, the DRAG-like methodology, the structural explanatory model(SE), was used. The estimation was carried out within the Bayesian frame-work. The results of the model selection procedure are compared and vali-dated through prediction and comparison with those of the DR model, giventhat the original data has a stochastic trend. The main contribution of thiswork is the model selection procedure called TIM (named after two-inputmodel, since the initial models used for variable selection use two inputs)that proves to be efficient. Moreover the results provide a better understand-ing and interpretation of fatal road accidents in Spain during the last decade.
Simulation-based model comparison methodology was carried out usingMonte Carlo simulation, computer experiment design and ANOVA. The mainobjective was to see how one type of model can be interpreted through anothertype. This study also tries to take into account the question emerged duringthe second study, i.e. how the DRAG or SE modeling should be carried outif the data includes a stochastic trend component. Considering that UCM
Chapter 1. Introduction 10
includes a specific stochastic trend term the comparison was carried out usingUCM as a true data generating process and carrying out estimation throughDRAG model. The simulation was carried out using the parameter estimatesthe UCM of the first study. In order to generate a stochastic process anadditional trend term was added. The main contribution of this researchwork is to provide a model comparison methodology that can be carried outwith the existing statistical tools. Moreover the findings suggest that evenif the model estimation can provide reliable goodness of fit measures, theexisting stochastic component should be modelled appropriately in order toprovide unbiased estimates.
The structure of the thesis closely follows the main goals and objectivesdescribed above. The thesis is divided into three parts that consists of 6chapters and Conclusions as described below:
Part I : Accidents and their consequences in the period 2000-2011. Potentialinfluential factors in accident analysis.
Chapter 1. Introduction.
Chapter 2. Data sets.
Part II : Computational Tools for the Evaluation and Analysis of Road Safety.
Chapter II. Introduction.
Chapter 3. Statistical methodology.
Chapter 4. Explanation of van-involved road accident indicators. Model com-parison.
Chapter 5. Analysis of fatal accidents: model selection methodology.
Chapter 6. Simulation experiment based model comparison methodology withapplication to road accident models.
Part III : Conclusions, contribution and future work
Chapter 2
Data set
This chapter discusses the data sets used in this study. For the empiricalstudy two sets of dependent variables are used: 1) van-involved road accidentsin Spain, covering the period of 2000-2009; and 2) total number of fatalaccidents in Spain, covering the period of 2000-2011. Both data sets wereobtained from the General Database owned by General Directorate of Traffic(DGT) in Spain. The first set, the van-involved road accidents, was studiedusing four monthly time series data for vans: 1) number of van-involved fatalaccidents; 2) number of van-involved accidents with seriously injured people;3) number of fatalities in van-involved accidents and; 4) number of seriouslyinjured people in van-involved accidents whereas the second set consists of onemonthly time series. In the next section both of the data sets are presented.The dependent variables will be presented in the next section.
The above indicated road safety measures are modelled using an exten-sive set of explanatory factors (independent variables) which is aggregated atthe country level. The independent variables will be presented in section 2.2of this chapter.
2.1 Dependent variables
Spain reached the European Union target of achieving a 50% reduction inthe number of road fatalities during 2001-2010, following Latvia, Estonia andLithuania (European Transport Safety Council , 2011). As it was pointed outin Introduction road safety policy has experienced a major political changesduring the last decade and different legislative measures as well as preventiveand corrective strategies have been conducted. Another factor that has also
11
Chapter 2. Data set 12
Fig. 2.1. Fatalities in accidents with vehicle type involved.(Index Year 2000 = 100.)
greatly affected the road safety measures in Spain during this period is theeconomic crisis and its consequences. In order to evaluate the effect of policymeasures and different macro economic factors on the decreasing number offatal accidents a new study was conducted, the main purpose of it being thedetermining the number of factors that have had a significant impact on theroad safety indicator, ACCTOT (see Section 2.1.1).
However the significant decrease observed in the number of fatal ac-cidents was not the case for the van-involved road accidents. Comparingthe road safety indicators across the vehicles it was observed that the num-ber of fatal accidents decreased by 57% and by 56% in passenger cars andlarge trucks respectively, while in van-involved fatal accidents only a 33%decrease was observed. As for the number of fatalities, there was a 38%decrease in van-involved accidents, while for passenger cars and trucks thefigures were 58% and 59% respectively (Figure 2.1). In order to understandthe factors influencing van-involved crashes, a research was carried out bythe researchers led by the Technical University of Madrid, during 2009-2011(FURGOSEG , 2011). The main objective of the research was, using the dataon van-involved road accidents, to determine the main causes of van-involvedaccidents through macro models, where the effect of different macroeconomicfactors, as well as policy measures were assessed (see Section 2.1.2).
13 2.1. Dependent variables
Fig. 2.2. Yearly data on fatal accidents, ACCTOT , 2000-2011: all vehicle types
included.
2.1.1 Fatal accidents
The number of fatal accidents in Spain, ACCTOT , is studied during theperiod of 2000-2011 (Figure 2.2). The main purpose of the research workwas assessing the factors that have affected to the decreasing number of fatalaccidents in Spain. For this purpose a model selection methodology was pro-posed. The methodology is based on SE models where the MCMC methodswere used for the model estimation and selection. The results of the modelselection methodology were compared to those of DR model. The proposedmethodology and its results where the number of fatal accidents were studiedwill be presented in chapter 5.
2.1.2 Van-involved road accidents
Van-involved accidents in Spain during the period of 2000-2009 were stud-ied in detail. For this purpose, four monthly time-series were considered fordata analysis: number of fatal accidents (ACCMOR); number of accidentswith seriously injured people (MORHER); number of fatalities (MUER)and number of seriously injured people (HERGRA) (Figure 2.3). In order
Chapter 2. Data set 14
2.3.a
2.3.b
15 2.1. Dependent variables
2.3.c
2.3.d
Fig. 2.3. Yearly data on van-involved road accident indicators, 2000-2009:
2.3.a)ACCMOR; 2.3.b)MORHER; 2.3.c)MUER; 2.3.d)HERGRA.
Chapter 2. Data set 16
to carry out the macro analysis, different methodologies were applied. Themain purpose of the research work was the explanation of the van-involvedroad accidents through different methodologies. For this purpose two dif-ferent macro models were used: DRAG and UCM. The comparison of twomodels was carried out both empirically and mathematically. The empiricalcomparison was carried out using the observed data for both models. Themathematical comparison of the two models was carried out using the simu-lated data. The empirical and mathematical study and their results will bepresented in chapters 4 and 6 respectively.
2.2 Explanatory factors
A road safety measure (e.g. frequency and severity) is modelled as a func-tion of different socio-economic factors. Although there is no well-establishedtheory indicating which factors should be included in a selected model, fac-tors causing the traffic crashes can be classified into different categories andstudied in an aggregate. The independent variables used in this chapter aredivided into following categories: exposure, economic factors, driver char-acteristics and surveillance, vehicle characteristics, road infrastructure, leg-islative measures, weather conditions and calendar effect (Table 2.1). Thegeneral data were obtained from the DGT, the Ministry of Public Works, theNational Meteorological Office, the National Statistics Office and the Min-istry of Economy and Finance. Since the data on explanatory variables arecollected from different sources that are not conditional on crash occurrencethe problem of the estimation bias is not present in this case (Anastasopoulosand Mannering , 2011, Mannering and Bhat , 2014).
2.2.1 Exposure
The measure of exposure is generally defined as the amount of travel within atraffic system Hakkert and Braimaister (2002). Exposure can also be referredas the traffic volume (Elvik et al. , 2009). The various ways of measuringthe amount of travel are referred to collectively as exposure data because theymeasure traveler’s exposure to the risk of death or injury (European TransportSafety Council , 1999). The most common method of measuring exposure isto use the kilometers/mileage travelled. The other means of measuring theexposure includes factors such as traffic volume and fuel consumption. Theexposure variable can also be represented using the rates, such as kilometers
17 2.2. Explanatory factors
Table 2.1: Explanatory factors.
Variable Definition Period Mean (in units)
Exposure
VHP Heavy Vehicles 2000-2011 2549 ·103
PRGFUR Van Fleet 2000-2009 2489 ·103
VKM Vehicle Kilometers Travelled 2000-2011 1472 ·106
CONOIL Diesel Consumption 2000-2011 1838 ·103 tons
CONGAS Gasoline Consumtion 2000-2011 609 ·103 tons
COMTOT Total Fuel Consumption 2000-2011 2455 ·103 tons
Economic factors
IPI Industrial Production Index 2000-2011 95 (Index)
INDVEN Sales Index 2000-2011 93 (Index)
INDCOM Commerce Index 2000-2009 96 (Index)
PRDCRN Meat Production 2000-2011 457 ·103 tons
CONCEM Cement Consumption 2000-2011 3464 ·103 tons
MANT Maintenance Investment 2000-2011 790 euro per km
CONST Construction Investment 2000-2011 299 ·103 euro
PRECOM Fuel Price 2000-2011 7 cent per km
INDACT Activity Index 2000-2009 97 (Index)
OCUP1 Total Employed 2000-2011 18 ·106
OCUP2 Employment Construction Sector 2000-2011 15 ·105
PARO Total Unemployment 2000-2011 1943 ·103
PARSER Unemployment Service Sector 2000-2011 1528 ·103
Driver characteristics
and surveillance
COND2 Young Drivers (2 years) 2000-2011 1341 ·103
CONALC Random Alcohol Checks 2000-2011 285 ·103
RADAR Speed Controls 2000-2011 1763 ·103
PRADAR Positives in Speed Controls 2000-2011 3 (%)
SUSP Driving License Suspended 2000-2011 13 ·103
PRLSUSP Driving License Suspended (B and B1 type) 2000-2011 9 ·103
Vehicle characteristics
VEH10 Vehicle Age (10 years), % of Total Fleet 2000-2011 36 (%)
AIRBAG Airbag Equipped, % of Total Fleet 2000-2009 41 (%)
ABS ABS Equipped, % of Total Fleet 2000-2011 45 (%)
Road infrastructure
LONRAC High Capacity Roads, % of Total Network 2000-2011 6 (%)
LONRED Length of Toll Roads 2000-2011 2215 km
Legislative measures
PPS Penalty Point System 2000-2011 Dummy
RPC Penal Code Reform 2000-2011 Dummy
RUIDO Safety Items in Press 2000-2009 311 (Index)
Weather conditions
PREC Rainfall 2000-2011 50 mm
DNIE Number of Snowing Days 2000-2011 0,2 day
DNIEB Foggy Days 2000-2011 2 days
SLNV Number of Days with Snow Covered Ground 2000-2011 0,1 day
HSOL Amount of Sunny Hours 2000-2011 217 hr
TEMP Average Temperature 2000-2011 15 ◦ C
Calendar effect
DLAB Working days 2000-2011 20 days
SDF Weekend and Holidays 2000-2011 9 days
SEMSAN Easter Break 2000-2011 Dummy
Chapter 2. Data set 18
2.4.a
2.4.b
2.4.c
19 2.2. Explanatory factors
2.4.d
2.4.e
2.4.f
Fig. 2.4. Exposure.
2.4.a)V HP ; 2.4.b)PRGFUR; 2.4.c)V KM ; 2.4.d)CONOIL; 2.4.e)CONGAS;
2.4.f)COMTOT .
Chapter 2. Data set 20
traveled per vehicle, fuel consumption per capita, etc. There is a straightfor-ward relationship between the exposure and the accident risk, i.e. higher theexposure, greater is the rate of accident occurrence.
In this study exposure is measured through fleet volume of heavy vehi-cles, V HP , and vans, PRGFUR, vehicle kilometers travelled V KM , fuel con-sumption: diesel consumption (CONOIL), gasoline consumption (CONGAS)and total fuel consumption (COMTOT ) (Figure 2.4). It can be observed thatPRGFUR has an increasing trend during 2000-2007. The average annual in-crease during this period has been 2.58%. The trend starts to decline from2007 on, with average rate of 6.39%. The van fleet however has an increasingtrend during 2000-2009, with the average annual rate of 5.54%. The timeseries for V KM exhibits a strong seasonal pattern with an increasing trendtill 2007, for which the annual average has been 6.41%. The trend starts todecrease from 2007 on with an average of 4.75%. The diesel and total fuelconsumption has an increasing trend till 2007 (6.23% and 3.55% increase onaverage respectively) followed by a decreasing trend since 2008 (3.37% and3.81% decrease respectively). The consumption has a decreasing trend withthe average annual rate of 4.24%.
2.2.2 Economic variables
The economic factors have a major influence on road safety and its impacthas been vastly analyzed in road safety literature. The effect of economy onroad safety can be categorized as short term and long term impact. Increas-ing economic situation of household has a negative impact on road safety inshort run (Fridstrøm , 2000, Garcıa-Ferrer et al. , 2006, Loeb and Clarke, 2007, Scuffham and Langley , 2002). This is explained by the fact thatincreasing household income will affect to the demand for cars and thus ex-posure. However in a long run, the economic growth can increase the roadsafety (Fridstrøm , 1999, Hakim et al. , 1991), since as the economic growthimproves the investment for the transport related infrastructure will increaseas well. It has been shown that generally the economic cycles and traffic ac-cidents have a common trend during major recessions and expansions (Evansand Graham , 1988, Garcıa-Ferrer et al. , 2006).
The short term effect of economy on road safety is analyzed throughindustrial production index (IPI), sales index (INDV EN), commerce index(INDCOM), meat production (PRDCRN), cement consumption (CONCEM),while the long term effect is estimated using the investment on road con-struction (CONST ) and maintenance (MANT ) (Figure 2.5). Three of the
21 2.2. Explanatory factors
2.5.a
2.5.b
2.5.c
Chapter 2. Data set 22
2.5.d
2.5.e
2.5.f
23 2.2. Explanatory factors
2.5.g
2.5.h
Chapter 2. Data set 24
2.5.i
2.5.j
2.5.k
25 2.2. Explanatory factors
2.5.l
2.5.m
Fig. 2.5. Economic factors.
2.5.a)IPI; 2.5.b)INDV EN ; 2.5.c)INDCOM ; 2.5.d)PRDCRN ;
2.5.e)CONCEM ;; 2.5.f)PRECOM ; 2.5.g)MANT ; 2.5.h)CONST ;
2.5.i)INDACT ; 2.5.j)OCUP1; 2.5.k)OCUP2; 2.5.l)PARO; 2.5.m)PARSER.
Chapter 2. Data set 26
variables representing indices of economic situation (IPI, INDV EN andINDCOM) have a seasonal pattern with similar behavior. The trend forthree variables is increasing till 2007 (1.19%, 2.92%, and 2.43% on averagerespectively) that starts to decrease from 2008 on, with the average annualrate of 6.01%, 4.95% and 5.68% respectively. The PRDCRN also exhibit aseasonal pattern with a slightly increasing trend till 2007 (1.97% increase onaverage) that starts to decrease during 2008-2009, with the average annualrate of 7.53%. The trend is increasing from 2009 on with the average annualrate of 3.38%. CONCEM is increasing till 2007 with the average annualrate of 5.52%. After this period there is a sharp reduction till 2011, with theaverage rate of 21%.
Both MANT and CONST experience a stepwise increasing trend till2009. The average increase rate during this period is 5.36% for MANT and3.44% for CONST . The trend starts to decrease till 2011 with the averagerate of 5.14% and 13.72% respectively.
Other economic factors used for the estimation of road safety are fuelprices, PRECOM . According to most studies carried out on traffic accidentsthe increase in fuel prices improves road safety (Chi et al. , 2010, 2013, Gaudryand Lassarre , 2000, Grabowski and Morrisey , 2004, 2006, Hyatt et al. , 2009,Portney et al. , 1991, Wilson et al. , 2009). This factor has specially beenobserved in the case of the fatal accidents. It has been indicated that thereare three intermediate factors through which the increasing fuel prices effectto fatal accidents and fatalities Chi et al. (2010), Gaudry and Lassarre(2000):
• the users drive in a more flexible fashion, which engenders a reductionin road risk;
• the users compensate for the rise in price by a consequent reduction inexposure;
• the users reduce their speed in order to lower their fuel consumption.
The third group of economic factors is the economic activity of the house-holds: activity index (INDACT ), total number of employed (OCUP1), em-ployed in construction sector (OCUP2), total unemployment (PARO) andunemployment in service sector (PARSER) (Figure 2.5). The economic ac-tivity variables INDACT , OCUP1 and OCUP2 are expected to increasethe accident rate. This is explained by a number of factors such as increasinghousehold income, longer journeys and higher exposure, which would have anegative effect on traffic safety (Fridstrøm , 2000). It can be observed that
27 2.2. Explanatory factors
these three variables are increasing during 2000-2007, with the average rate2.50% for INDACT , 3.96% for OCUP1 and 6.10% for OCUP2 respectively.The trend starts to decrease during 2008-2011, with the average annual rateof 1.96%, 3.68% and 18.16% for INDACT , OCUP1 and OCUP2 respec-tively. Likewise, PARO and PARSER have a decreasing effect on accidentrisk, i.e. as the number of unemployment increases the rate of accidents de-crease (Chi et al. , 2010, Gaudry and Lassarre , 2000, Hakim et al. , 1991,Joksch , 1984, Scuffham and Langley , 2002). Theoretically the unemploy-ment rate will have a positive effect on road safety (Chi et al. , 2010, Gaudryand Lassarre , 2000, Hakim et al. , 1991, Newstead et al. , 1995, Scuffhamand Langley , 2002, Wagenaar , 1984). The total unemployment, PARO hasa slightly increasing trend during 2000-2004 (1.77%). The trend decreasesduring 2005-2007 with the rate of 2.23% on average. The trend starts toincrease again during 2008-2011 (18.33% in average). The unemployment inthe service sector, PARSER, has an increasing trend during 2000-2007. Theaverage annual rate during this period is 1.50%. During 2008-2011 the num-ber of unemployed in service sector decreases sharply, with the average rateof 18.41%.
2.2.3 Driver characteristics and surveillance
Driver characteristics and surveillance refer to the variables associated withthe age and risky behavior of drivers and the surveillance measures taken toprevent it. The driver skills are significant factors in estimation of accidentrisk. In order to estimate the effect of driving skills on road accident measuresthe driver experience, COND2, is considered, which shows the number ofdrivers who have obtained the driving license during the last two years priorto the data collection. It can be observed that the trend for COND2 isgradually increasing till 2008, with the average annual rate of 4.56%. Thetrend starts to decrease abruptly for the rest of the series, 2009-2011, at anaverage rate of 22.27% (Figure 2.6).
The surveillance of risky driver behavior is an important factor to bestudied. This factor is represented by the control on alcohol consumption,CONALC, radar checks, RADAR, percentage of positives in radar checks,PRADAR, driving license suspension, SUSP and suspension of type B andB1 licenses, PRLSUSP . An increase in the alcohol consumption has a di-rect impact on the road risk indicators (Evans , 1990, Hoxie and Skinner ,1987, Loeb , 1987, Ross et al. , 1981, Zlatoper , 1984). The U.S. Depart-ment of Transportation estimates that alcohol is present in roughly 8% of all
Chapter 2. Data set 28
2.6.a
2.6.b
2.6.c
29 2.2. Explanatory factors
2.6.d
2.6.e
2.6.f
Fig. 2.6. Driver characteristics.
2.6.a)COND2; 2.6.b)CONALC; 2.6.c)RADAR; 2.6.d)PRADAR; 2.6.e)SUSP ;
2.6.f)PRLSUSP .
Chapter 2. Data set 30
crashes. According to the estimates by DGT alcohol and illegal drugs havebeen found in 42% of deaths in road accidents. Alcohol has particularily sig-nificant impact on fatal accidents. For example, the literature review doneby Moskowitz et al. (1974) shows that alcohol was present in 23% of thedrivers in fatal accidents. In another study conducted by Haworth et al.(1997) it is shown that illegal blood alcohol concentration (BAC) level > 0.05were found in 35% of drivers of fatal crashes. The data shows that the controlon alcohol consumption (random breath tests) is increasing with the averageannual rate of 14.38% during 2000-2011. Moreover we can observe a seasonalpattern, with the peaks occurring during the summer months.
The relationship between the speed and the road risk is relatively intu-itive: ”The more the user increases the speed the less he can take the effec-tive action against any disruption in his environment” (Jaeger and Lassarre ,2000). It has been stated that there is an increasing relationship between thehigher speed and severity of the accidents ( Chen et al. , 2000, Gaudry andLassarre , 2000). That is the reason why almost 22% of the accident relatedfatalities have been caused by inadequate speed. There has been an extensiveresearch on trying to systemize how the speed enforcements affects the roadsafety (Brackett and Edwards , 1977, Elvik , 1997, Finch , 1994, Hauer etal. , 1982, McCarthy , 1994, Østvik and Elvik , 1991, Tay , 2000, Tayloret al. , 2000). The surveillance on speed can take effect through differentmethods, such as mobile radars, speed enforcement cameras, etc. A numberof studies have analyzed the effectiveness of these methods on the reductionof the speed and thus the traffic accidents ( Chen et al. , 2000, Goldenbeldand Van Schagen , 2005, Hirst et al. , 2005, Wilson et al. , 2006). In thisstudy, as speed control variable the data from radar checks have been ana-lyzed. It can be observed that RADAR is mainly increasing with the averageannual rate of 5.99%. PRADAR is however decreasing till 2006 with the av-erage annual rate of 2.93%. The trend starts to increase from 2006 on, withthe average rate of 3.50%. Both RADAR and PRADAR have a somewhatseasonal pattern.
The suspension of driving licenses, SUSP , has similarly been found tobe effective in reducing traffic accident frequency, since the number of crashesincreases with all driving offences (Siskind , 1996). The trend for SUSP ismainly increasing, with the average annual rate of 6.87% during 2000-2011.PRLSUSP has an increasing trend with the level shift during year 2009. Theaverage annual increase rate till this period is 7.59%. After the level shift,which accounts for 26.90% decrease in one year (2009-2010), the trend startsto increase again, with the average rate of 7.97%, during 2010-2011.
31 2.2. Explanatory factors
2.2.4 Vehicle characteristics
Fleet characteristics represent the older vehicles and the safety devices thevehicles are equipped with. This category includes the percentages of fleet vol-ume equipped with an antilock brake system device, ABS, airbag AIRBAGand percentage of vehicles older than > 10 years, V EH10 (Figure 2.7). Thenumber of vans equipped with ABS devices has been developed by IEA(2009) which was part of the research team of the FURGOSEG (2011)project. The volume of fleet equipped with both of the devices show anincreasing trend. The percentage of total fleet equipped with AIRBAG hasincreased from 9% to 61% during 2000-2009 (18.50% per year on average),while the proportion of total fleet equipped with ABS has increased from10% to 69% (16.28% per year on average) during 2000-2011.
The impact of older vehicles on road safety in Spain has been studied byMendez et al. (2010). The existing literature on road safety shows that thevehicle age is usually associated with increasing rates of accident frequency(Blows , 2003, Mendez et al. , 2010), thus an increasing number of oldervehicles can have a negative impact on road safety. The percentage of thetotal fleet representing vehicle older than 10 years is increasing till 2004, withan average rate of 3.53%. The trend is decreasing during 2004-2007 with anaverage rate of 2.72%. This however is followed by an increasing trend againstarting from 2008 on (5.91% per year on average).
2.2.5 Road infrastructure
The studies related to the road safety consider the road infrastructure asone of the most important factors affecting the traffic accident frequencyand severity. Road infrastructure can be represented both by the geometricdesign of the road and the investment expenditure on the road infrastructure.Normally the latter factor would be considered and studied as an economicfactor (CONST and MANT ). Most of the studies on road infrastructurehave focused on specific design elements such as cross section design, roadsidefeatures, lane width, pavement condition, etc. and tried to quantify theirpotential to reduce the accident rate. Early studies include the work byAgent and Deen (1976), Jovanis and Chang (1986), Knuiman et al. (1993),Miaou et al. (1992) and Milton and Mannering (1998). One of the mostimportant findings of these studies is related to the lane width and numbers.The results show that a narrow lane width and number of lanes increase theaccident occurrence (Abdel-Aty and Radwan , 2000, Milton and Mannering ,1998, Noland , 2001, 2003). On the other hand it has been shown that wider
Chapter 2. Data set 32
2.7.a
2.7.b
2.7.c
Fig. 2.7. Vehicle characteristics.
2.7.a)AIRBAG; 2.7.b)ABS; 2.7.c)V EH10.
33 2.2. Explanatory factors
2.8.a
2.8.b
Fig. 2.8. Road infrastructure.
2.8.a)LONRAC; 2.8.b)LONRED.
Chapter 2. Data set 34
medians reduce the frequency of the accident rate, thus improving road safety(Anastosopoulos et al. , 2007, Karlaftis and Golias , 2002, Knuiman et al. ,1993, Noland , 2003).
The variables representing the road infrastructure in this study are theproportion of length of the high capacity roads in the whole interurban net-work, LONRAC, and of the toll road network, LONRED (Figure 2.8).LONRAC is considered as a proxy to the median lane width, i.e. it rep-resents the length of the high capacity roads with higher median width. Theproportion of high capacity roads in the total network has an increasing trend,with the average rate of 4.47%. The toll roads are characterized by less traf-fic volume and better geometric characteristics (high quality, less curvature)which makes them less prone to accident occurrence. The length of toll roadshas a stepwise increasing trend during the period under study, with an averageannual increase rate of 3.49%.
2.2.6 Legislative measures
Considering the significant impact of the driver behavior on traffic accidentsthe institutions involved in traffic safety recommend a number of the measureshave to be taken by the authorities. These measures include penalty pointsystems which refers to the suspension or the revocation of the right to drive.The direct effect of these enforcement laws does not only depend on the mereexistence of the legislation but also how strictly they are enforced. In therecent years there have been mainly two regulatory measures taken by theSpanish authorities in order to improve road safety:Penalty Point System(PPS) and Penal Code Reform (RPC) (Figure 2.9). In addition to theenforcement laws, the DGT has been involved in different publicity campaignsand adds promoting traffic safety through the media, that were representedby safety items covered in the press, RUIDO, in this study. RUIDO is thenumber of news items or references to road safety in the national press as anindicator of the presence or intensity in all kinds of news media. It can beobserved that RUIDO has a smoothly increasing trend till 2004 that startsto sharpen after this period (Figure 2.9). On average RUIDO has increased50.16% per year during 2000-2009.
2.2.6.1 Penalty Point System
PPS was enforced on July 1st , 2006 (Boletın Oficial del Estado numero:172/2005; 28/2006) with the goal to re-educate and penalize the persistent
35 2.2. Explanatory factors
2.9.a
2.9.b
2.9.c
Fig. 2.9. Legislative measures.
2.9.a)PPS; 2.9.b)RPC; 2.9.c)RUIDO.
Chapter 2. Data set 36
offenders by a reduction or loss of the 12 credit points given to the driverssince the time the law came into force. The loss of points in this case hap-pens due to exceeding the speed limit, carrying out high risk maneuvers, anddriving under the influence of alcohol or other prohibited substances. ThePPS has been implemented in different countries, among them United King-dom (1972), Germany (1974), France (1992), Austria (1993), Poland (1993),Greece (1993), Ireland (2002), Italy (2003). To estimate the effect of the PPSon traffic safety, a number of studies have been carried out. These studies canbe grouped into 3 categories: studies on effectiveness of the system, studies onhealth issues, and studies on driver behavior changes (Aparicio et al. , 2011).The effect of the PPS in Spain has been studied by Aparicio et al. (2011),Castillo-Manzano et al. (2010), Pulido et al. (2009). Pulido et al. (2009)find out that during the period 2000-2007 the number of fatalities have fallenby 14.5%. Castillo-Manzano et al. (2010) analyze the effect of the PPS onthe safety indicators such as number of deaths and injured during the 24 hoursin highway and built-up areas in. Studying the time period of 1980-2007 theyconclude that the PPS has caused 12.6% reduction in the number of deathsin highway accidents. The study shows that the introduction of the PPShas also caused a decrease in the number of injuries in highway accidents andin built up areas by 15.3% and 17.2% respectively, however this effect fadedaway in the following year after the law came into force. Aparicio et al.(2011) study the effect of the PPS on the road safety measures. Studyingthe time period of 1995-2009, it was found out that introduction of PPShas caused 11.27-13.9% reduction in the number of fatalities during 24 hours.Apart from this effect the PPS had an immediate impact on the number offatalities during the summer months following the introduction of the systemwhich was maintained over the following summers.
2.2.6.2 Penal Code Reform
RPC was enforced December 2nd, 2007 (Boletın Oficial del Estado numero:288/2007). The RPC is depicting the harsher measures taken by the gov-ernment for the road safety offences. According to the law certain trafficoffences such as driving at a speed of 60 km/h over the legal speed limit inurban roads and 80 km/h on urban roads, driving under the influence of toxicdrugs, narcotic, psychotropic substance or alcohol beverages (over 1.2 gr/l)were regarded as a criminal offence from then on and can be penalized withprison sentence, fines and community work. The RPC effect was studied byAparicio et al. (2011), Castillo-Manzano et al. (2011). Aparicio et al.
37 2.2. Explanatory factors
(2011) found out that the RPC had a positive effect on reducing the numberof fatalities starting from November 2007, a month before the law came intoforce, which they explain with the media impact and social debate that wasobserved prior to the enactment of the law. It is shown that there was a 17.7-20.7 % reduction in the number of fatalities over 24 hours in the followingfirst year. Castillo-Manzano et al. (2011) evaluate the impact of the RPC onroad traffic fatalities during 24 hours and try to forecast the time that effectwould last. They also conclude that the RPC had decreased the road trafficfatalities starting from November 2007. Between November 2007 and Decem-ber 2007 the fatality rate was reduced by 534 (24.7%). During the following13 months the reduction stayed at a constant 16% and the study concludesthat this effect seemed to be more persistent than PPS enforcement.
2.2.7 Weather conditions
Among the factors affecting the crashes and the severity level of the accidentsthere are also weather conditions. A significant variation observed in numberof accidents and severity level of it depending on the level of precipitation andthe season, because driving exposure changes by these factors. The influenceof the climate conditions on road safety has been studied mainly in two direc-tions: the effect of the temperature and the effect of the precipitation (rainfallor snow). The results of these studies can be generalized as follows: highertemperature (summer months) and rainfall are associated with increasing ac-cident risk specially in the case of fatal accidents (Andreescu and Frost , 1998,Bertness , 1980, Brodsky and Hakkert , 1988, Fridstrøm et al. , 1995, Sternand Zehavi , 1990), while the fatal accident risk reaches its minimum duringthe winter months and the snowfall (Brijs , 2008, Eisenberg , 2004, Farmerand Williams , 2005, Fridstrøm et al. , 1995). These findings are explained bythe fact that exposure increases during the summer period and on the otherhand it decreases during the winter period, particularly during the snowfall.
The weather conditions are represented by precipitation and tempera-ture variables. The precipitation is represented by the amount of rainfall(PREC), number of snowing days (DNIE), number of foggy days (DNIEB),and number of days with snow-covered ground (SLNV ). The temperature isrepresented by the amount of sunny hours (HSOL), and average temperature(TEMP ) (Figure 2.10). Weather variables were averaged first with 42 mete-orological stations covering 11 regions and then the weighted average for thewhole country was computed. PREC fluctuates between 10-130 mm, withan average value of 50 mm. On average DNIE is at most 3 and at least 0
Chapter 2. Data set 38
2.10.a
2.10.b
2.10.c
39 2.2. Explanatory factors
2.10.d
2.10.e
2.10.f
Fig. 2.10. Weather conditions.
2.10.a)PREC; 2.10.b)DNIE; 2.10.c)DNIEB; 2.10.d)SLNV ; 2.10.e)HSOL;
2.10.f)TEMP .
Chapter 2. Data set 40
(days) during a single month. These values for DNIEB are 7 and 1 (days)respectively. The average temperature, TEMP , fluctuates around 6-26 ◦C,while the average amount of sunny hours, HSOL, changes between 103-343hours.
2.2.8 Calendar effect
Calendar effects are represented by the number of weekdays (DLAB), num-ber of weekends and holidays (SDF ) and Easter break (SEMSAN) (Figure2.11). All of the variables were averaged for the whole country. The calendareffect variables (SDF and SEMSAN) have been shown to have a negativeeffect on road safety, since during the weekends, holidays and Easter breakthe travel volume increases (Liu and Sharma , 2006), thus increasing the acci-dent rate (Fridstrøm , 1999, Garcıa-Ferrer et al. , 2006, Gaudry and Lassarre, 2000).
2.3 Adjusting the data: missing values
The missing values of the variables that were absent in the data due to thedelay in the collection and recording process were obtained by forecastingthrough ARIMA models. For this purpose the automatic forecasting proce-dure provided by TRAMO/SEATS software (Maravall and Gomez , 1996)was applied. TRAMO stands for ”Time series Regression with ARIMAnoise, Missing values and Outliers” and SEATS for ”Signal Extraction inARIMA Time Series”. TRAMO is a program for estimating and forecast-ing regression models with possibly non-stationary (ARIMA) errors and anysequence of missing values. It detects several types of outliers as well asTrading Day and Easter effects which are modeled through intervention vari-ables. TRAMO pre-adjusts the series that is going to be subsequently fittedby SEATS. The missing value treatment was carried out for the followingvariables: PARO, CONALC, RADAR, PRADAR, SUSP , PRLSUSP ,V EH10 and RUIDO.
2.4 Summary
In this chapter the data used in this study are presented. The dependentvariables represent the road safety indicators in Spain that will be further
41 2.4. Summary
2.11.a
2.11.b
2.11.c
Fig. 2.11. Calendar effect.
2.8.a)DLAB; 2.8.b)SDF ; 2.8.c)SEMSAN .
Chapter 2. Data set 42
analyzed in the next chapters. They consist of 2 sets of times series: 1) van-involved road accident frequency and severity; and 2) total fatal accidents.The first set of data cover the period of 2000-2009, while the second datawere studied for the period of 2000-2011. These indicators will be studiedas the function of independent variables. The independent variables in turnare divided into several categories, such as exposure, economic factors, drivercharacteristics and surveillance, vehicle characteristics, road infrastructure,legislative measures, weather conditions and calendar effects. The behaviorof each independent variable is separately analyzed through the indicatedperiod.
Part II
Computational Tools for the
Evaluation and Analysis of
Road Safety.
43
Overview
As indicated in the Part I, the objectives of the thesis are the analysis of theroad safety indicators in Spain. For this purpose two data sets, representingthe current problems in road safety in Spain are analyzed. The analysis arecarried out through econometric models, to be presented in chapter 3. Themethodological contribution of the thesis is mainly divided into three partsand presented in three different chapters as presented below.
• Chapter 4: This study is intended to analyze the main factors explainingvan accident behavior during the period 2000-2009 and to get a furtherinsight into dynamic macro models for road accidents. For this purposefour time series related to the frequency and severity of van accidentson Spanish roads were considered. The estimation and prediction werecarried out for two different macro models, DRAG, and UCM. Since thechoice of the appropriate macro model for the analysis of road traffic ac-cidents is not a trivial matter, we are considering multiple factors such asgoodness of fit and interpretation, as well as the prediction accuracy inorder to choose the best model. Apart from explaining the van-involvedroad accident indicators, the main contribution of this chapter was themacro model comparison for the road safety analysis. The choice ofthe methodological approach for the analysis of road safety indicatorsis still an ongoing study. Therefore a special attention was given tothe differences between the results provided by different methodologies.Overall, the final results agree with the literature as far as the statis-tical fit measures were concerned. It was found that the DRAG- typemodel yields slightly better predictions for all four models compared toUCM. With these macroeconomic models, the effect of some influentialfactors (fleet, drivers, exposure variables, economic factors, as well aslegislative actions) can be addressed. Estimating the effect of the vigi-lance and surveillance actions can help safety authorities in their policyevaluation and in the allocation of resources.
45
46
• Chapter 5: The main objective of this chapter was the analysis of num-ber of fatal accidents in Spain, during 2000-2011 and determining themain factors that had a significant effect. Determining the main fac-tors affecting the behavior of number of fatal accidents is main questionof this chapter. Macro model selection exercise is considered to be alengthy and most of the time biased process, specially if the modelselection is based on the user defined fit statistics, such as p−values.In this case the choice of fully specified models versus parsimoniousmodels needs a special consideration. Taking these issues observedin road safety literature into account a model selection methodologyis proposed. Considering the results of chapter 4 the methodology iscarried out using a DRAG like parsimonious SE model, where the es-timation was carried out within the Bayesian framework and basedon MCMC methods. The model selection procedure was later cross-validated through prediction analysis and the results were comparedwith fully specified DR model. The results of the model selection pro-cedure showed that the economic factors, legislative measures and roadinfrastructure have more significant effect on the number of fatal acci-dents during the period under study.
• Chapter 6: The main objective of the chapter was to analyze howthe parameters of a selected model capture the parameters of the truemodel. The methodology is based on application of factorial design andANOVA techniques, to compare two of the most relevant time seriesmodels used for traffic data. Study was carried out using simulateddata, hence the name simulation experiment based methodology wasgiven. Taking into account the results of chapter 5, a special attentionwas given to the modeling of stochastic component that might be ex-istent in the true data, through a stationary model like DRAG or SE.The UCM includes a specific stochastic trend component that can beseparately modelled. Thus considering the empirical study carried outin chapter 4, this work was carried out using DRAG and UCM, henceto generate a new data the results of the indicated study was used. Inorder to generate a stochastic process, the data was simulated using ad-ditional trend component. The ”true” data was thus generated throughUCM methodology, and a DRAG model was estimated using the gen-erated data. The results of the research shows that although the trueeffects of the variables are captured in the DRAG model, a stochasticcomponent can have a significant impact on regression elasticities thuson the interpretation of model.
Chapter 3
Statistical methodology
This chapter is dedicated to the macro models for the analysis of road safetymeasures. In the section 3.1 model functional forms and their application inroad safety literature are presented. In section 3.2 model estimation method-ology and the goodness of fit measures are discussed. Sections 3.3 and 3.4are dedicated to variable analysis, i.e. elasticity- interpretation of variableimpact and multicollinearity- the collinearity observed between two or morevariables.
3.1 Functional form
3.1.1 Dynamic regression
Dynamic regression (DR) states how an output, Yt, is linearly related tocurrent and past values of the inputs, Xkt (Pankratz , 2012), i.e.:
Yt = β0Xt + β1Xt−1 + β2Xt−2 + ...+ ut (3.1)
where the coefficients, β0, β1..., represent the dynamic relationship betweenthe series Yt and Xt. Equation (3.1) is referred as the transfer function. Thisequation can be re-written using the lag operator, B, in the following form:
Yt = β(B)Xt + ut (3.2)
where
β(B) = β0 + β1B + β2B2 + ... (3.3)
47
Chapter 3. Statistical methodology 48
which can be represented as the polynomial in lag operator through:
β(B) =ω(B)
δ(B)(3.4)
If both series, Yt and Xt, are stationary, then the error term, ut willfollow an autoregressive moving average (ARMA) process defined as:
φ(B)ut = θ(B)wt (3.5)
where wt is assumed to be a white noise. This model based on equations (3.1)-(3.5) is known as DR or transfer function model between the two variables.
In order to estimate DR model, equations (3.1)-(3.5) are simplified intothe following form:
Yt =ω(B)
δ(B)Xt +
θ(B)
φ(B)wt (3.6)
The general form of equation (3.4), where the integration of variables isnecessary, is as follows:
Yt =ω(B)
δ(B)Xt +
θ(B)Θ(Bs)
φ(B)Φ(Bs)∇∇swt (3.7)
where ∇ and ∇s represent the regular and seasonal integration respectivelyof the series Yt and Xt, and the error term has regular and seasonal ARparameters φ(B) and Φ(Bs) and regular and seasonal MA parameters θ(B)and Θ(Bs). The DR models are described in more detail in Pena (2005) andPankratz (2012).
3.1.1.1 Structural explanatory models
One special case of DR model that will be used in this thesis is the structuralexplanatory (SE) model. The SE model is based on linear regression withautoregressive errors. The earlier version of these type of models was studiedby Zellner and Tiao (1965) and Zellner (1971). The model with AR(2) errorstructure, studied by Zellner (1971) has the following functional form:
Yt =∑k
βkXkt + ut (3.8)
(3.9)
49 3.1. Functional form
ut = ρ1ut−1 + ρ2ut−2 + wt (3.10)
where Yt is the dependent variable, usually a road safety indicator; Xkt rep-resents different factors that are assumed to have an impact on safety; βk arethe regression coefficients; ut is an error term with the AR(2) structure; andwt are assumed to be white noise IID with N(0, σ2
w).
3.1.2 Demand for Road use, Accidents and their Grav-
ity (DRAG)
The functional form of DRAG modeling is specified as the following regressionmodel (Liem et al. , 2008):
Yt =∑k
βkXkt + ut (3.11)
ut =[exp
(δm · Z
(λZm )mt
)]1/2· vt (3.12)
vt =∑l
ρlvt−l + wt (3.13)
where Yt is the dependent variable, usually a road safety indicator, and Xkt
represents different factors that are assumed to have an impact on the safety.the error structure includes heteroskedasticity term, Zmt, with coefficient δmand is assumed to follow an AR(l) process. The first-stage vector of residuals,ut are heteroskedastic; the second-stage residuals, vt are autocorrelated andthe third-stage residuals, wt are assumed to be IID, with normal distributionN(0, σ2
w). All model variables, Yt, Xkt, and Zmt are Box-Cox transformed(Box and Cox , 1964).
3.1.2.1 Box-Cox transformation
Usually in traffic accident analysis count data are most frequent. However,continuous data models are preferred because they consider the autocorre-lated structure of time series and can be handled easily by considering theunobserved components. Thus the modeling of count data using continuousdata models has become a common exercise in road safety analysis. One wayof doing this is using the Box-Cox family of power transformations (Box and
Chapter 3. Statistical methodology 50
Table 3.1: DRAG family models.
Country Authors Monthly period Model
Germany Blum and Gaudry 1968-1989 SNUS
France Jaeger and Lassarre 1957-1993 TAG
Norway Fridstrøm 1973-1994 TRULS
Sweden Tegner 1970-1995 DRAG-Stockholm
California McCarthy 1981-1989 TRACS-CA
Spain Aparicio et al. 1990-2004 DRAG I-DE Spain
Algeria Gaudry and Himouri 1970-2007 DRAG-ALZ-1
Cox , 1964), which helps to achieve normality and a linear growth function.The predictive accuracy has also been shown to improve substantially whenthe model variables are Box-Cox transformed (Keramidas and Lee , 1990,Lee et al. , 1987). The Box-Cox transformation (BCT) lets the data deter-mine the most appropriate functional form under which the variables shouldappear:
Y(λY )t =
{YλYt −1λY
, if λ 6= 0
ln(Yt), if λ = 0(3.14)
where λY is the transformation coefficient.
3.1.2.2 DRAG family models
Based on the original DRAG model for Quebec, a family of DRAG-inspiredmodels were developed for another countries and regions (Table 3.1 ). Thelist of the DRAG family models and their main characteristics is discussedbelow.
• SNUS (Straßenverkehrs-Nachfrage, Unfalle und ihre Schwere) was de-veloped by Blum and Gaudry (2000) covering West Germany. Theestimation period for this model was 1968-1989. The main particu-larity of this model is the inclusion of the material damage accidents,considering both light and severe damages. Also two separate modelsfor diesel and fuel vehicles were constructed.
For the SNUS model some specific issues characteristic to case of Ger-many had to be taken into account: the absence of speed limit, impor-tant car industry, and the turning points observed in the data, causedby the unification of the country.
51 3.1. Functional form
As to the results of the study, the material damage was found to beincreasing by the influence of exposure, high temperatures, seat belt useand shopping habits. The severity of the road accidents were found tobe increasing by exposure, higher temperatures and beer consumption.Increasing fuel prices and introduction of speed limits seemed to havea positive impact on the safety indicators.
• TAG (Transport routiers, Accidents et Gravite) was developed by Jaegerand Lassarre (2000) for France. The estimation period for the TAGmodel was 1957-1993. The model consists of four layers: risk exposure(kilometers traveled), the risk behavior (average speed), injury accidentfrequency and accident gravity. There were fifty explanatory variablesintroduced to all four models. The risk exposure was found to be posi-tively related with the employment index, wine consumption per adult,stock of private cars and the average temperature. The risk exposureon the other hand decreases by the impact of the technical inspectionof vehicle and increase in fuel prices. The risk behavior was found tobe increasing as the motor vehicle price index and percentage of theprivate motor cars increases. Also the seat belt use was found to havea positive effect on the risk behavior. The legislative measures and fuelprices were found to reduce the average speed. The factors such as av-erage speed, number of motorcycles, the total kilometers traveled, wineconsumption and the industrial activity increase the accident frequencyand gravity, while the road safety measure were essential in decreasingthese road safety indicators. Also temporary factors, like the Gulf war(consequently increasing fuel prices) had a positive impact on decreasingthe accident frequency.
• TRULS (TRaffik, Ulykker og deres Skadegrad) was developed by Frid-strøm (2000) for Norway, covering the period 1973-1994. Unlike theother DRAG family models , Fridstrøm assumes a Poisson distributionfor the causality counts. The model includes additional econometricmodels explaining the seat belt laws and car ownership. Further a layerof light and heavy road use are included and the results are disaggre-gated by road users categories (pedestrians, cyclists, motorcyclists andcar drivers). The main results of the TRULS model are summarized asfollows: the injury accidents increase in proportion to the traffic vol-ume, also the use of heavy vehicles increases the injury accidents. Thesnowfall has an increasing effect on the injury accidents, however theseverity of the accidents diminishes. Moreover there are less injury acci-
Chapter 3. Statistical methodology 52
dents when the ground is covered by snow. Rainfall also has decreasingeffect, this is partially explained by the fact that on the rainy days theexposure of unprotected road user (pedestrians, cyclists) is reduced.During the first quarter of pregnancy the frequency of injury accidentsare increasing. The severity of the accidents is reduced by wearing theseat belts and temperature falling below zero. The severity increase bythe alcohol consumption. As to the car ownership, it is shown that itincreases ceteris paribus with the size of population and the increase inhousehold income.
• DRAG-Stockholm model for Stockholm was developed by Tegner andLoncar-Lucassi (1997), covering the time period 1970-1995. The modelestimates three road safety indicators: the exposure, accident frequencyand accident severity. This model has many U-shaped effects, suchas the effect of vehicle-kilometers, volume of heavy vehicles and moremotorways. Although these factors contribute to worsening of safety onthe roads, after the congestion occurs they have a decreasing effect onthe dependent variables. Another U-shaped effect was found betweenalcohol and medicine consumption and number of injury accidents. Atlow consumption levels the accident risk is reduced , however when theconsumption increases the risk augments rapidly. Additionally the seatbelt usage reduces the number of injury accidents and impact of theheadlight use during daytime increases the number of fatalities.
• TRACS-CA model was developed by McCarthy (2000) for Califor-nia, covering the period of 1981-1989. The model estimates accidentfrequency and severity including with the material damage accidents.The three main components are risk exposure, accident frequency (fa-tal, injury, material damage) and accident severity (number of deathsand injuries). The predictors are grouped into three categories: socio-economic, transport system, and environmental factors. The results ofthe study show that the exposure increases with beer consumption andincreased speed limit. The factors such as risk exposure and consump-tion of beer are positively related to fatal crashes, while the rainfall andlegislative measures have a decreasing effect. The injury crashes increasewith the wine consumption, rainfall, increased speed limit and seat beltuse , while the latter has risk substitution effect, i.e. when crash occursless people are injured. The injury related crashes decrease with the in-creasing fuel prices. As to the material damage accidents, it was foundto be reducing as fuel prices increase and increasing with the exposure
53 3.1. Functional form
and increased enforcement law. The reason for the latter needs furtherinvestigation.
• DRAG-Spain was developed by Aparicio et al. (2013) for Spain. Theestimation was done for the period of 1990-2004 and was applied to thenetwork of interurban roads. DRAG-Spain model is a three layer modelthat includes the exposure, accident frequency and accident severity.The data included in the model contained monthly, quarterly and an-nual data. The quarterly and annual was disaggregated using indicatorvariables. The missing variables were obtained by extrapolation. Theanalysis show that most significant factor is exposure, which togetherwith inexperienced drivers, speed and the aging vehicle stock, have anegative effect on the road safety and were found to be increasing thesafety indicators, while an increase in road surveillance and techno-logical improvements to vehicles were found to have decreasing effecton both accident frequency and accident severity. Additionally the ef-fects of other factors such as climatology and labor conditions wereestimated. Like the TRULS model it was shown that during the dayswhen the ground is covered with the snow the frequency of accidentsincrease but the severity decreases. The rainfall had a similar effect.While high temperatures increase the frequency and the severity of theaccidents. The number of weekend and holidays was also found to havea negative impact on road safety.
• DRAG-ALZ-1 is the latest DRAG family model. It was developed byGaudry and Himouri (2013) for Algeria. The model covers the period of1975-2007. It is a three layer model (exposure, accident frequency andseverity, victims ). The model includes additionally subsidiary equa-tions for speed and seat belt wearing. The results of the study indicatethat the use of heavy vehicles increase the frequency of the accidents butreduce the severity. Higher temperature and more daylight increases theexposure and the speed, consequently increasing fatal accidents. Thelegislation showed to have positive effect on road safety, decreasing bothfrequency and severity of the accidents. The fuel prices did not seem tohave significant effect on road safety indicators. This was explained bythe fact that the price of fuel is very cheap compared to other countriesincluded in the previous DRAG models. The economic activity, as itwas expected increases the exposure and consequently the frequencyand severity of the accidents, while the unemployment decreases the fa-tal accidents and the number of deaths. During the special events, such
Chapter 3. Statistical methodology 54
as religious holidays, the number of accidents and the severity increasesbut the effect is very weak.
3.1.3 Unobserved Components Model (UCM)
The stochastic framework for UCM is based on state-space methodologywhere the measurement equation incorporates unobserved components suchas trend and seasonal patterns (Harvey and Durbin , 1986):
Yt = µt + γt + εt (3.15)
where µt represents the trend, γt the seasonal component and εt the irregulardisturbance term. The measurement equation can be extended to include theexplanatory and intervention variables.
The parameter and component estimation is based on Kalman filtering.The measurement equation decomposes the observed time series into unob-served deterministic or stochastic components that are modeled separatelyusing state equations:
µt = µt−1 + βt−1 + ηt (3.16)
where βt is slope:βt = βt−1 + ζt (3.17)
and ηt and ζt are error terms, that are normally distributed as ηt ∼ N(0, σ2ηt)
and ζt ∼ N(0, σ2ζt
) respectively. By setting σ2ζt
= 0 the model becomes a lineartrend with a fixed slope, while setting σ2
ηt = 0 will result in a smoother trend.The model becomes a deterministic linear time trend if both the variances(σ2
ζt= σ2
ηt = 0) are zero, µt = µ0 + β0 · t.The seasonal component is capturing the fluctuations in the time series
data and is handled by a trigonometric function:
γt+1 =s−1∑m=1
γt+1−m + ωt (3.18)
where s represent the integer period for which the sum,∑s−1
m=1 γt−m, is zero inthe mean. The error terms ωt are i.i.d., ωt ∼ N(0, σ2). The cycles ψt,j have
frequencies ωj =2πjs
and are specified by the following matrix:[ψt,jψ∗t,j
]=
[cosψj sinψj− sinψj cosψj
] [ψt−1,jψ∗t−1,j
]+
[ωt,jω∗t,j
](3.19)
where ωt,j and ω∗t,j are assumed to be independent.
55 3.2. Model estimation and diagnosis
In this thesis we consider the UCM that will be estimated by adding theexplanatory and intervention variables to the measurement equation (3.15):
Yt = µt + γt +J∑j=1
δjXjt + ωt + εt (3.20)
where Xjt is the value of the jth explanatory variable at time t, and δj is thecoefficient. The ωt is the intervention variable defined as a dummy variable:
ωt =
{0, if t < τ1, if t ≥ τ
(3.21)
where τ indicates the time point when the change was made.
3.2 Model estimation and diagnosis
For model estimation maximum likelihood and Markov Chain Monte Carlomethods were applied. The estimation procedure for each type of model isdiscussed below.
3.2.1 Maximum likelihood estimation
Both DRAG and UC models are estimated using ML estimation. The MLestimation is based on the optimization of a given log likelihood function withrespect to the model parameters.
3.2.1.1 DRAG model
Assume the model (3.11)- 3.13) is simplified in a matrix form:
Y∗∗ = βX∗∗ + w (3.22)
The estimates of model parameters are then obtained through:
β =(X∗∗
′X∗∗
)−1X∗∗
′Y∗∗ (3.23)
σ2w =
1
N
(Y∗∗ − βX
∗∗)′ (Y∗∗ − βX
∗∗)
Chapter 3. Statistical methodology 56
where
Y ∗∗t = Y ∗t −∑l
ρlY∗t (3.24)
X∗∗kt = X∗kt −∑l
ρlX∗t
When the heterosckedasticity term is allowed then Y ∗t and X∗kt are de-fined as:
Y ∗t = Y(λY )t /f(Zt)
1/2 (3.25)
X∗t = X(λX)t /f(Zt)
1/2
where Y(λY )t and X
(λX)kt are Box-Cox transformed.
The estimates are used to obtain the concentrated log-likelihood functionas:
L(θMLESE ) = −N
2[1 + ln(2π)]− N
2ln σ2
w −1
2
∑t
ln f(Zt) + (λy − 1)∑t
lnYt
(3.26)which is the function of model parameters, θMLE
SE = (λx, λy, λz, δ, ρ). Themaximization of the concentrated likelihood function with respect to modelparameters is based on the Davidon-Fletcher-Powell (DFP) algorithm, whichallows for the simultaneous maximization of all the parameters. The DFPalgorithm is similar to Newton-Raphson’s, but it does not require the analyticcalculations of second derivatives and approximates them iteratively.
3.2.1.2 UC model
Assume the model (3.15)-(3.16) has the following vector autoregressive (VAR)form:
Yt = AYt−1 + Ut (3.27)
The likelihood function for UCM is then constructed as:
L(θMLEUCM) =
∏t
f(Yt|Yt−1, θMLEUCM) (3.28)
where f(·) is normal density function:
f(Yt|Yt−1, θMLEUCM) =
1√(2π)n|Σε +HΣµ
t|t−1H′|
exp
(−u′t(Σε +HΣµ
t|t−1H′)−1ut
2
)(3.29)
57 3.2. Model estimation and diagnosis
where Σ(·) denotes the variance vector, and
Σµt|t−1 = BΣµ
t−1|t−1B′ + Ση (3.30)
A, B, and H are system matrices.The ML estimation of UCM is based on Gradient-based methods, such
as Newton’s method.
3.2.2 Markov Chain Monte Carlo estimation
The SE model is estimated through Bayesian inference. In Bayesian estima-tion the prior beliefs on the observed data are updated by Bayes’ theorem toobtain the posterior information (Raftery , 1995):
π(θ | x) ∝ π(θ)l(x | θ) (3.31)
where π(θ) is the prior distribution and l(x|θ) is the likelihood function.The major limitation for the use of Bayesian approaches is the computa-
tion of the posterior distribution that requires integration of high-dimensionalfunctions when a larger set of parameters is included in the model. Thisproblem has been overcome by Markov Chain Monte Carlo (MCMC) meth-ods, which simulate direct samples from some complex distribution of inter-est (Gelfand and Smith , 1990). MCMC methods have their roots in theMetropolis algorithm (Metropolis et al. , 1953), developed by physicists tocompute complex integrals by expressing them as expectations for some dis-tribution and then estimate this expectation by drawing samples from thatdistribution.
One particular MCMC method, is the Gibbs sampler, originally devel-oped for image processing (Geman and Geman , 1984). The Gibbs sampleris an iterative MCMC method designed to draw samples from the intractablejoint distributions by sampling tractable full conditionals (Casella and George, 1992).
Considering the parameters θ = {θ1, θ2, ..., θn}, with joint distribution[θ1, θ2, ..., θn] and full conditional distributions [θ1|θ2, ..., θn] and [θn|θ1, ..., θn−1],the Gibbs sampler algorithm for obtaining the marginal distribution fromjoint distribution proceeds as follows:
1. Specify initial values, θ(0)1 , ..., θ
(0)n , and set i = 1.
2. Update:
Chapter 3. Statistical methodology 58
(a) θ(i)1 from [θ1|θ(i−1)2 , ..., θ
(i−1)n ]
(b) θ(i)n from [θn|θ(i−1)1 , ..., θ
(i−1)n−1 ]
3. Set i = i+ 1, and go to 2.
After N iterations, the sample of θ(N)1 , ..., θ
(N)n is obtained. Under the
regularity conditions as M →∞, the sampled values converge in distributionto the relevant marginal and joint distribution, i.e. θ
(N)i → θj ∼ [θj] and
(θ(N)1 , ..., θ
(N)n )→ (θ1, ..., θn) ∼ [θ1, ..., θn].
Assume the structural model (3.11)-(3.13) where the prior distributionof the model parameters, θMCMC
SE = {β, ρ, σ2w}, is given as:
π(β, ρ, σ2w) = π(β|σ2
w)π(σ2w)π(ρ) (3.32)
The model parameters are assigned Jeffrey’s uninformative priors (Zell-ner , 1971):
β|σ2w ∼ Nk(β0, σ
2wB−10 ) (3.33)
σ2w ∼ IG
(ν02,δ02
)ρ ∝ Nl(ρ0,Φ
−10 )
i.e. a combination of multivariate normal for β, an inverted gamma for σ2w
and a multivariate normal for ρ, where β0, B0, ν0, δ0, ρ0, and Φ0 are thehyperparameters that are set to be a equal to a constant.
3.2.3 Goodness of fit measures
Goodness of fit measures are used in order to estimate how well the model fitsthe data. One of the ways of checking goodness of fit is computing the likeli-hood level of a model, that is, how well the model maximizes the likelihoodfunction. The following goodness of fit measures are used:
1. Akaike information criteria
2. Bayesian information criteria
3. Deviance information criteria
4. R2−like measures
59 3.2. Model estimation and diagnosis
3.2.3.1 Akaike information criteria
The Akaike Information Criterion (AIC) was developed by Akaike (1973)and is based on minimization of the Kullback-Leibler distance between themaximum likelihood estimate and the true value. This measure also usesthe log-likelihood, but adds a penalizing term associated with the numberof variables. It is well known that by adding variables, one can improve thefit of models. Thus, the AIC tries to balance the goodness-of-fit versus theinclusion of variables in the model. The AIC is computed as:
AIC = −2(ln(likelihood)) + 2K (3.34)
where likelihood is the probability of the data given a model and K is thenumber of free parameters in the model. A smaller AIC value means a betterfit.
3.2.3.2 Bayesian information criteria
Similar to the AIC, the BIC also employs a penalty term associated with thenumber of parameters (K) and the sample size (n). This measure is alsoknown as the Schwarz Information Criterion. It is computed as follows:
BIC = −2(ln(likelihood)) +K · ln(n) (3.35)
Again, smaller values mean a better fit.
3.2.3.3 Deviance information criteria
Deviance information criterion (DIC) is the Bayesian version of the AIC andwas first proposed by Spiegelhalter et al. (2002). They assume the followingprinciple for Bayesian model comparison:
DIC = goodness of fit+complexity (3.36)
Goodness of fit is measured via the deviance. For a likelihood l(Y |θ )the posterior mean of deviance is defined as :
D (θ) = −2 log l(Y |θ ) (3.37)
Complexity is measured by the estimate of the effective number of pa-rameters:
pD = Eθ|Y [D]−D(Eθ|Y [θ])
= D −D(θ) (3.38)
Chapter 3. Statistical methodology 60
i.e. posterior mean deviance, D, minus deviance evaluated at the posteriormean, D(θ). Then DIC is defined as :
DIC = D (θ) + pD =
= D (θ) + D −D(θ)
= 2D −D(θ) (3.39)
The model that provides the best predictions will have the lowest DICvalue. DIC values can only be compared between models that were builtusing the same set of information (Mitra and Washington , 2007).
3.2.3.4 R2−like measures
When the dependent variable is power-transformed, the R2 value using theordinary least squares linear regression is not available. In this case as good-ness of fit measure, Pearson’s R2 are considered (Liem et al. , 2008). This fitmeasure will be used for SE and DRAG models, where both dependent andindependent variables are power-transformed.
R2: computed with the expected value of Yt, E(Yt).
R2 =
[∑t
(Yt − E(Yt))(Yt − E(Yt))
]2∑t
(Yt − E(Yt))2∑
t
(Yt − E(Yt)
)2 (3.40)
where Yt are the estimated values of the dependent variable:
Yt =
{Y
(λY )t · λY + 1 if λY 6= 0
exp(Y(λY )t ) if λY = 0
(3.41)
And Y(λY )t are power transformed estimates of the dependent variable com-
puted as:
Y(λY )t =
∑k
βkX(λX)kt +
∑l
ρl
[Y
(λY )t−l −
∑k
βkX(λX)k,t−l
](3.42)
βk and ρl are the estimates of regression coefficients and autoregressive pa-rameters.
61 3.3. Elasticity estimation
3.3 Elasticity estimation
In order to estimate the sensitivity of a dependent variable Y with respect tochanges in independent variable Xk, the elasticities are taken into account.Elasticity is the ratio of the percentage change in independent variable, Xk
to the percentage change in dependent variable, Y . The elasticity of Y withrespect to Xk is computed as
ηYXk =∂E(Yt)
∂Xkt
· Xkt
E(Yt)= βk ·
Xkt
E(Yt)(3.43)
That is a 1% increase in Xk results a ηYXk% increase in Y .
Table 3.2: Elasticity estimates for different functional forms (McCarthy ,
2001).
Model Elasticity
Linear βk
(XktE(Yt)
)Log-linear βk (Xkt)
Linear-log βk
(1
E(Yt)
)Double log βk
The elasticities of the SE and DRAG models are computed as follows(equation (3.43)):
ηYXk =∂E(Yt)
∂Xkt
· Xkt
E(Yt)= βk ·
XλXkt
Y λYt
(3.44)
since the model variables are transformed.In the DRAG model the intervention variables representing regressors
such as enforcement laws are introduced to the model as a dummy whichtakes values 0 and 1. For the computation purposes these variables are notsubject to BCT thus the elasticity for the intervention variable is:
ηYXk =∂E(Yt)
∂Xkt
· Xkt
E(Yt)= βk ·
Xkt
Y λYt
(3.45)
Since the UC model estimation is carried out using the natural loga-rithms of the continuous variables, the regressor estimates of UCM can beinterpreted as the elasticities, i.e.:
Chapter 3. Statistical methodology 62
ηYXk =∂E(Yt)
∂Xkt
· Xkt
E(Yt)=d log(E(Yt))
d log(Xkt)= βk (3.46)
3.4 Multicollinearity
To estimate the multicollinearity among the variables the correlation matrixfor the independent and dependent variables, in terms of the original values,is computed before the maximization procedure. To detect multicollinearitythe spectral decomposition of X ′X is used (Judge et al. , 1986):
X ′X =k∑t=1
γipip′i (3.47)
where pi is the (K × 1) eigenvector associated with the i−th eigenvalue γiof X ′X. Following the approach by Belsley (1980) the condition number of
a matrix, ηi = (γmax/γi)1/2 , is used in order to detect the near dependen-
cies among the columns of X. To assess the significance of the independentvariables, normal and conditional t-statistics are computed.
Another method for detecting multicollinearity is the estimation of vari-ance inflation factor (VIF), which is calculated as follows:
V IF (βk) =1
1−R2k
(3.48)
where (1−R2k) is the tolerance and is calculated as a function of the coefficient
estimate variance:
1−R2k =
σ2
n− 1· 1
V AR(Xkt)V AR(βk)(3.49)
Most commonly, a value of 10 has been recommended as the maximumlevel of VIF (Neter et al. , 1989).
3.5 Summary
In this chapter the dynamic statistical models used for the time series roadaccident data were presented. The application of this class of models inmodeling of road safety measures is mainly based on the fact that these typeof the models take the autocorrelated errors into account, that is observed in
63 3.5. Summary
the time series. In this thesis three main categories of models are considered:SE, DRAG and UCM models. The first two models estimate the accidentdata as the function of explanatory variables, considering an AR(l) structureof errors. In case of DR models, the error structure can be extended to followan ARIMA process. The third type of models estimate the accident data byseparating it into unobserved components such as trend and seasonality. Itis assumed that separating the data into these components the data filtersout autocorrelation observed in the series. The application and estimation ofcontinuous models on road safety will be discussed in details in Chapters 4-5.
Chapter 3. Statistical methodology 64
Chapter 4
Explanation of van-involved
road accident indicators. Model
comparison
4.1 Introduction
The objective of this chapter is twofold: firstly, to select a model for theaccidental behavior of vans (see Section 2.1.2) with significant parameter es-timates that complies with the existing literature on road safety and presentsbetter prediction accuracy. Secondly, to get an insight into comparative mod-eling with two frequently applied dynamic models, DRAG and UCM.
Two macro models are considered for the analysis of van-involved ac-cidents: UCM (Section 3.1.3) and DRAG (Section 3.1.2) model. The twomodels are compared based on goodness-of-fit measures and prediction ac-curacy. The main difference between UCM and DRAG is the specificationand separate modeling of unobserved components, i.e. trend and seasonalcomponents, in the case of UCM. In the road safety literature the UCM arepreferred over classical, non-linear regression and DRAG models because asmentioned above, they can be used to explicitly decompose a time series intointeresting components such as trend and seasonal effect. They are also flex-ible and well able to handle the dependencies in time series. Furthermore,they work transparently with missing data and are easily generalized to themultivariate analysis of time series, while the DRAG model is simpler andhas a more straightforward interpretation. There is a very close relationship
65
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 66
between UCM and ARIMA models, in such a way that one can almost al-ways find, given a specific model of any type, an equivalent in the other one.There is important literature on this issue (Harvey and Scott , 1994, Hillmerand Tiao , 1982, Maravall , 1985). However, in practice, DRAG, which isestimated using the TRIO package Gaudry et al. (2005), does not coverall the ARIMA model range since its stationary autocorrelation modeling isrestricted to AR structures.
In the following section the model estimation and selection process aregiven in detail. In Section 4.2 and 4.3 the data used in the chapter arediscussed. In Section 4.4 the model construction and estimation are presented.In Sections 4.5 and 4.6 the results of the model estimation and the predictionare analyzed. Finally, Section 4.7 the summary and the discussions of thischapter are presented.
4.2 Van-involved road accidents
Prior to the macro modeling of the safety measures involving vans, the fourtime series were decomposed into different components for the trend andseasonality check of the series. The prior time series analysis were carriedout using an automatic procedure provided by TRAMO/SEATS (Maravalland Gomez , 1996). During the automatic adjustment by TRAMO/SEATS,each dependent variable was decomposed into seasonal, trend and irregularcomponents (Figure 4.1). All four models were transformed into their naturallogarithms and were adjusted using the ”airline model”. The results of thisautomatic procedure are set out in Table 4.2. As we can see from the graph,there is no evolution of the estimated seasonal factors and the procedure yieldszero residual seasonality and no outliers, but Easter and trading day effectswere detected. The absence of the seasonality can be due to the turning point
Table 4.1: Dependent variables.
Variables Definition
ACCMOR Number of fatal accidents
MORHERN Number of accidents with seriously injured victims
MUER Number of fatalities
HERGRA Number of injured victims
67 4.2. Van-involved road accidents
4.1.a)
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 68
4.1.b)
69 4.2. Van-involved road accidents
4.1.c)
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 70
4.1.d)
Fig. 4.1. Decomposition of series into trend-cycle and seasonal components with
TRAMO/SEATS:
4.1.a)ACCMOR; 4.1.b)MORHER; 4.1.c)MUER; 4.1.d)HERGRA.
71 4.3. Independent variables
Table 4.2: Summary of TRAMO/SEATS results∗.
Estimate ACCMOR MORHER MUER HERGRA
statistics
MA1 -0.9765 -0.5850 -0.9930 -0.6352
MA12 -0.9872 -0.9889 -0.9926 -0.8870
BIC -31.311 -47.297 -28.732 -41.523
SE(at) 0.1985 0.0908 0.2258 0.1211
N(at) 0.5787 0.6423 0.1385 2.221
Q24(at) 20.40 12.88 24.40 14.72
QS(at) 0 0 0 0
∗MA1 and MA12 are the moving average parameters; BIC-Bayesian Information
Criteria; SE(at)− standard error of the residuals, should be small; N(at) is the
Bowman-Shenton test of normality of residuals, which should be smaller than 6;
Q24(at) is the Ljung-Box test for residual autocorrelation; QS(at) is the test for
the residual seasonality autocorrelation.
effect that apparently took place almost in the middle of the series (aroundJuly 2006), which shifts the series mean thus causing misspecification of thetrue model. This effect can also be observed looking at the trend cycle graph.Although it was not statistically tested, we assume that this shift was dueto the introduction of the Penalty Point System (2.2.6.1) in July 2006. Butsomehow the shift in the trend was not detected as a level shift outlier. Thefurther macro analysis of road safety measures including the frequency andseverity of van-involved accidents are presented the next chapter.
4.3 Independent variables
The explanatory variables used as traffic safety factors were divided into thefollowing categories: exposure, economic factors, driver behavior and surveil-lance, fleet characteristics, road infrastructure, legislative measures, weatherconditions and calendar effect (Table 4.3).
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 72
Table 4.3: Explanatory variables, 2000-2009.
Variable Definition
Exposure
PRGFUR Van Fleet
VKM Vehicle Kilometers Travelled
CONOIL Diesel Consumption
COMTOT Fuel Consumption Total
Economic factors
IPI IPI
INDVEN Sales Index
INDCOM Commerce Index
MANT Maintenance Investment
CONST Construction Investment
PREC Fuel Price
INDACT Activity Index
PARO Total Unemployment
PARSER Unemployment Service Sector
Driver behavior surveillance
CONALC Random Alcohol Checks
RADAR Speed Controls
PRADAR Positives in Speed Controls
SUSP Driving License Suspended
PRLSUSP Driving License Suspended (B and B1 type)
Vehicle characteristics
AIRBAG Airbag Equipped,% of Total Fleet
ABS ABS Equipped, % of Total Fleet
Road infrastructure
LONRAC High Capacity Roads, % of Total Network
LONRED Length of Toll Roads
Legislative measures
PPS Penalty Point System
RPC Penal Code Reform
RUIDO Safety Items in Press
Weather conditions
DNIE Number of Snowing Days
SLNV Number of Days with Snow Covered Ground
TEMP Average Temperature
Calendar effect
DLAB Working days
SDF Weekend and Holidays
73 4.4. Model construction and estimation
4.4 Model construction and estimation
The DRAG model for van accidents consists of 2 layers: accident frequency(fatal and seriously injured) and accident gravity (fatal and seriously injured).As mentioned above, for constructing the models using the DRAG methodol-ogy, the TRIO software was used (see Appendix I for TRIO outcomes). Themodel construction begins by estimating the power transformation (eitherdifferent or the same coefficients for dependent and independent variables)and the autoregressive order of the errors and then including the indepen-dent variables. In the case of the ACCMOR, MORHER and MUER models,the BCT parameter was the same within each model for all variables, bothdependent and independent. In the case of HERGRA, the BCT values forthe set of independent variables, on the one hand, and the dependent one, onthe other, were different. The intervention variables (RPC and PPS) and thevariables with zeros (SLNV and DNIE) were not power transformed. Afterdefining the BCT and AR structure as the basic parameters, the remainingestimation was carried out (Table 4.4). First the variables that were assumedto have an effect on traffic accidents were added to the model and estimated.The variables with less significant and less interpretable effects were elimi-nated and new models were estimated. It should be pointed out that, duringthis stage, the BCT value and AR structure of the model can be fitted again.This will depend on how significant the fit statistics are.
After this step, different models with better fit statistics and significantestimates were obtained. In order to select the final DRAG model, predictionaccuracy was computed for each, and the final one was selected based on thebest forecast. The fit statistics for the selected DRAG models are listed inTable 4.4.
108 observation points were used for estimation. The adjusted R2 for thenumber of fatal accidents, number of accidents with seriously injured victims,number of fatalities and number of injured victims were 0.463, 0.714, 0.440 and0.630 respectively.
The data used in the statistical analysis are monthly observations, thusthere is a 12th order autocorrelation. Since the Durbin-Watson test of auto-correlation assumes that there are no higher order correlations, it would beless useful for residual analysis than the log-likelihood test.
For the UCM analysis the data were transformed into natural logarithms.The UCMs were built using the SAS/ PROC UCM software (Selukar , 2011)(see Appendix II for SAS outcomes). The UCM estimation consists of twoparts. First the models were built using three descriptive- level, slope and sea-
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 74
Table 4.4: Parameter estimates of DRAG models.
BCT ACCMOR MORHER MUER HERGRA
coefficients
λY 0.168 0.067 -0.084 -0.019
λX1 0.168 0.067 -0.084 -0.373
λX2 -0.196
AR ACCMOR MORHER MUER HERGRA
coefficients
ρ1 -0.324 -0.485 0.103
ρ2 -0.275 0.058 -0.315 -0.020
ρ3 -0.128 0.061 -0.107 0.062
ρ4 -0.248 0.193 -0.210 0.150
ρ5 0.117 0.042
ρ6 0.037 0.198
ρ7 -0.043 -0.076
ρ8 0.138 0.189
ρ9 -0.095 -0.206
ρ10 -0.268 -0.261
ρ11 -0.035 -0.097
ρ12 -0.020
ρ14 -0.186 -0.206
Table 4.5: Fit statistics of DRAG models.
Fit statistics ACCMOR MORHER MUER HERGRA
Log-likelihood: -309.861 -368.933 -333.696 -409.788
Pseudo-R2:
-(E) 0.578 0.785 0.576 0.729
-(E) Adjusted 0.463 0 .714 0 .440 0 .630
Observations 108 108 108 108
75 4.4. Model construction and estimation
Table 4.6: Fit statistics of UCM components.
Fit statistics ACCMOR MORHER MUER HERGRA
Full Log-likelihood 24.806 83.078 73.494 -8.156
AIC -47.61 -164.2 -12.7 18.31
BIC -44.88 -161.5 -9.954 20.94
χ2Seasonal NP 29.6 NP 38.66
D.F. (11) (11)
Error variance, σ2γ 0 0 0 0.0151
sonal components and the intervention variables, then adding the explanatoryvariables that are assumed to have a significant effect on road safety (Hirstet al. , 2005). There are two steps to consider while including the descriptivecomponents in the model. The first step is to decide whether the componentis time varying and secondly whether it is contributing to the response vari-ability. The components can enter the model either stochastically (non- zerovariance) or deterministically (zero variance) and are included in the model ifsignificant. We require the p-value to be below 10% (Hermans et al. , 2006).Note that in order to choose the best UCM we have used fit statistics suchas AIC and BIC.
The results of the final descriptive models are listed in Table 4.6. In allfour UCM both the slope and level error variances were set to zero (σ2
η =σ2ξ = 0), meaning the models have a linear trend. The seasonal compo-
nent was absent in the ACCMOR and MUER models but was includedfor MORHER and HERGRA. In the MORHER model the seasonal com-ponent was introduced as a deterministic component, (χ2
Seasonal = 29.6),while in the case of the HERGRA model it enters as a stochastic compo-nent (χ2
Seasonal = 38.66;σ2γ = 0.0151). The intervention variables (PPS and
RPC) were removed from all the models, except for HERGRA, where onlyRPC was found to be significant (bRPC = −0.05).
As the final step in UCM building, the effects of the explanatory vari-ables were estimated: as in the case of DRAG models, first all the explana-tory variables that were assumed to have a significant effect on traffic acci-dent severity and frequency were included in the descriptive model and thenthe variables with non-significant estimates were eliminated using a stepwiseprocedure. Both dependent and independent variables are transformed intonatural logarithms. As before, a 10% significance level was considered as thevariable selection criteria. It was initially assumed that some of the explana-tory variables have a lagged effect on the accident risk and fatality, thus some
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 76
Table 4.7: Normality test of UCM errors.
Dependent Shapiro- Pr<W Kolmogorov Pr>D
variable Wilk Smirnov
ACCMOR 0.986167 0.4286 0.078734 >0.1500
MORHER 0.98172 0.2130 0.081657 0.1238
MUER 0.983705 0.2492 0.062932 >0.1500
HERGRA 0.982682 0.2493 0.124208 <0.0100
were introduced with and without their lagged values (Garcıa-Ferrer et al., 2006, 2007). After comparing the model fit statistics only CONALC wasincluded in ACCMOR and MUER with its lagged value. The best modelwas chosen according to the AIC statistics. It should be noted that, unlikeDRAG, where the performance and the goodness of fit of the model improveas more variables are added, the UC estimation procedure used here does notallow the inclusion of so many variables because of multicollinearity. In thecase of the UCM a better prediction was obtained when the model includedhighly significant estimates of the variables, which in turn yields better AICstatistics.
The residual analysis of UCM was carried out by checking the validity ofthe hypothesis of normality, homoscedasticity and independence of the errors(Figure 4.2). For normality, we have carried out graphic inspection (Figure4.2) and Kolmogorov- Smirnov and Shapiro-Wilk normality tests (Table 4.7).Homoscedascity is checked by examining the time evolution of the spread ofthe residuals.
4.5 Results
The final estimation results are reported in Tables 4.8-4.14. The coefficientsof the DRAG models are presented in elasticities, while the UCM coefficientsare a priori the regressor estimates. However, since to carry out the UCManalysis, the original data was transformed into natural logarithms, the re-gressor estimates of UCM can be interpreted as the elasticities as well:
ηk =d log Ytd logXkt
=dYtdXkt
· Xk
Y= βk ·
Xkt
Yt(4.1)
To explain the effect of the variables on the response in percentages,
77 4.5. Results
4.2.a)
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 78
4.2.b)
79 4.5. Results
4.2.c)
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 80
4.2.d)
Fig. 4.2. Residual analysis of road safety measures.
4.2.a)ACCMOR; 4.2.b)MORHER; 4.2.c)MUER; 4.2.d)HERGRA.
81 4.5. Results
Table 4.8: Exposure.
Variables ACCMOR MORHER MUER HERGRA
(cond. t-stat.) DRAG UCM DRAG UCM DRAG UCM DRAG UCM
VKM 0.382
(1.20)
LAM 1
CONOIL 0.772 0.145
(1.26) (0.16)
LAM 1 LAM 1
COMTOT 0.97 1.195 1.72 0.73 1.137 1.86
(-4.3) (4.44) (-5.29) (-3.1) (3.65) (-6.36)
LAM 1 LAM 1
PRGFUR 2.290 3.813
(1.50) (2.19)
LAM 1 LAM 1
the elasticity estimates for the transformed variables are multiplied by 10,while for the untransformed variable the multiplier coefficient is 100. Sinceeach measure has been estimated using two models, a label of DRAG andUCM will be added to explain the results of a given model. The results andtheir conformity with the traffic accidents literature are discussed in detail asfollows.
4.5.1 Exposure
The elasticities of exposure variables have a positive sign implying that anincrease in exposure increases the frequency and severity of traffic accidents.The results show that a 10% increase in VKM will increase ACCMOR-DRAGby 3.8%. A 10% increase in COMTOT will raise ACCMOR-UCM by 9.7% and, MORHER-DRAG by 11.9%, MORHER-UCM by 17.2%, MUER-UCM by 7.3%, HERGRA-DRAG by 11.3% and HERGRA-UCM by 18.6%.CONOIL and PRGFUR are found to have an effect on fatality-related mod-els (ACCMOR-DRAG and MUER-DRAG) only. In the case of ACCMOR-DRAG the increments are 7.7% and 22.9%, and 1.4% and 38.1% respectivelyfor MUER-DRAG.
4.5.2 Economic factors
Three of the economic factors representing the economic situation, INDCOM,IPI and INDVEN conform to the findings in literature, i.e. a 10% increase
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 82
Table 4.9: Economic factors.
Variables ACCMOR MORHER MUER HERGRA
(cond. t-stat.) DRAG UCM DRAG UCM DRAG UCM DRAG UCM
INDCOM 0.612
(1.17)
LAM 1
IPI 0.315
(0.73)
LAM 1
INDVEN 0.129 0.127
(1.83) (1.18)
LAM 1 LAM 1
CONST -0.866 -1.638
(-2.79) (-3.91)
LAM 1 LAM 1
PRCOM -0.044 -0.095 -0.289
(-0.11) (-0.54) (-0.61)
LAM 1 LAM 1 LAM 1
INDACT 2.114 1.63 1.856
(0.75) (-2.49) (0.65)
LAM 1 LAM 1
PARO -0.510 -0.21 -0.338 -0.18
(-1.99) (-3.2) (-0.87) (-2.4)
LAM 1 LAM 1
PARSER -0.24 -0.4
(-2.43) (-3.79)
in INDCOM will increase ACCMOR-DRAG by 6.1%, while a 10% increasein IPI will increase MUER-DRAG by 3.1%. A 10% increase in INDVEN willincrease both MORHER-DRAG and HERGRA-DRAG by 1.2%. On the otherhand, investment projects in road safety, such as construction (representedby CONST) and maintenance are found to have a positive effect on roadsafety. The results show that a 10% increase in CONST has a decreasingeffect on ACCMOR-DRAG and MUER-DRAG, estimated as an 8.6% and16.3% reduction respectively.
The results agree with previous work (Chi et al. , 2010, Gaudry and Las-sarre , 2000, Grabowski and Morrisey , 2004) showing that an increase in fuelprices would decrease traffic accident frequency and severity. The estimationresults show that a 10% increase in PRCOM would reduce ACCMOR-DRAGby 0.4%; MORHER-DRAG by 0.9% and MUER-DRAG by 2.8%.
As to the economic activity, the results show that the increase in IN-DACT has a negative impact on road safety (21.1%, 16.3% and 18.5% in-crease in ACCMOR-DRAG, MORHER-UCM and HERGRA-DRAG respec-
83 4.5. Results
tively), while the changes in PARO (5.1%, 2.1%, 3.3% and 1.8% decrease inMORHER-DRAG, MORHER-UCM, HERGRA-DRAG and HERGRA-UCMrespectively) and PARSER (2.4% and 4% decrease in ACCMOR-UCM andMUER-UCM respectively) have a decreasing effect on safety measures.
4.5.3 Driver behavior surveillance
Among the driver behavior surveillance variables CONALC was present inalmost all models and has a positive impact on traffic safety, namely a 10%increase in alcohol controls leads to a 1.7% decrease in ACCMOR-DRAG,0.5% decrease in MORHER-DRAG, 0.6% decrease in MUER-DRAG, 4.5%decrease in decrease in HERGRA-DRAG and 2.8% decrease in HERGRA-UCM. In UC models CONALC was introduced with lagged effect. The resultsshow that a 10% increase in this variable can decrease ACCMOR-UCM by3.8% and MUER-UCM by 1.1%. It is logical to assume that different surveil-lance and control measures lead to effects that are more intense as driversbecome more aware of them. The process of awareness is a lengthy processover time, which explains why the effects are produced with a certain lag.When it comes to breath tests (CONALC), campaigns are run over certainperiods of time. These campaigns are announced through the communica-tions media and implemented by stepping up checks in the period after theannouncement. These checks have a major influence on how drivers perceivethe measure. If we take the year 2001 as reference, 1 out of 10 drivers mayhave been required to take the test. In the most recent period (2008-2010)over 5 million tests were carried out each year, which means 1 out of 4 driverscould have been affected, influencing the propagation process pointed out.
RADAR has a more significant impact on fatality-related measures (AC-CMOR and MUER). The effect is estimated as a 1.9%, 0.2%, 5.3% and0.8% decrease in ACCMOR-DRAG, MORHER-DRAG, MUER-DRAG andHERGRA-DRAG when there is a 10% increment in RADAR.
Both of the suspension-related variables, SUSP and PRLSUSP, are foundto have a positive impact on safety. The estimated elasticities are 3.1%(ACCMOR-UCM), 1.1% (MORHER-DRAG), 3.0% (HERGRA-DRAG) and4.3% (HERGRA-UCM) decrease as the result of SUSP and 2.6% (ACCMOR-DRAG), 1.6% (MORHER-UCM) and 4.5% (MUER-DRAG) decrease as theresult of PRLSUSP.
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 84
Table 4.10: Driver behavior surveillance.
Variables ACCMOR MORHER MUER HERGRA
(cond. t-stat.) DRAG UCM DRAG UCM DRAG UCM DRAG UCM
CONALC -0.172 -0.38 a -0.051 -0.067 -0.45a -0.118 -0.28
(-1.09) (-6.83) (-0.72) (-0.36) (-7.54) (-1.04) (-6.40)
LAM 1 LAM 1 LAM 1 LAM 1
RADAR -0.190 -0.025 -0.530 -0.087
(-1.16) (-0.38) (-2.44) (-0.98)
LAM 1 LAM 1 LAM 1 LAM 1
PRADAR -0.963
(-2.42)
LAM 1
SUSP -0.31 -0.117 -0.302 -0.43
(-2.63) (-1.06) (-1.86) (-4.82)
LAM 1 LAM 1
PRLSUSP -0.262 -0.16 -0.454
(-1.11) (-1.98) (-2.11)
LAM 1 LAM 1
aThe estimate belongs to the lagged value of CONALC variable.
Table 4.11: Fleet characteristics.
Variables ACCMOR MORHER MUER HERGRA
(cond. t-stat.) DRAG UCM DRAG UCM DRAG UCM DRAG UCM
AIRBAG -0.721 -0.15 -0.406
(-1.92) (-3.96) (-1.19)
LAM 1 LAM 1
4.5.4 Fleet characteristics
Among the safety devices included in the models the AIRBAG seemed tohave a significant positive impact on ACCMOR-DRAG, MORHER-UCM andMUER-DRAG; the elasticities being a 7.2%, 1.5% and 4.06% decrease respec-tively.
4.5.5 Road infrastructure
The results show that LONRAC has a decreasing effect on the HERGRA-DRAG model: a 3.7% decrease when there is a 10% increase in LONRAC.
LONRED has a significant effect on the dependent variables. The esti-mations show that a 10% increase in LONRED will have a positive impact
85 4.5. Results
Table 4.12: Road infrastructure.
Variables ACCMOR MORHER MUER HERGRA
(cond. t-stat.) DRAG UCM DRAG UCM DRAG UCM DRAG UCM
LONRAC -0.375
(-0.83)
LAM 1
LONRED -1.485 -1.064 -1.61 -2.192
(-1.62) (-3.27) (-7.48) (-2.25)
LAM 1 LAM 1 LAM 2
Table 4.13: Legislative measures.
Variables ACCMOR MORHER MUER HERGRA
(cond. t-stat.) DRAG UCM DRAG UCM DRAG UCM DRAG UCM
PPS -0.100 -0.294
(-0.91) (-2.30)
RPC -0.152 -0.333 -0.111 -0.05
(-2.47) (-4.41) (-1.02) (-1.44)
RUIDO -0.008 -0.05
(-0.33) (-3.36)
LAM 1
on road safety, with the estimated effects of a 14.8%, 10.6%, 16.1% and21.9% decrease in ACCMOR-DRAG, MORHER-DRAG, MORHER-UCMand MUER-DRAG respectively. Such a high elasticity can be explained bythe fact that there is usually less traffic on toll roads. Also the geometric char-acteristics (high quality, less curvature, etc.) of these types of roads enhancethe convenience of road users, thus contributing positively to road safety.
4.5.6 Legislative measures
The results show that there was a 10% decrease in ACCMOR-DRAG and a29% decrease in MUER-DRAG since the introduction of the PPS. Accord-ing to the DRAG estimations, RPC introduction has led to a 15.2% reduc-tion in ACCMOR-DRAG, 33.3% decrease in MUER-DRAG, 11.1% drop inHERGRA-DRAG and 5% drop in HERGRA-UCM. RUIDO seemed to have apositive effect on the dependent variable HERGRA, 0.08% and 0.5% decreaseaccording to DRAG and UCM respectively.
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 86
Table 4.14: Calendar effect and weather conditions.
Variables ACCMOR MORHER MUER HERGRA
(cond. t-stat.) DRAG UCM DRAG UCM DRAG UCM DRAG UCM
DLAB 0.670 2.03 1.911 2.62 0.380
(1.09) (-4.3) (1.88) (-5.03) (1.20)
LAM 1 LAM 1 LAM 1
SDF 0.07 0.017 0.01 0.489 0.11
(-3.47) (0.18) (-1.83) (1.29) (-5.21)
LAM 1 LAM 1
DNIE 0.151 0.006 0.175
(2.47) (0.56) (3.39)
SLNV -0.162 -0.225
(-1.75) (-3.02)
TEMP -0.002
(-0.02)
LAM 1
4.5.7 Calendar effect and weather conditions
As the results suggest, DLAB and SDF generally have a negative impacton road safety. The estimates show that DLAB increases ACCMOR-DRAG6.7%, ACCMOR-UCM 20.3%, MUER-DRAG 19.1%, MUER-UCM 26.2%and HERGRA-DRAG 3.8%, while for SDF the estimates are a 0.7% in-crease in ACCMOR-UCM, 0.1% increase in MORHER-DRAG, 0.1% increasein MORHER-UCM, 4.8% increase in MUER-DRAG and 1.1% increase inMUER-DRAG .
Among the weather condition variables DNIE was found to have a neg-ative effect on safety: 15.1% increase in ACCMOR-DRAG; 0.6% increase inMORHER-DRAG and 17.5% increase in MUER-DRAG, while SLNV had apositive impact (16.2% decrease in ACCMOR-DRAG and 22.5% decrease inMUER-DRAG) on road safety. The positive significant impact of SLNV onfatality-related measures can be explained by the fact that during high snow-depth days, vans do not travel much thus decreasing exposure (Eisenberg ,2004). TEMP was found to have a quite insignificant effect: 0.02% decreasein MUER-DRAG.
4.6 Prediction analysis
The final DRAG and UC models were compared using the prediction resultsby means of a cross-validation exercise: first the models were estimated with
87 4.6. Prediction analysis
the first 108 observations (years 2000-2008) and then the remaining 12 obser-vations (year 2009) were used for prediction (Table 4.15). By analyzing theprediction values and graphs (Figure 4.4) it can be observed that, in the caseof ACCMOR, the volatility of the observed data during the months January-July is relatively better captured by DRAG than by UCM. After this periodthe predictions with both models have an almost linear trend, which do notcapture the seasonality present in the data. In the case of the MORHER,we can see that both models perform equally well. The seasonality of theMUER data however was better captured by the UCM, especially the peaks(January, March, May, October and December) and troughs (April, June,September and November) of prediction with UCM coincide with the truedata. In the case of HERGRA, DRAG seems to have a better prediction per-formance. The graphical analysis in general shows that the seasonality wascaptured relatively better with UCM. This can be due to the fact that theUCM has a specific seasonality component. Prediction accuracy was mea-sured by percentage error, calculated as follows:
PEYt =T∑t=1
100 ·
∣∣∣∣∣(Yt − Yt)Yt
∣∣∣∣∣where yt and yt are the observed and forecast values respectively. The pre-diction errors are reported in Table 4.16. As can be seen, the aggregatedprediction errors produced by DRAG models are lower for all four dependentvariables. In both DRAG and UCM, for the number of accidents with in-jured victims, MORHER (7.6% DRAG y 8.9% UCM) and number of injuredvictims, HERGRA (8.6% DRAG y 13.2% UCM) had a smaller average pre-diction error compared to fatal accidents, ACCMOR (15.5% DRAG y 18.8%UCM) and number of fatalities, MUER (18.9% DRAG y 20.6% UCM).
We can observe that prediction errors are much higher for fatality-relatedmeasures, ACCMOR and MUER, for both DRAG and UCM. Averaging overthe prediction errors of road safety indicators during the summer months(July and August - when traffic safety is especially vulnerable due to high mo-bility and exposure), we can observe that all the DRAG models have a lowerPE (16.3%-ACCMOR; 4.5%- MORHER; 28.6%- MUER; 2%-HERGRA) ver-sus (18.5%-ACCMOR; 5%- MORHER; 31%- MUER; 14%-HERGRA) forUCM (Figure 4.4).
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 88
4.3.a.
4.3.b.
89 4.6. Prediction analysis
4.3.c.
4.3.d.
Fig. 4.3. Observed versus predicted values of four road safety indicators, corresponding
to year 2009.
4.3.a) ACCMOR; 4.3.b) MORHER; 4.3.c) MUER,; 4.3.d) HERGRA.
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 90
Table 4.15: A year ahead prediction, year 2009.
Date ACCMOR MORHER MUER HERGRA
DRAG OBS UCM DRAG OBS UCM DRAG OBS UCM DRAG OBS UCM
Jan 16 15 17 104 97 100 19 18 20 118 99 133
Feb 14 15 16 94 91 96 17 15 18 105 100 120
Mar 18 26 21 97 119 99 22 28 24 111 123 123
Apr 16 12 19 98 102 94 18 13 21 106 115 105
May 15 22 20 98 115 97 16 25 24 99 129 119
Jun 19 18 20 112 115 108 20 19 22 132 139 164
Jul 22 21 24 118 122 118 24 21 26 140 136 171
Aug 18 25 20 100 106 99 20 35 22 114 116 114
Sep 18 17 19 99 84 91 21 22 20 110 97 111
Oct 17 23 21 103 106 104 19 26 24 113 108 133
Nov 15 15 18 91 94 90 19 16 20 101 99 101
Dec 17 16 20 101 110 90 18 18 22 113 124 126
Table 4.16: Prediction error in percentage for DRAG and UCM.
Date ACCMOR MORHER MUER HERGRA
DRAG UCM DRAG UCM DRAG UCM DRAG UCM
Jan 6.67 13.33 7.22 3.09 5.56 11.11 19.19 34.34
Feb 6.67 6.67 3.30 5.49 13.33 20.00 5.00 20.00
Mar 30.77 19.23 18.49 16.81 21.43 14.29 9.76 0.00
Apr 33.33 58.33 3.92 7.84 38.46 61.54 7.83 8.70
May 31.82 9.09 14.78 15.65 36.00 4.00 23.26 7.75
Jun 5.56 11.11 2.61 6.09 5.26 15.79 5.04 17.99
Jul 4.76 14.29 3.28 3.28 14.29 23.81 2.94 25.74
Aug 28.00 20.00 5.66 6.60 42.86 37.14 1.72 1.72
Sep 5.88 11.76 17.86 8.33 4.55 9.09 13.40 14.43
Oct 26.09 8.70 2.83 1.89 26.92 7.69 4.63 23.15
Nov 0.00 20.00 3.19 4.26 18.75 25.00 2.02 2.02
Dec 6.25 25.00 8.18 18.18 0.00 22.22 8.87 1.61
91 4.7. Summary and discussions
Fig. 4.4. Prediction errors corresponding to quarterly data.
4.7 Summary and discussions
This research work was triggered by the behavior of severe accidents involv-ing vans that was observed in the Spanish data. The frequency (ACCMORand MORHER) and severity (MUER and HERGRA) of van-involved acci-dents were studied through two established statistical methodologies: UCMand DRAG. The results suggest that the fatality measures, ACCMOR andMUER, are influenced by the same factors, within each type of model (DRAGor UCM). As can be observed, the number of independent variables includedin the DRAG models for the fatality-related measures is higher (17 in AC-CMOR and 19 in MUER respectively) than in the UCM (6 in ACCMORand 5 in MUER respectively). According to DRAG estimation, all of theexplanatory variables categories are present in both ACCMOR and MUER,and the most significant factors belong to the following categories: exposure,driver behavior surveillance, economic factors and legislative measures. UCMestimation, however, includes relatively few significant factors. The factorsthat are common to ACCMOR and MUER belong to the following cate-gories: exposure (COMTOT), economic activity (PARSER), driver surveil-lance (CONALC) and calendar effect (DLAB and SDF). It can be observedthat, when the same factor appears both in DRAG and UCM, the elasticityestimates are nearly the same. This pattern is not observed for DLAB only.
Injury- related measures, MORHER and HERGRA, are affected by the
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 92
same factors, within each methodology (DRAG and UCM). Moreover, byanalyzing the results, it can be concluded that the factors are almost common:9 and 8 for DRAG and 8 and 6 for UCM. The most significant variables belongto the following categories: driver behavior surveillance, economic factorsand road infrastructure. The variables with significant estimates generallyhave similar elasticities for both methodologies. For example, in the caseof MORHER the total fuel consumption variable (COMTOT) is included inboth DRAG and UCM and elasticities are 12% and 17% respectively.
Reviewing the results of model estimation, one can say that they makesense and in general conform to the literature. The signs and orders of mag-nitude of the regression coefficients coincide with the literature for all ex-planatory variables in both DRAG and UCM, which is an encouraging indi-cation regarding the adequacy of the models. Besides the model estimationand explanation of the van-involved accidents, the following observations andconclusions can be reached as the result of model comparison:
1. Although not significantly different, in general the DRAG methodologyprovides better predictions than UCM.
2. UCM captures the seasonality during the prediction procedure moreefficiently than DRAG.
3. The UCM prediction accuracy highly depends on the model selectioncriteria- AIC, as mentioned before. In order to get a good fit statisticsvalue the model requirement is to keep statistically significant variablesin the model (in our case this threshold was set as the p-value below10%). Given this threshold and the multicollinearity among the ex-planatory factors the UCM does not allow for the inclusion of so manyregressors as DRAG. The advantage of this is that, since stepwise elim-ination is employed during UCM selection, we obtain a rather small setof candidate models, from which it is quite straightforward to choosethe best model. But since it was of our interest to estimate the ef-fect of many more macroeconomic variables than the UCM thresholdallows us to, it is not really appropriate to apply this class of modelto a macro level with a high threshold. As an example, if we considerthe MORHER model, where the average UCM prediction error is muchless than for the rest of the (UCM) outputs, we can observe that therewere only 7 predictors versus 10 for DRAG. For a traffic accident an-alyst it is straightforward to assume that a model such as MORHERis affected by the macroeconomic variables. However, we can observe
93 4.7. Summary and discussions
that the UCM applied to this variable only finds significant the effect ofeconomic activity among the economic factor group. But, as mentionedabove, if we try to overcome this problem by including less significantvariables (lower p-values in this case) prediction accuracy will decreaseconsiderably.
4. In DRAG model selection, we have a very large number of candidatemodels. Since there are multiple parameters (BCT parameter, AR errorstructure and regression coefficients for explanatory variables, where theinclusion of the latter can be manipulated by the user), we can end upwith a very large set of models which need to be built, estimated andpredicted separately. This can be considered an advantage since one canalways build a model that outperforms the UCM, as far as estimationand prediction are concerned. But as indicated, having such a large setof DRAG candidate models is a source of difficulty for the user.
Chapter 4. Explanation of van-involved road accident indicators. Modelcomparison 94
Chapter 5
Analysis of fatal accidents:
model selection methodology
5.1 Introduction
When modeling the accident data as a function of a several explanatory vari-ables one issue the researcher is faced with is the choice of parsimonious versusfully specified models (Mannering and Bhat , 2014). The main purpose of thischapter is proposing a macro model selection methodology using somewhatparsimonious SE model structure, where the estimation is based on Bayesianinference (Markov Chain Monte Carlo). The main reason for using Bayesianestimation is the fact that, during Bayesian estimation the model parametersare treated as random variables, which provides a more uniform and thusmore elegant framework to treat uncertainty versus the frequentist approachwhere the parameters are treated as fixed and unknown constants. By usingthe Bayesian approach a model is treated and estimated as a whole (Raftery, 1995) and its adequacy is tested based on criteria such as posterior modelprobability and deviance information criteria (DIC) rather than estimatingeach explanatory variable individually as done during model building usingfrequentist approach. In the past few years Bayesian methods have beenwidely applied to road safety (Mannering and Bhat , 2014).
The proposed model selection methodology addresses the question of pa-rameter (explanatory variables and power transformation) selection and errorautocorrelation. The variable selection was carried out through a method-ology called two-input models (TIM), where several models are constructedusing two inputs and power transformation structure. Given the selected
95
Chapter 5. Analysis of fatal accidents: model selection methodology 96
variables and SE model structure, the final model is selected based on thegoodness of fit measures, such as DIC and pseudo-R2. The selected model iscross validated through prediction analysis. The estimation results are thencompared with the fully specified DR model. The proposed methodology isapplied to the number of monthly fatal accidents in Spain during 2000-2011.
The rest of this chapter is organized as follows. In Sections 5.2 and5.3 the data are discussed. In Section 5.4 the model selection procedure isintroduced. In Sections 5.5 and 5.6 the estimation and prediction results arepresented. The chapter ends with the summary and discussions.
5.2 Fatal accidents
The total number of fatal accidents, ACCTOT , during years 2000-2011 isstudied to address the impact of explanatory factors (Section 2.1.1). Forthe preliminary analysis of the data, the time series was transformed intonatural logarithms. The decomposition of the series into trend and seasonalcomponents was carried out through TRAMO/SEATS (Figure 5.1). As itcan be seen the series has a decreasing trend and seasonal pattern. On a firstvisualization of the series, the observations during July 2000, August 2000,August 2003 and February-April 2010 look like outliers. The estimation ofthe data using the airline model, ARIMA(0, 1, 1)(0, 1, 1)s, however does notdetect any outliers. The modified score test (MAD) for the observation July2000, which has the most extreme value, was 1.64 (< 3.5) thus showing thatthe observation is not an outlier (Table 5.2). The fit statistics of the estimatedmodel are shown in Table 5.1.
5.3 Independent variables
The explanatory variables used as traffic safety factors were divided intothe following groups: exposure, economic factors, driver characteristics andsurveillance, fleet characteristics, road infrastructure, legislative measures,weather conditions and calendar effect (Table 5.3).
5.4 Model selection procedure
As specified in the introduction, the model selection procedure has been ap-plied to the SE models and is carried out within the Bayesian framework
97 5.4. Model selection procedure
Table 5.1: Summary of TRAMO/SEATS results, ACCTOT .
Fit statistics ACCTOT
Mean 265.007
MA1 -0.6425
MA12 -0.9492
BIC -5.1209
SE(at) <0.0001
N(at) 0.4259
Q24(at) 20.78
QS(at) 0.20
Table 5.2: Outlier detection.
Date Value Studentized Values a Studentized Values Median Absolute
Without Deletion With Deletion Deviation (MAD) b
Feb-2010 120.0 -1.85199 -1.88126 -1.50771
Feb-2011 120.0 -1.85199 -1.88126 -1.50771
Apr-2010 123.0 -1.81367 -1.84141 -1.47795
Apr-2011 123.0 -1.81367 -1.84141 -1.47795
Mar-2011 136.0 -1.64764 -1.66938 -1.349
...
Aug-2000 406.0 1.80072 1.82795 1.32916
Aug-2001 422.0 2.00507 2.04112 1.48787
Aug-2002 428.0 2.0817 2.12153 1.54738
Aug-2003 437.0 2.19664 2.24269 1.63665
Jul-2000 438.0 2.20942 2.25619 1.64657
aThe Studentized values measure how many standard deviations each value is from the
sample mean ofbMAD > 3.5 might be an outlier
Chapter 5. Analysis of fatal accidents: model selection methodology 98
Fig. 5.1. Decomposition of ACCTOT into trend-cycle and seasonal components with
TRAMO/SEATS.
99 5.4. Model selection procedure
Table 5.3: Explanatory variables, 2000-2011.
Variable Definition
Exposure
VHP Heavy Vehicles
VKM Vehicle Kilometers Travelled
CONGAS Gasolne Consumtion
Economic factors
IPI IPI
PRDCRN Meat Production
CONCEM Cement Consumption
MANT Maintenance Investment
PREC Fuel Price
OCUP1 Total Employed
OCUP2 Employment Construction Sector
PARO Total Unemployment
Driver characteristics and surveillance
COND2 Young Drivers (2 years)
CONALC Random Alcohol Checks
RADAR Speed Controls
SUSP Driving License Suspended
Vehicle characteristics
VEH10 Vehicle Age (10 years), % of Total Fleet
ABS ABS Equipped, % of Total Fleet
Road infrastructure
LONRAC High Capacity Roads, % of Total Network
LONRED Length of Toll Roads
Legislative measures
PPS Penalty Point System
RPC Penal Code Reform
Weather conditions
PREC Rainfall
DNIEB Foggy Days
SLNV Number of Days with Snow Covered Ground
HSOL Amount of Sunny Hours
Calendar effect
DLAB Working days
SDF Weekend and Holidays
SEMSAN Easter Break
Chapter 5. Analysis of fatal accidents: model selection methodology 100
through MCMC estimation. The procedure is based on the application oftwo-input models (TIM) and consists of three stages implemented sequen-tially: 1. explanatory variable selection; 2. power transformation estimation;and 3. final model selection:
1. Stage 1: Selection of explanatory variable.
1.1 Build a set of two-input models (TIM), using 28 explanatory variables,thus each model contains a combination of two variables. There are(282
)= 378 combinations and thus 378 possible models. The model
structure is as given by equations (3.9)-(3.10), i.e. SE withAR(2) errors.The model parameters are assigned non-informative prior distributions.TIMs facilitate the selection of variables across the models and help topartially take care of the multicollinearity among independent variablesas it will be detailed in 1.4.
1.2 The explanatory variables belonging to the same TIMs are transformedwith the same value of Box-Cox transformation value, λX , while the de-pendent variable is not. There are three fixed values of λX = (−0.5, 0.1,0.5). Variables belonging to each TIM are transformed with the samevalue of λX . Given that there are 378 variable combinations and threeBCT values λX , a total of 3 · 378 = 1134 models are estimated.
1.3 Sort the TIMs by goodness of fit measure, pseudo-R2. Higher pseudo-R2 value means better fit. For each value of λX , select the first 50 TIMswith the best goodness of fit measure thus, a total of 3 · 50 = 150 TIMsare selected.
1.4 The first stage is completed by selecting the explanatory variables. Todo this, among the selected 150 TIMs, the ones that were repeated 3times (i.e. for the three values of λX) were selected. Selection based onthis method avoids the problem of selecting one variable based on itspower transformation, i.e. if a given variable achieves a better estima-tion with a given value of BCT then there is a probability that severalTIM’s that contain this variable will have a better goodness of fit mea-sure and can fall within the 50 models threshold. The same variable canalso appear in the models with higher goodness of fit measures becauseof being highly correlated with the other explanatory variables. Then ifthe variables are selected solely based on the fact that they appear threeor more times across three sets of 50 selected models, it can’t be assuredwhether the same variable appear in all three sets of selected 50 models
101 5.4. Model selection procedure
or the same variable appears more than once in one set of model andnone in the other. Thus selecting the TIMs rather than variables canensure that a given variable achieves a better fit with all three valuesof λX and the problem of multicollinearity can be somewhat avoided.
2.1 Stage 2.1: Estimation of power transformation parameter for the re-sponse.
2.1.1 Using the explanatory variables selected in Stage 1 optimize the BCTvalue for the dependent variable with respect to λY . For this purposean algorithm by Venables and Ripley (Venables and Ripley , 2002)was used. The explanatory variables were kept untransformed. Theoptimization is carried out through log-likelihood estimation.
2.2 Stage 2.2: Estimation of power transformation parameter for the ex-planatory variables.
2.2.1 Build a model using the explanatory variables selected in the first stage.The model has the same form as in equations (3.9)-(3.10) (Chapter 3).Both the dependent and independent variables are power transformed.The dependent variable is transformed using the optimal λY obtained inStage 2.1. The explanatory variables are divided into groups describedin Table 5.3 and power transformed using three previously fixed valuesof λX = (−0.5, 0.1, 0.5). Considering that one group of variables canperform better by transforming under one λ than other, all the possi-bilities are considered by transforming the variables belonging to thesame group with the same value of λX . For computational purposes thedummy and quasi-dummy variables are not transformed. A total of 3N
models are constructed, where N is the number of groups.
3. Stage 3: Final model selection according to goodness of fit measure andthe expected signs of explanatory variables.
3.1 Determining the expected signs of the explanatory variables selected inStage 1 based on the literature review. The model adequacy requiresthat the direction of the effect (i.e. the signs of the explanatory vari-ables) agrees with the results from the previous empirical studies.
3.2 Model selection based on goodness of fit measures (DIC) and interpre-tation of the model variables. A lower DIC value means a better fit.
4. Stage 4: Cross-validation through prediction.
Chapter 5. Analysis of fatal accidents: model selection methodology 102
Table 5.4: Stage 1: Pseudo-R2 values of selected two-input models for
three different values of power transformation, λX .
Pseudo R2
TIM X1 X2 λX = −0.5 λX = 0.1 λX = 0.5
28 V KM CONGAS 0.804 0.803 0.815
107 OCUP1 MANT 0.867 0.837 0.802
236 PRECOM LONRAC 0.834 0.833 0.810
314 CONALC SUSP 0.823 0.812 0.811
325 RADAR V EH10 0.819 0.819 0.835
327 RADAR LONRAC 0.810 0.828 0.836
329 RADAR PPS 0.820 0.810 0.811
334 SUSP V EH10 0.804 0.810 0.810
346 V EH10 PPS 0.803 0.804 0.802
4.1 The final model is cross validated through prediction. For this purposethe last 12 observations are estimated.
5.5 Results
In this Section the results of the model selection strategy and comparisonwith the DR model are presented.
5.5.1 Explanatory variable selection
The explanatory variable selection was carried out through the above pro-posed TIM methodology (Stage 1). The estimation methodology is MCMCwhich was implemented using R and WinBUGS (Lunn et al. , 2000) soft-wares (see Appendix III for WinBUGS code). The Gibbs sampler was runin 20, 000 iterations in 3 chains. The model convergence was checked usingtrace plots. In this stage a total of 378 · 3 = 1134 models were estimated (seeAppendix IV for WinBUGS outcome for variable selection stage). Among theselected 150 TIM’s 9 TIMs consisting of 11 variables were selected: V KM ,CONGAS, OCUP1, MANT , PRECOM , CONALC, RADAR, SUSP ,V EH10, LONRAC and PPS (Table 5.4). The selected explanatory vari-ables belong to 6 categories, namely exposure, economic factors, driver be-
103 5.5. Results
Table 5.5: Explanatory variables selection.
Group Variables SE model
Exposure VHP
VKM 3
CONGAS 3
Economic IPI
factors CONCEM
PRDCRN
MANT 3
PRECOM 3
PARO1
OCUP1 3
OCUP2
Driver COND2
characteristics CONALC 3
and surveillance RADAR 3
SUSP 3
Vehicle VEH10 3
characteristics ABS
Road LONRED
infrastructure LONRAC 3
Legislative measures PPS 3
RPC
Weather PREC
conditions HSOL
SLNV
DNIEB
Calendar SDF
effect SEMSAN
DLAB
havior surveillance, vehicle characteristics, road infrastructure and legislativemeasures.
5.5.2 Estimation of power transformation parameter
The transformation value for the dependent variable (SE model) was op-timized using the selected 11 explanatory variables. The optimal λY wasselected from the same interval as the λX , λ ∈ [−0.5, 0.5]. The optimal valuefor λY was set to λY = 0.25 (Figure 5.2).
The explanatory variables selected as the outcome of the input variablesselection procedure (stage 1) are grouped into 6 categories (Table 5.6). The
Chapter 5. Analysis of fatal accidents: model selection methodology 104
Fig. 5.2. BCT optimization, Yt.
explanatory variables belonging to the same category were transformed withthe same value of λX . Since one of the groups consists of a single dummyvariable (PPS), this variable group is not subject to the power transformation.Thus, considering that there are 5 input variable groups subject to powertransformation and 3 fixed values of λX = (−0.5, 0.1, 0.5), a set of 35 = 243models were constructed, where the explanatory variables are transformedwith 3 different values of λX .
5.5.3 Model selection
For final SE model selection the models were constructed using the selected11 variables and the power transformation values. The MCMC estimationwas applied to a total of 243 models using three chains taken to 100, 000 it-erations (see Appendix V for WinBUGS outcome for model selection stage).Final model selection was based on the correct signs of the selected vari-ables according to previous empirical research on road safety (Table 5.6) andgoodness of fit measures (DIC values).
The estimation results indicate that 10 out of 243 the models fit thedata as far as the variable signs are concerned. As it can be observed inTable 5.7 pseudo-R2 value is around 0.94 across the models, thus the selected
105 5.5. Results
Table 5.6: Selected variables and the expected signs, based on previous
empirical studies.
Group Description Variable Expected
sign
1. Exposure V KM +
CONGAS +
2. Economic OCUP1 +
factors MANT -
PRECOM -
3. Driver surveillance CONALC -
RADAR -
SUSP -
4. Vehicle characteristics V EH10 +
5. Road infrastructure LONRAC -
6. Legislative measures PPS -
Table 5.7: Fit statistics of selected 10 SE models.
Models Fit statistics
Pseudo- R2 DIC
SE122 0.9398 88
SE128 0.9354 92
SE155 0.9377 92
SE161 0.9379 92
SE203 0.9391 90
SE204 0.9394 88
SE207 0.9401 86
SE212 0.9401 89
SE213 0.9401 88
SE215 0.9388 88
Chapter 5. Analysis of fatal accidents: model selection methodology 106
11 variables explain around 94% of model variability in general.
The model SE207 has the lowest DIC (= 86) value, and highest pseudo-R2 (= 0.94). The estimation results of elasticities for SE207 (Table 5.9) showthat a 10% increase in V KM , CONGAS, V EH10 and OCUP1 will increasethe number of fatal accident by 1.3%, 2.6%, 3.6% and 27.9% respectively.While a 10% increase in MANT , PRECOM , CONALC, RADAR, SUSPand LONRAC will reduce the accident rate by 6.2%, 1.4%, 0.1%, 0.6%, 6.9%and 9.9% respectively. The effect of PPS is counted as a 1.1% decrease infatal accident frequency.
The results of the variable selection (TIM, 5.5.1) indicates that amongthe initial 28 variables, the selected variables with a positive impact on roadsafety are two economic variables, MANT and PRECOM , four surveillanceand legislative factors, CONALC, RADAR, SUSP and PPS, and a roadinfrastructure variable, LONRAC. The results of model selection procedureindicates that economic and infrastructure variables have relatively higherimpact compared to surveillance and legislative factors (Table 5.9). This canbe observed in the elasticities. However the standard deviation associated tothese estimates are higher compared to those of surveillance and legislativemeasures, meaning that the elasticity estimates for the latter factor group isrelatively unbiased compared to the previous groups and can be consideredas real effects.
The variables with the negative effect on safety are exposure (V KM andCONGAS), vehicle age (V EH10) and employment (OCUP1), as selected bythe TIM procedure. The selected variables support the previous findings inthe road safety literature. The effects vary between 1-4%, for the exposureand vehicle age, except for OCUP1, which is almost 28%. However thestandard deviation for this estimate is relatively higher. In general, it can beobserved that the elasticity estimates with relatively higher coefficients havea corresponding higher standard deviation. This is true for all the variables,OCUP1, MANT and LONRAC, except for SUSP .
5.5.4 Dynamic regression model
As mentioned above, the selected model was compared with the DR model.The DR model was built using the selected 11 variables. The model selec-tion was based on the Ljung-Box (LBQ) test of residuals and AIC statis-tic. The error structure of the first DR model, DR1, was first obtainedthrough an automatic procedure. The final error structure was selected asARIMA(1, 0, 0)(0, 0, 0)s. The AIC statistic for this model was −278.97,
107 5.5. Results
Table 5.8: Fit statistics of DR models.
Fit Models
statistics DR1 DR2
AIC -278.97 -270.70
BIC -238.61 -224.70
σ2 0.0057 0.0056
LBQ(12) 23.56 25.05
(p−value) 0.0233 0.0145
LBQ(24) 37.88 42.18
(p−value) 0.0357 0.0123
Observations 132 132
Table 5.9: Estimation results of selected models, DR2 and SE207.
Parameters DR2 SE207
Elasticity(%) S.D. Elasticity(%) S.D. BCT
Variables
V KM 2.3 -0.096 1.3 0.016 λX = 0.5
CONGAS 3.2 0.197 2.6 0.058 λX = 0.5
V EH10 3.1 0.424 3.6 0.484 λX = 0.5
OCUP1 11.0 0.263 27.9 3.150 λX = 0.1
MANT -2.9 0.264 -6.2 4.451 λX = 0.1
PRECOM -0.7 0.131 -1.4 4.548 λX = 0.1
CONALC 0.0 0.045 -0.1 0.535 λX = 0.1
RADAR -0.8 0.048 -0.6 0.204 λX = 0.1
SUSP -1.7 0.066 -6.9 0.995 λX = 0.1
LONRAC -14.4 0.518 -9.9 14.250 λX = 0.5
PPS -2.3 0.056 -1.1 0.232 NA
Coefficient Coefficient
estimate S.D. estimate S.D.
Other parameters
φ1 0.1493 0.149 0.1858 0.099
φ2 0.1355 0.136 0.1450 0.105
φ12 0.1334 0.133
θ1 0.0203 0.020
τ 9.9150 1.256
Chapter 5. Analysis of fatal accidents: model selection methodology 108
while the LBQ test of first 12 and 24 lags were equal to 23.56 and 33.89 withp−values 0.0233 and 0.0145 respectively (Table 5.8).
The errror structure of second DR model, DR2, was selected as ARIMA(2, 1, 1)(1, 0, 0)s. The fit for this model improved compared to DR1, withAIC = −270.7. The LBQ test of first 12 and 24 lags were equal to 25.05 and42.18 with p−values 0.0357 and 0.0123 respectively (Table 5.8). The selectedDR model thus has the following form:
∇Yt =11∑k=1
βkXkt +1− θ1B
(1− φ1B − φ2B2)(1− φ12B12)swt (5.1)
σ2w = 0.0056 (5.2)
The estimation results for the DR2 model (Table 5.9) indicate that a10% increase in V KM , CONGAS, V EH10 and OCUP1 will increase thenumber of fatal accident by 2.2%, 3.1%, 3.0% and 10.9% respectively, whilea 10% increase in MANT , PRECOM , CONALC, RADAR, SUSP andLONRAC will reduce the accident rate by 2.9%, 0.7%, 0.01%, 0.7%, 1.7%and 14.4% respectively. The effect of PPS is counted as a 2.2% decrease infatal accident frequency. The estimation results of DR2 model are very closeto those of model SE207. As in the case of SE207, the economic factorsseem to have a higher impact on the road safety measure, ACCTOT , com-pared to surveillance factors and policy measures. In general the elasticityestimates of DR2 model follow the same hierarchical order as of the SE207.However, unlike the SE207, higher elasticity values are not associated withthe higher standard deviations. It can be observed that in fact the standarddeviations are smaller, thus the estimates can be considered as less biased.One can observe that as far as the variable estimation is concerned the resultsof DR2 estimation conform to the existing literature, i.e. exposure, vehiclecharacteristics and economic variables indicating the employment rate havea negative impact, while surveillance and legislative measures, road infras-tructure and economic factors related to investment and fuel prices have apositive impact on road safety indicator, ACCTOT . As a result the variableselection methodology can be considered as effective one.
109 5.5. Results
Table
5.1
0:
Pos
teri
orp
red
icti
onin
terv
als
ofse
lect
edm
od
els.
Par
amet
ers
Ob
serv
edD
R2
SE
207
Low
P.I
.(9
5%)
Pre
dic
ted
Hig
hP
.I.
(95%
)L
owP
.I.
(95%
)P
red
icte
dH
igh
P.I
.(9
5%)
Jan
-11
129
129
150
174
118
147
180
Feb
-11
117
125
145
168
111
142
174
Mar
-11
118
129
150
174
116
146
182
Ap
r-11
122
140
163
190
126
161
200
May
-11
149
132
153
178
117
148
183
Ju
n-1
112
713
816
118
812
615
619
5
Ju
l-11
183
156
181
211
141
176
219
Au
g-11
176
152
177
206
140
176
216
Sep
-11
150
136
159
185
120
154
195
Oct
-11
139
129
151
175
115
145
182
Nov
-11
139
119
139
162
104
133
167
Dec
-11
134
131
152
177
108
144
195
Chapter 5. Analysis of fatal accidents: model selection methodology 110
Table 5.11: Prediction accuracy of selected models
Measure DR2 SE207
MAE 16.76 14.42
MSE 468.68 361.08
MAPE 13.29 11.43
5.6 Prediction analysis
The prediction analyses were conducted for cross validation and comparisonpurpose of the model estimation results. For estimation, 132 observationswere included in the model while the remaining 12 observations were usedto assess prediction performance. The SE207 model estimation starts afterperiod t = 3. New observation values of dependent variables are predicted byemploying the MCMC estimates of the parameters obtained from the resultsof model selection. The Gibbs sampler was run in 100, 000 iterations in 3chains. To evaluate the prediction performance of the model, 95% posteriorprediction intervals were computed. As can be seen in Figure 5.3 all obser-vations, except for April − 2011 fall within the posterior prediction interval,namely 92% of the observations fall within the prediction interval estimatedby the SE207 model.
The predicted values through the DR2 model are very close to thoseof SE207 model. However only 7 out of 12 observations, i.e. 58% of theobservations, fall within the prediction interval estimated by the DR2 model.
In order to compare the prediction performance of the models the pre-diction accuracy of the models were computed using three measures: meanabsolute error (MAE), mean squared error (MSE) and mean absolute predic-tion error (MAPE), where:
MAE =1
n
n∑t=1
∣∣∣Yt − Yt∣∣∣ (5.3)
MSE =1
n
n∑t=1
(Yt − Yt
)(5.4)
MAPE =1
n
n∑t=1
100 ·
∣∣∣∣∣(Yt − Yt)Yt
∣∣∣∣∣ (5.5)
It can be observed from Table 5.11 that SE207 has the smaller prediction
111 5.6. Prediction analysis
5.3.a.
5.3.b.
Fig. 5.3. Prediction intervals for selected models.
5.3.a) SE207; 5.3.b) DR2
Chapter 5. Analysis of fatal accidents: model selection methodology 112
error that the DR2 model, for all prediction accuracy measures.
5.7 Summary and discussions
The objective of this chapter was the analysis of fatal road accidents in Spainduring 2000-2011 and the determination of the factors that had a majorimpact on it.
Although there are numerous statistical methodologies applied to theanalysis of road safety analysis, the selection of appropriate methodology fora given data and thus the model selection has not been thoroughly studiedand there is still a lack of formal guidance on how the variables are selectedand how to carry out the estimation. This problem specially prominent whenmacroeconomic data such as fatal accidents for a whole region or countryare concerned. The main objective of this chapter was thus to propose amodel selection methodology where the explanatory factors that have a majorimpact on road safety measures were determined.
For this purpose a model selection strategy using SE model and MCMCestimation was proposed. The model used in the study is parsimonious. Theexplanatory variable selection procedure has used models with combinationsof only two explanatory variables. This restriction adopted for simplicity hasproved adequate in view of the results. Given the model variables and set ofpower transformation values the methodology allows to build all the possiblemodels and select the most adequate one among these models. By limitingthe initial number of parameters (AR structure of the error term and thepower transformation values) to few values, the focus on the model selec-tion procedure is on the explanatory variable selection and BCT parameterestimation for both explanatory and response variables.
The variable selection procedure based on TIMs achieves rather efficientresults, in terms of road safety analysis. As it can be observed the selectedvariables are highly relevant factors in the road accidents, e.g. exposure,vehicle age, surveillance and legislative factors, etc. The variable selectionprocedure considers all the possible combinations of inputs, thus eliminatingthe possibility of discarding important inputs, as it is usually done during theother variable selection procedures such as stepwise elimination for example.The results of the model selection procedure are very intuitive and closelyfollow those obtained in previous empirical studies on road safety analysis.Moreover, the prediction analysis yields better results compared to a fullyspecified DR model. The methodology has thus proved to be successful in
113 5.7. Summary and discussions
providing a quick, simple and effective model selection strategy, which couldeasily be sophisticated and generalized with some additional but feasible com-putational cost.
Chapter 5. Analysis of fatal accidents: model selection methodology 114
Chapter 6
Simulation experiment based
model comparison methodology
with application to road
accident models
6.1 Introduction
The purpose of this chapter is the development of a methodology for the-oretical comparison of two statistical models, with an application to macromodeling of time series road accident data. It often occurs in applied statisticsthat two or more alternative models compete to describe the data generatingprocess in hand. It is then of great interest to understand the similarities anddifferences between the two models from a theoretical point of view. Ideallythis would be done analytically, but this is very often an unfeasible solution,it is thus necessary to apply Monte Carlo simulation to replace theorems.The methodology proposed for the theoretical comparison is based on MonteCarlo simulations and leans on computer experiment design and ANOVA.
The methodological choice of statistical models is a topic of high interestin road accident data modelling. Accidents are assumed to be the outcomeof complex random processes whose general characteristics can be estimatedthrough statistical models. Normally the choice of statistical model for thispurpose will depend on the data, since the preference of one model over an-other can not often be proven mathematically. However, even with the same
115
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 116
data, comparison of models can leave much to be desired in terms of provid-ing a statistical evidence, Mannering and Bhat (2014). Considering theseissues, the main goal of this chapter is, given two competing statistical mod-els applied to road accident data, to relate them by obtaining the samplingdistributions of parameter estimates of one of the models when the true datagenerating process is the other model.
Monte Carlo simulation has been, since the 50’s (Metropolis et al. ,1953) an essential tool of numerical mathematics, with applications to solvingpartial differential equations (PDE), optimization, or numerical integration.Relevant references for these applications are Sabelfeld (1989) for solvingPDE’s, or Kroese et al. (2011) for a handbook of techniques. Statisticalapplications are mainly concerned with numerical integration in, for exam-ple, Bayesian inference or optimization for maximum likelihood estimation(Robert and Casella , 2004). Generally speaking, Monte Carlo simulationcan be in many situations more successful or even the only feasible alterna-tive versus traditional numerical techniques.
The modelling of time series road accident data is carried out taking intoaccount the autocorrelated errors. Two ways of modelling this phenomenonis either modelling the errors using Box-Jenkins ARIMA models or filteringout the unobserved components such as trend and seasonality. A special caseof the first type of models are the DRAG family models (Demand for Roaduse, Accidents and their Gravity) (Gaudry , 1984, Gaudry and Lassarre ,2000), where the errors are treated as an autoregressive (AR) process. Thesecond class of models that have been used in road safety literature are theunobserved components model (UCM) (Harvey and Durbin , 1986).
The comparison of two types of models can be carried out in termsof interpretation of one model type through the other. This approach hasbeen used by some authors in time series literature (Harvey and Scott , 1994,Hillmer and Tiao , 1982, Maravall , 1985), where UCM has been interpretedas Box-Jenkins ARIMA. Nevertheless, in practice the autocorrelation model-ing of DRAG does not cover all the ARIMA model range since it is restrictedto AR structures. Although it is not very clear how a stationary model likeDRAG would capture UCM trend and seasonality, we could guess that theywould be picked up by the DRAG autoregressive error term. If this is thecase, then using either UCM or DRAG to model road accident data will yieldunbiased regression coefficients. If, on the contrary, the regression coeffi-cients partially pick up the trend and/or seasonality the estimation of effectswould be biased. Thus, there is a need for more precise quantification on thecorrespondence between both kinds of models, which can be done through
117 6.2. Simulation experiment methodology
simulation, since, as mentioned above, analytical tools become cumbersomeor nearly unfeasible. Moreover, in the context of road accident modeling anaccurate estimation of factor effects, particularly of countermeasures carriedout by administrations, is important for the decision makers in a very relevantsocial problem.
This chapter is organized as follows. In Section 6.2 the experimental de-sign study is described followed by the introduction of the previous empiricalstudy in Section 6.3. The results of the simulation experiment methodologyare presented in Section 6.4. Finally, in Section 6.5 the summary and somediscussions are presented.
6.2 Simulation experiment methodology
The methodology consists in generating samples of a UCM and observing howthe distribution of the parameter estimates of the DRAG model are relatedto the parameter values of the simulated UCM. Each UCM parameter willbe ”captured” by a specific subset of the DRAG estimates; for example itis reasonable to expect that a UCM regression coefficient will be capturedby the corresponding DRAG coefficient but there is uncertainty about whichDRAG coefficient will capture the effect of the UCM trend parameter.
In order for the generated data to be as close as possible to the realroad accident data, the simulation was carried out using the parameter esti-mates from previous UCM modeling of van-involved accident data providedby Spanish Accident Data Base (Dadashova et al. , 2014).
The simulation experiment methodology has the following steps (Figure6.1):
1. Designing a simulation experiment covering the range of the parametersof the unobserved components model (UCM). These ranges have beenestimated from the results of previous empirical work, as detailed inSection 6.3.
2. Generate samples of UCM with the parameters of the design of step 1.
3. Estimate DRAG models using the UCM samples generated in the sec-ond stage. The DRAG models were constructed following standardpractice, with a selection based on the goodness of fit measures.
4. Estimate the relationship between UCM and DRAG parameters throughANOVA. ANOVA provides quantification of how the variability of the
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 118
Fig. 6.1. Simulation methodology.
DRAG estimates is disaggregated into the contributions of the UCMparameters, either individually (main effects) or jointly (interactions).
In the next section the results of the empirical study mentioned in step1 is reviewed, to establish the parameter ranges in the experiment, and sub-sequently explain in detail the four steps above.
6.3 Empirical study
The empirical study (Dadashova et al. , 2014) used for generating the samplesfor the simulation study is described below. The objective of the researchwork was to estimate the effect the different factors had on the number of thetraffic accidents involving vans (ACCMOR) using the unobserved componentsmodel.
6.3.1 Data
The empirical analysis was carried out using the monthly data on van-involvedtraffic accidents in Spain. The data cover the period from 2000-2009. Theresponse variable is the number of fatal accidents (ACCMOR). The fol-lowing explanatory variables were included in the model: fuel consumption(COMTOT ), number of random surveillance breath tests (CONALC), num-ber of driving license suspended (SUSP ), unemployment in service sector(PARSER) and number of working days (DLAB), (Table 6.1).
119 6.3. Empirical study
6.3.2 Model estimation
The data was converted into the natural logarithms and the final model wasobtained through two stages: descriptive and explanatory analysis. In thefirst stage the accident frequency was analyzed by decomposing the data intothree descriptive - level, slope and seasonal components. There are two stepsto consider while including the descriptive components in the model, first isto decide whether the component is time varying, second whether it is con-tributing to the response variability. The components can enter the modeleither stochastically (non zero variance) or deterministically (zero variance)and are included in the model if significant. The significance level, in this casethe p-value was set to be below 10%. The final descriptive model was selectedaccording to the Akaike Information Criteria (AIC) and the significance ofthe descriptive components (Table 6.2). According to the estimation out-come the final descriptive model was defined as a deterministic linear trend(σ2ζ = σ2
κ = 0)
with no seasonal component.
In the second stage the explanatory variables were introduced to thedescriptive model and the final model was selected based on the AIC and thesignificance of the regressor, with the significance below 10%. For this pur-pose the stepwise elimination procedure was used. Also the multicollinearityamong the regressors was taken into account. Finally the residual analysis ofUCM was carried out by checking the validity of the hypothesis of normality,homoscedasticity and independence of the errors (Figure 6.2). The followingvariables were kept in the model: COMTOT , CONALC, SUSP , PARSERand DLAB (Table 6.2). Thus the final UCM used for the empirical studyhave the following form:
YACCMOR = δPARSER ·X1,t + δCONALC ·X2,t + δSUSP ·X3,t+
+ δDLAB ·X4,t + δCOMTOT ·X5,t + εt (6.1)
where εt is i.i.d. with N(0, σ2ε).
Table 6.1: Explanatory variables.
COMTOT Fuel consumption
CONALC Number of random surveillance breath tests
SUSP Number of driving license suspended
PARSER Unemployment in service sector
DLAB Working days
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 120
6.2.a
6.2.b
6.2.c
Fig. 6.2. Residual analysis of ACCMOR
6.2.a) Distribution of residuals; 6.2.b) Residual autocorrelation; 6.2.c) Residual
white noise test.
121 6.4. Experimental design: estimation and results
Table 6.2: Results of empirical study: fit statistics and parameter
estimates.
Fit statistics
Full Log Likelihood 248.06
AIC (smaller is better) -47.61
BIC (smaller is better) -44.88
Regessors Estimatesa
δPARSER -0.24
δCONALC -0.38
δSUSP -0.31
δDLAB 2.03
δCOMTOT 0.97
σ2ε 0.05
aUCM regressor estimates are considered as the elasticities as well.
6.4 Experimental design: estimation and re-
sults
6.4.1 Experimental design
The experimental design study begins with the simulation of data. As indi-cated, for this purpose the parameter estimates from previous work (Dadashovaet al. , 2014) were used, in order to obtain proxy samples that would replicatethe accident data as close as possible. The model in the reference, equation(6.1), however does not include some of the terms, i.e. an intervention variableand an unobserved component (trend/seasonality), with which the originalUCM (Harvey and Durbin , 1986) had been built. Thus in order to obtaindata samples that would satisfy the conditions of UCM, the equation (6.1)was re-formulated including a stochastic trend, with a non-zero variance (σ2ζ 6= 0) and an intervention variable, Reform Penal Code (RPC):
YACCMOR = δPARSER ·X1,t + δCONALC ·X2,t + δSUSP ·X3,t+
+ δDLAB ·X4,t + δCOMTOT ·X5,t + δRPC · ωt + εt (6.2)
µt = µt−1 + ζt (6.3)
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 122
Table 6.3: Parameter estimates.
Main effects UCM param. Values
Level I Level II
A δPARSER -0.24 -0.19
B δCONALC -0.38 -0.30
C δSUSP -0.31 -0.24
D δDLAB 2.03 1.62
E δCOMTOT 0.97 0.77
F σ2ζ 0.020 0.025
where εt and ζt are i.i.d. with N(0, σ2ε) and N(0, σ2
ζ ) respectively, and δk areregression coefficients and ωt is dummy variable with coefficient δRPC thattakes values:
ωt =
{0, if t < 961, if t ≥ 96
(6.4)
where 96th observation corresponds to the date (December 2007) when PenalCode Reform was enacted.
The presence of stochastic term is considered to be very important. Asit was seen in chapter 5, the true data when modelled through DR modelincluded an integration term of order 1, ∇ = 1 (equation (5.2)). Howeverin a stationary model like DRAG there is no separate term for a stochasticcomponent. Thus it is crucial to see whether the stochastic trend, if present inthe true data, should be modelled and treated separately (e.g. by differencingof the data beforehand).
Thus there are a total of 6 parameters set as the factors of the computersimulation experiment instead of only 5 variables, as described in Table 6.3:5 regression coefficients, δPARSER, δCONALC , δSUSP , δDLAB, δCOMTOT and atrend variance, σ2
ζ . The values of δRPC and σ2ε were kept as constant. Each
factor takes two values, the first level values are the UCM estimates (Table6.2). The second level values of UCM regressors are obtained by multiplyingthe estimate values by 0.8 (Table 6.3). The multiplicator is set to 0.8 withthe purpose of generating sample paths of response variable that are withina reasonable range and avoid generating the sample paths with close values.The second level value of trend variance, σ2
ζ was selected as the result of theapproximate calibration with respect to the real data. A full factorial designwas built with the 26 combinations of the 2 levels of six parameters. Thereare no replications.
123 6.4. Experimental design: estimation and resultsS
Pa
SV
bP
aram
eter
esti
mat
esF
itst
atis
tics
η PARSER
η CONALC
η SUSP
η DLAB
η COMTOT
λρ1
ρ2
Log
-li.
R2 1c
R2 2d
1O
-0.6
2-0
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931
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9A
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30.
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63.1
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932
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26
10A
D-0
.60
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30.
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17-2
48.8
490.
934
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29
11A
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.60
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4-0
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0.81
0.20
-0.3
20.
300.
17-3
69.6
590.
926
0.9
20
12B
C-0
.63
-0.3
1-0
.16
0.81
0.28
-0.3
40.
300.
17-2
76.4
330.
927
0.9
21
13B
D-0
.63
-0.3
1-0
.19
0.64
0.28
-0.3
40.
300.
16-2
62.1
160.
930
0.9
24
14B
E-0
.62
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1-0
.19
0.81
0.20
-0.3
30.
300.
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58.4
850.
930
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25
15C
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0.63
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30.
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933
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925
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19
18A
F-0
.08
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0-0
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0.78
0.63
0.13
0.16
0.25
-311
.107
0.92
60.9
20
19B
F-0
.10
-0.1
7-0
.11
0.78
0.63
0.16
0.16
0.25
-296
.790
0.92
90.9
23
20C
F-0
.10
-0.2
0-0
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0.78
0.63
0.11
0.16
0.25
-293
.157
0.93
00.9
24
21D
F-0
.10
-0.2
0-0
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0.61
0.63
0.15
0.16
0.25
-185
.623
0.93
30.9
28
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 124
SPa
SV
bP
aram
eter
esti
mat
esF
itst
atis
tics
η PARSER
η CONALC
η SUSP
η DLAB
η COMTOT
λρ1
ρ2
Log
-li.
R2 1c
R2 2d
22E
F-0
.10
-0.2
0-0
.11
0.78
0.54
0.13
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-278
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0.93
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23A
BC
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60.
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0.92
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33A
BF
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780.
630.
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39B
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767
0.7
47
125 6.4. Experimental design: estimation and resultsS
Pa
SV
bP
aram
eter
esti
mat
esF
itst
atis
tics
η PARSER
η CONALC
η SUSP
η DLAB
η COMTOT
λρ1
ρ2
Log
-li.
R2 1c
R2 2d
43A
BC
D-0
.61
-0.3
1-0
.16
0.63
0.28
-0.3
60.
300.
17-4
22.4
740.
736
0.7
14
44A
BC
E-0
.60
-0.3
1-0
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0.81
0.20
-0.3
50.
300.
17-3
29.1
130.
727
0.7
05
45B
CD
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-0.3
50.
300.
1731
4.84
70.
744
0.7
22
46A
CD
E-0
.60
-0.3
4-0
.16
0.63
0.20
-0.3
30.
300.
17-3
11.3
920.
750
0.7
29
47A
BC
F-0
.08
-0.1
7-0
.08
0.78
0.63
0.15
0.16
0.25
-297
.127
0.76
50.7
46
48A
BD
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7-0
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0.61
0.63
0.19
0.16
0.25
-203
.763
0.76
10.7
41
49A
BE
F-0
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-0.1
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0.78
0.54
0.17
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0.72
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06
50A
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-0.2
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0.60
0.63
0.14
0.16
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0.71
80.6
95
51A
DE
F-0
.08
-0.2
0-0
.11
0.61
0.54
0.16
0.16
0.25
-349
.525
0.73
60.7
14
52A
CE
F-0
.08
-0.2
0-0
.08
0.78
0.55
0.12
0.16
0.25
-346
.072
0.74
20.7
20
53B
CD
F-0
.10
-0.1
7-0
.08
0.61
0.63
0.17
0.16
0.25
-238
.443
0.75
30.7
33
54B
CE
F-0
.10
-0.1
7-0
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0.78
0.55
0.15
0.16
0.25
-331
.808
0.75
80.7
38
55B
DE
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359.
178
0.71
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94
56C
DE
F-0
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-0.2
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0.25
-344
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0.73
50.7
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57A
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0.7
05
58A
BC
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630.
20-0
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0.75
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30
59A
BC
DF
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8-0
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-0.0
80.
610.
630.
170.
160.
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93.8
560.
708
0.6
84
60A
BC
EF
-0.0
8-0
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-0.0
80.
780.
550.
160.
160.
25-3
79.5
900.
726
0.7
04
61B
CD
EF
-0.1
0-0
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80.
610.
540.
180.
160.
25-2
81.6
110.
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0.6
93
62A
CD
EF
-0.0
8-0
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-0.0
80.
610.
540.
140.
160.
25-2
68.5
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743
0.7
22
63A
BD
EF
-0.0
8-0
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-0.1
10.
610.
540.
200.
160.
25-2
68.5
080.
743
0.7
22
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 126
SPa
SV
bP
aram
eter
esti
mat
esF
itst
atis
tics
η PARSER
η CONALC
η SUSP
η DLAB
η COMTOT
λρ1
ρ2
Log
-li.
R2 1c
R2 2d
64A
BC
DE
F-0
.08
-0.1
7-0
.08
0.61
0.54
0.18
0.16
0.25
-316
.290
0.70
70.6
83
Table
6.7
:D
RA
Ges
tim
atio
n.
aSample
path
sgenera
ted
by
UCM
.
bSourceofvariation.
cR
2 1−
Pse
udo-R
2.
dR
2 2−
Adju
sted
pse
udo-R
2.
127 6.4. Experimental design: estimation and results
6.4.2 Generating UCM samples
The 26 UCM samples were generated using the Matlab package. As mentionedabove, since there are no replications, a single observation was generated foreach combination, thus resulting 26 = 64 sample paths (realization- timeseries) (Figure 6.3).
As mentioned earlier each UCM sample path was generated using equa-tions (3.12)-(3.14), with the I and II level values of parameters, δPARSER ={−0.24,−0.19}, δCONALC = {−0.38,−0.30}, δSUSP = {−0.31,−0.24}, δDLAB ={2.03, 1.62}, δCOMTOT = {0.97, 0.77} and σ2
ζ = {0.020, 0.025} (Table 6.3).The parameters δRPC and σ2
ε were kept constant. The simulation was carriedout with the estimated value of σ2
ε = 0.05 (see Section 6.3.2). The estimateof δRPC was defined to be equal to, δRPC = −0.15, based on the results of theprevious work on this variable (see Dadashova et al. (2014)).
6.4.3 Estimating DRAG models using the UCM sam-
ples
One layer DRAG models (Liem et al. , 2008), accident frequency, were builtusing the TRIO software. The number of independent variables included inthe models are the same as the simulated UCM (equation (6.2)-(6.4)), i.e.COMTOT , CONALC, SUSP , PARSER, DLAB and RPC. Taking theindependent variables into account, the BCT structure and the autoregres-sive order of error term are determined next. The optimization is carried outthrough the Davidon-Fletcher (DFP) algorithm, which allows for the max-imization of all the parameters simultaneously. It was found out that withthe same BCT value for both dependent and independent variables and ARstructure of order, l = 2, DRAG models achieved the best goodness of fit mea-sures, i.e. pseudo-R2 measures, log likelihood and conditional t−statistics ofparameters (see Appendix VI). The model estimation was carried out for 64time series, with each having 120 simulated observations.
The results of the DRAG modeling show that DRAG models do notseem to suffer from the absence of a specific trend term, i.e., the three classesof parameters: regression coefficients (estimates and elasticity), BCT coeffi-cients and autoregressive parameters provide a reasonable explanation of thedata generating process as quantified by pseudo-R2 and t- statistic signifi-cance tests for the independent variables. More precisely, the pseudo-R2 for64 models range around 70% to 90%, the BCT, AR coefficients and regres-sor estimates are statistically significant. Since the DRAG model regressors
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 128
6.3.a
6.3.b
Fig. 6.3. Generated samples
6.3.a) σ2ζ = 0.020; 6.3.b) σ2ζ = 0.025.
129 6.4. Experimental design: estimation and results
are explained by the elasticities (equation 3.43) rather than by the regres-sor estimates themselves, the parameters of interest of DRAG model are theelasticities of 5 regressors: ηPARSER, ηCONALC , ηSUSP , ηDLAB, and ηCOMTOT ;BCT coefficient, λ, and two autoregressive parameters, ρ1 and ρ2, thus sum-ming up to 8 response variables. The results of DRAG estimation togetherwith the goodness of fit statistics are reported in Table 6.7.
6.4.4 ANOVA
The ANOVAs (Montgomery , 2000, Pena , 1987) of the eight responses werecarried out to quantify on average the individual (main effects) and joint (in-teractions) effects of the inputs (UCM parameters) on the outputs (DRAGestimates). Each of the eight ANOVA’s corresponds to a different DRAGparameter, thus each of the eight variance analysis were carried out inde-pendently. The relative importance of main effect or interaction is givenindistinctly by its factor estimates, sum of squares or F -statistics. Here wehave shown interactions up to fourth order, and used sums of squares of 5th
and 6th order as residual variance. It should be pointed out that, given thespecial nature of computer experiments this choice is slightly arbitrary andof not much relevance. The significance of the factors is based on the sumsof squares, thus the higher order interactions that are not significant can beneglected, since they do not contribute any additional value to the results ofthe experimental design study.
6.4.5 Results of the experimental design-ANOVA
The most significant effects for each of the eight responses are reported in Ta-ble 6.8 (see Appendix VII). Reviewing the results we can observe the followingsimilar behavior among them:
1. The corresponding UCM variable coefficient (elasticity) is a very signif-icant factor for all of the regressor elasticities.
2. The trend component variance, σ2ζt
of UCM is the one of the two mostsignificant factors for all of the parameters.
Item (1) implies that, the elasticities capture partially the true effect ofthe given variable, while (2) shows that the stochastic trend component (F ),if present in the real data, will be captured mainly by the regressor elasticities(strong factor effect).
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 130
Table 6.8: Significant main effects for DRAG parameters.
DRAG UCM Effect Sum Mean D.F. F test Pr(>F) Percentage
Parameter Factors Estimates Squares Square Contribution
ηPARSER
F 0.5230 4. 3759 4. 3759 1 7. 19E+05 < 2. 20E-16 99. 822
A 0.0216 0. 0075 0. 0075 1 1. 23E+03 4. 03E-09 0. 171
ηCONALC
F 0.1399 0. 31332 0. 31332 1 16734. 3095 4. 35E-13 94. 543
B 0.0326 0. 017096 0. 017096 1 913. 0677 1. 12E-08 5. 159
ηSUSP
F 0.0274 0. 099146 0. 099146 1 6345361 < 2. 20E-16 89. 097
C 0.0787 0. 012018 0. 012018 1 769129 2. 20E-16 10. 800
ηDLAB
D -0.1757 0. 49386 0. 49386 1 2. 13E+06 < 2. 20E-16 97. 251
F -0.0292 0. 01363 0. 01363 1 5. 87E+04 5. 38E-15 2. 684
ηCOMTOT
F 0.3433 1. 88582 1. 88582 1 19405. 6728 2. 59E-13 94. 331
E -0.0818 0. 10709 0. 10709 1 1102. 0183 5. 83E-09 5. 357
ρ1
F -0.1464 0. 34325 0. 34325 1 1. 03E+07 < 2. 20E-16 99. 997
ρ2
F 0.3065 0. 103765 0. 103765 1 6. 55E+05 < 2. 20E-16 99. 897
λ
F 0.4886 3. 7893 3. 7893 1 3. 25E+05 < 2. 20E-16 99. 491
For example, the standard expression of the model for the 2k design inthe case of the DRAG parameter ηDLAB (DRAG model elasticity of variableDLAB), only including significant main effects and interactions (p−value<0.0001) is as follows:
ηDLAB = c+D
2XD +
F
2XF +
DF
2XDXF +
C
2XC+
+B
2XB +
EF
2XEXF +
CE
2XCXE (6.5)
where c is the average response, D, F , etc. are the effect estimates and XD,XF , etc. are the contrast coefficients taking values (−1) and (+1) describingfactor Levels I and II respectively. For example, equation (6.6) correspondsto the (-1) level of all factors included as significant in the model:
ηDLAB = 0.7074 +−0.1757
2(−1) +
−0.0292
2(−1) +
0.0013
2(−1)(−1)+
+−0.0023
2(−1) +
0.0019
2(−1) +
0.0157
2(−1)(−1)+
+0.0003
2(−1)(−1) = 0.8173 (6.6)
131 6.4. Experimental design: estimation and results
Fig. 6.4. Interaction plot between D and F , for the DRAG parameter ηDLAB .
In accordance with the standard parameterization of 2k designs, whenfactor D changes its value from Level I to Level II (i.e., from 2.03 to 1.62in Table 6.3) the average response decreases by 0.1757. This main effect isof course an average over the remaining factors. However, the presence ofsignificant interactions is also worth interpreting. For example, a significantinteraction between D and F for this response (ηDLAB), indicates that theeffect of D on the response depends on the value taken by F (Figure 6.4). Ascan be seen in Table 6.12, this interaction is the most significant factor aftermain effects D and F .
In Table 6.8, one can observe that for those responses that 1) are relatedto the effect of the variables on the time series, i.e, PARSER, CONALC,SUSP , and COMTOT ; and 2) the main effect of trend is positive, then thetrend is the most significant factor and accounts for 99%, 94%, 89%, and94% of total variability in PARSER, CONALC, SUSP , and COMTOTrespectively. On the other hand, for the ηDLAB, the effect of trend is negativeand the trend is the second most significant main effect, accounting for 2.68%of the total response variability. The effect of the corresponding UCM factor
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 132
for DLAB, D, accounts for 97.25% of variability in this case. The resultsin general show that the sensitivity of elasticity estimators to the changes instochastic trend variance is significantly high.
Thus, the regressor elasticities of the DRAG models do not only repre-sent the effect of the independent variables but also pick up the trend variancepresent in the data. The autoregressive error structure of the DRAG modelcan partially pick up the effect of the trend, i.e. the stochastic trend presentin the data is picked up both by regressors and the autoregressive error.
6.5 Summary and discussions
It is true that the results of the estimation can differ depending on the typeof model used. However the question is how significant is this difference? Ananalytical quantification of the differences between the two types of models,e.g. explanatory and descriptive models is an almost unfeasible process. Thischapter tries to answer this question using existing statistical tools, MonteCarlo simulation, experimental design and ANOVA. The main idea is how agiven model can be interpreted through another. This approach shows howthe parameters of two different classes of models: DRAG and UCM, capturethe effect of an unobserved stochastic component that can be present in thedata.
As it was indicated the final results of experimental design using thesimulated data show that:
1. The regressor elasticities of DRAG model are capturing the change inthe corresponding UCM elasticities as it was initially assumed.
2. The stochastic trend component of UCM was not only captured by theautoregressive parameters of the DRAG model but also by the regressorelasticity parameters.
The results reveal some interesting aspects on that could be overlookedduring the model selection process. This research work shows how a misspec-ification of the stochastic component present in true data generating processcan lead to biased estimates and thus to erroneous interpretation. Also, thatthe stochastic trend component has the most significant effect on the re-gression elasticity estimates of the model used for estimation. Although theregressor estimates capture the true effect of the variables, they are moresensitive to changes in the stochastic trend component present in the truedata.
133 6.5. Summary and discussions
The findings show that, although the goodness of fit measures can pro-vide reliable information, the stochastic component in the data should behandled and adjusted properly in order to provide unbiased estimates. Thisis a very important issue specially in case of road accident modelling sinceone of the main purposes of any road accident modelling is to identify thefactors that have significant impact on accidents. One way of prior fitting isdifferencing the data before estimation. For this purpose the right integrationorder of the data should be determined. However the integration order canbe affected when introducing the explanatory factors, specially if there is alagged relationship between output and input. Future research will be carriedout considering these findings and problems that can be encountered duringthe modelling process.
Chapter 6. Simulation experiment based model comparison methodologywith application to road accident models 134
Part III
Conclusions
135
Conclusions
This thesis has been developed with the purpose of studying the road safetyfactors in Spain during the period 2000-2011, and analyzing the impact ofi.a., policy measures and economic factors. The findings, main contributionsand future work in this direction are presented below.
Contribution
The thesis has both empirical and theoretical contributions to the road safetyliterature that can be presented in several blocks:
1. The first contribution of the thesis is the comparison of two macro mod-els: demand for road use, accidents and their gravity, and unobservedcomponents model. Although there are numerous articles written on theperformance of the models, however a systematic comparison of thesemodels and their ability to interpret and predict the traffic accidentmeasures has not been addressed previously. The study was carriedout using the database on frequency and severity of van-involved roadaccidents in Spain during 2000-2011 and has the following findings andcontributions:
1.1 Structural explanatory models (DRAG type models) prove to be quiteadjustable to the traffic data and provide better predictions than struc-tural descriptive models (unobserved components model). But UC mod-els capture the seasonality in the predicted data more efficiently, mainlydue to the fact that the terms such as trend and seasonality are sep-arately modeled in UCM. The goodness of fit of the model shows it-self strongly in prediction accuracy. In the descriptive models a bettergoodness of fit is achieved when the variables included in the modelare statistically significant. This means that the variables with highest
137
138
p-values should be eliminated (stepwise elimination). The advantage ofthis is that, since stepwise elimination is employed during the model se-lection process, we obtain a rather small set of candidate models, amongwhich it is quite trivial to choose the best one. This however is not veryefficient if the analyst intends to assess the effect of several variables.
1.2 Unlike the descriptive models the explanatory models are very parsi-monious and thus the number of candidate models can be very large.Although this provides a better prediction accuracy compared to the de-scriptive models, selecting the most appropriate model can be a lengthyprocess, since the explanatory models employed in road safety analysisnot only differ in the explanatory variables but also include differentparameters. The examples include the variable transformation param-eter or the parameters associated with the error structure of the model,since it has been shown in different studies that the error term of themodels employed in road safety should not be considered as Gaussian.
1.4 The explanatory models can provide better predictions and prove to bevery useful tool for modeling traffic accident data, allowing to evaluatethe effect of different factors on road safety indicators. These modelshowever lack the ability to capture the unobserved components suchas trend and seasonality that might be present in accident data. Theresults of the experimental design prove this point and it was shown thata term like the stochastic trend which is present in data is captured bythe parameters such as elasticities or even the parameters associatedwith the error term. However they do succeed when estimating the realeffect of the respective factor.
1.5 The results suggest that the fatality measures, number of fatal accidentsand the number of deaths in van-involved accidents are influenced by thesame factors, within each type of model (DRAG or UCM). According toDRAG estimation, all of the explanatory variables categories are presentin models for both indicators. The most significant factors in case ofDRAG estimation belong to the following categories: exposure, driverbehavior surveillance, economic factors and legislative measures. UCMestimation, however, includes relatively few significant factors. Thefactors that are common to these two indicators belong to the followingcategories: exposure (COMTOT), economic activity (PARSER), driversurveillance (CONALC) and calendar effect (DLAB and SDF). It canbe observed that, when the same factor appears both in DRAG and
139
UCM, the elasticity estimates are nearly the same, with the exceptionof DLAB.
1.6 Injury- related measures, number of accidents with injuries and num-ber of injured victims in van-involved accidents are affected by the samefactors, within each methodology (DRAG and UCM). Moreover, by an-alyzing the results, it can be concluded that the factors are almostcommon for both methodologies. The most significant variables belongto the following categories: driver behavior surveillance, economic fac-tors and road infrastructure. The variables with significant estimatesgenerally have similar elasticities for both methodologies.
2. The second most important contribution of the thesis is the model se-lection methodology proposed for the macro analysis of road safety in-dicators. Analyzing every possible combination of the parameters andexplanatory factors can be a very lengthy and unfeasible process. Thisstudy was carried out with the purpose of providing an efficient way ofmodel selection. The estimation is carried out within Bayesian frame-work and a parsimonious time series model is used. The study wascarried out using the data on total fatal accidents in Spain for the pe-riod of 2000-2011. The most important findings and contributions ofthe study are:
2.1 The methodology is applied to a parsimonious model. The results of theBayesian estimation do not contradict the results obtained in previousempirical studies on road safety analysis. This is shown in goodness offit measures, prediction accuracy and interpretability of the results.
2.2 The comparison with a fully specified DR model shows that the resultsof the model selection procedure, as far as the estimation and predictionare concerned, are valid.
2.3 The results of variable selection show that inputs such as economicfactors, and legislative and surveillance measures have played significantroles in decreasing the number of fatal accidents during the last decade.These findings agree with the previous assumptions that the changes inthis road safety indicator could be attributed to the improving policymeasures and changing economic situation in the country.
3. The other major contribution of the thesis is the simulation-based method-ology for the model comparison. The main contributions and findingsof this study are:
140
3.1 It is true that the estimation results can differ depending on the typeof model used. However, the question is how significant is this differ-ence? An analytical quantification of the differences between two typesof models, e.g. explanatory and descriptive models, is an almost unfea-sible process and requires excessive mathematical computations. Thisstudy tries to answer this question using Monte Carlo simulation, ex-perimental design and ANOVA. The main idea is how a certain modelcan be interpreted through another model.
3.2 The results reveal some interesting aspects on traffic accident researchwhich can be overlooked during the model choice process. This studyshows how a misspecification of the stochastic component present inthe true data generating process, can lead to biased estimates and thusto different interpretation. The results show that the stochastic trendcomponent has the most significant effect on the regression elasticityestimates of the model used for estimation. Although the regressorestimates capture the true effect of the variables, these estimates aremore sensitive to the stochastic trend component present in the data.
3.3 The findings show that although the goodness of fit measures can pro-vide a reliable information the stochastic component in the data shouldbe handled properly in order to provide unbiased estimates. Speciallybearing in mind that the ultimate goal of any road accident model is toidentify the factors that have significant impact on the traffic accidentsthis point has to be dealt with carefully.
Future work
The future empirical and theoretical research will be undertaken followingthe main achievements and contributions of the thesis. The possible lines ofthe future work include:
• Improvement of the TIM selection methodology by including more inputvariables rather than only two inputs. Inclusion of only two inputs cansometimes result in selection of non-optimal variable if the variables arehighly correlated. In order to avoid this problem the variable selectionmethodology, TIM, will be extended to include three or four variables.
• Improvement of the model selection methodology by building sophis-ticated models, i.e. higher autoregressive error structure, more power
141
transformation values, etc. This will result in a larger number of modelsto be estimated but will increase the probability of defining the mostlikely model. Given that this process is time consuming and needs morecomputational means the colloboration with the Supercomputing andVisualization Center of Madrid (CeSViMa) and the Spanish Supercom-puting Network (RES) for this purpose is already under way.
• Introducing unobserved components to the basic structural explanatorymodel structure, e.g. SE models with a seasonal autoregressive errorinstead of regular autoregressive errors. Considering that the accidentdata is monthly, it is expected that the seasonality will be present formost of the road safety indicators. The main challenge will be selectionof the right priors for the AR parameters.
• Treatment of stochastic trend component present in the true data byfiltering out the stochastic component. In this case the dependent vari-ables with a stochastic trend will be differenced before the modellingprocess. As it was found out during the experimental design study ifnot handled properly the presence of the stochastic trend could resultin biased estimates and thus in misinterpretation of the variable effects.This research work could be carried out in two directions: 1. theo-retical analysis through simulation study; 2. empirical analysis withthe observed data. The main purpose of the former research will beto test if the prior adjustment of data through differencing can resultin unbiased estimates. For this purpose the new data samples withthe stochastic trend will be generated through SE. The generated datawill be differenced and the UCM estimation will be carried out bothfor the data with the stochastic trend and the differenced data. Theinterpretation of one model through another will be carried out usingvariance analysis as before. Its expected that in case of the differenceddata the effect of the trend variance on the variable estimates shouldbe smaller or non-existent. The second study will consist of the modelselection procedure for the data with a stochastic component. In thisstudy the original data with the stochastic trend will be differenced andthe model selection procedure will be applied to both the original andthe differenced data.
• Application of the methodologies developed in this thesis to differentindicators depicting the road accident frequency and severity in othertypes of vehicles, e.g. trucks, motorcycles, etc. This will help to definehow different factors may affect to different road safety indicators.
142
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156
Appendix I: DRAG Estimation
=========================================================================================
I. ELASTICITY S(y) (EP) TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1
VARIANT = ACCMOR3 MORHER2 MUER2 HERGRA2
(COND. T-STATISTIC) VERSION = 109 74 134 95
DEP.VAR. = accmor morher muer hergra
=========================================================================================
--------------------------
FLEET CHARACTERISTICS
--------------------------
PRQAB -.721 -.406
(-1.92) (-1.19)
LAM 1 LAM 1
-----
CLIMATOLOGY
-----
DNIE .151 .006 .175
---- (2.47) (.56) (3.39)
SLNV -.162 -.225
---- (-1.75) (-3.02)
TEMP -.002
(-.02)
LAM 1
----------
LABOR
----------
DLAB .670 1.911 .380
(1.09) (1.88) (1.20)
LAM 1 LAM 1 LAM 1
SDF .017 .489
(.18) (1.29)
LAM 1 LAM 1
=========================================================================================
I. ELASTICITY S(y) (EP) TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1
VARIANT = ACCMOR3 MORHER2 MUER2 HERGRA2
(COND. T-STATISTIC) VERSION = 109 74 134 95
DEP.VAR. = accmor morher muer hergra
=========================================================================================
---
ROAD INFRASTRUCTURE
---
LONRAC -.375
(-.83)
LAM 1
LONRED -1.485 -1.064 -2.192
(-1.62) (-3.27) (-2.25)
LAM 1 LAM 1 LAM 2
CONST -.866 -1.638
(-2.79) (-3.91)
LAM 1 LAM 1
-----
LEGISLATION
-----
PPS -.100 -.294
=== (-.91) (-2.30)
RPC -.152 -.333 -.111
=== (-2.47) (-4.41) (-1.02)
RUIDO -.008
(-.33)
LAM 1
-------
ECONOMIC FACTORS
-------
IPI .315
(.73)
LAM 1
INDVEN .129 .127
(1.83) (1.18)
LAM 1 LAM 1
INDCOM .612
(1.17)
LAM 1
PRCOM -.044 -.095 -.289
(-.11) (-.54) (-.61)
LAM 1 LAM 1 LAM 1
INDACT 2.114 1.856
(.75) (.65)
LAM 1 LAM 1
PARO -.510 -.338
(-1.99) (-.87)
LAM 1 LAM 1
=========================================================================================
I. ELASTICITY S(y) (EP) TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1
VARIANT = ACCMOR3 MORHER2 MUER2 HERGRA2
(COND. T-STATISTIC) VERSION = 109 74 134 95
DEP.VAR. = accmor morher muer hergra
=========================================================================================
-----------------------
SUREILLANCE
-----------------------
CONALC -.172 -.051 -.067 -.118
(-1.09) (-.72) (-.36) (-1.04)
LAM 1 LAM 1 LAM 1 LAM 1
PRADAR -.963
(-2.42)
LAM 1
RADAR -.190 -.025 -.530 -.087
(-1.16) (-.38) (-2.44) (-.98)
LAM 1 LAM 1 LAM 1 LAM 1
PRLSUSP -.262 -.454
(-1.11) (-2.11)
LAM 1 LAM 1
SUSP -.117 -.302
(-1.06) (-1.86)
LAM 1 LAM 1
-----------
EXPOSURE
-----------
PRGFUR 2.290 3.813
(1.50) (2.19)
LAM 1 LAM 1
CNSOIL .772 .145
(1.26) (.16)
LAM 1 LAM 1
COMTOT 1.195 1.137
(4.44) (3.65)
LAM 1 LAM 1
VKM .382
(1.20)
LAM 1
REGRESSION CONSTANT CONSTANT - - - -
(-1.34) (3.02) (-.89) (1.25)
=========================================================================================
II. PARAMETERS TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1
VARIANT = ACCMOR3 MORHER2 MUER2 HERGRA2
(COND. T-STATISTIC) VERSION = 109 74 134 95
DEP.VAR. = accmor morher muer hergra
=========================================================================================
------------------------------------------------------------------
BOX-COX TRANSFORMATIONS: UNCOND: [T-STATISTIC=0] / [T-STATISTIC=1]
------------------------------------------------------------------
LAMBDA(Y) hergra -.019
[-.03]
[-1.65]
LAMBDA(Y) - GROUP 1 LAM 1 .168 .067 -.084
[.38] [.15] [-.20]
[-1.86] [-2.12] [-2.54]
LAMBDA(X) - GROUP 1 LAM 1 .168 .067 -.084 -.373
[.38] [.15] [-.20] [-.35]
[-1.86] [-2.12] [-2.54] [-1.28]
LAMBDA(X) - GROUP 2 LAM 2 -.196
[-.06]
[-.38]
=========================================================================================
II. PARAMETERS TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1
VARIANT = ACCMOR3 MORHER2 MUER2 HERGRA2
(COND. T-STATISTIC) VERSION = 109 74 134 95
DEP.VAR. = accmor morher muer hergra
=========================================================================================
---------------
AUTOCORRELATION
---------------
ORDER 1 RHO 1 -.324 -.485 .103
(-2.46) (-3.16) (.81)
ORDER 2 RHO 2 -.275 .058 -.315 -.020
(-2.30) (.48) (-2.19) (-.19)
ORDER 3 RHO 3 -.128 .061 -.107 .062
(-.86) (.48) (-.76) (.46)
ORDER 4 RHO 4 -.248 .193 -.210 .150
(-1.84) (1.38) (-1.56) (1.17)
ORDER 5 RHO 5 .117 .042
(.98) (.39)
ORDER 6 RHO 6 .037 .198
(.26) (1.89)
ORDER 7 RHO 7 -.043 -.076
(-.36) (-.65)
ORDER 8 RHO 8 .138 .189
(1.12) (1.52)
ORDER 9 RHO 9 -.095 -.206
(-.68) (-1.86)
ORDER 10 RHO 10 -.268 -.261
(-2.43) (-2.48)
ORDER 11 RHO 11 -.035 -.097
(-.29) (-.84)
ORDER 12 RHO 12 -.020 .000
(-.16) (.00)
ORDER 14 RHO 14 -.186 -.206
(-1.36) (-1.76)
=========================================================================================
III.GENERAL STATISTICS TYPE = LEVEL-1 LEVEL-1 LEVEL-1 LEVEL-1
VARIANT = ACCMOR3 MORHER2 MUER2 HERGRA2
VERSION = 109 74 134 95
DEP.VAR. = accmor morher muer hergra
=========================================================================================
LOG-LIKELIHOOD -309.861 -368.933 -333.696 -409.788
PSEUDO-R2 : - (E) .578 .785 .576 .729
- (L) .595 .795 .625 .750
- (E) ADJUSTED FOR D.F. .463 .714 .440 .630
- (L) ADJUSTED FOR D.F. .486 .728 .505 .658
AVERAGE PROBABILITY (Y=LIMIT OBSERV.) .000 .000 .000 .000
SAMPLE : - NUMBER OF OBSERVATIONS 104 94 104 94
- FIRST OBSERVATION 5 15 5 15
- LAST OBSERVATION 108 108 108 108
NUMBER OF ESTIMATED PARAMETERS :
- FIXED PART :
. BETAS 18 11 20 11
. BOX-COX 1 1 2 2
. ASSOCIATED DUMMIES 0 0 0 0
- AUTOCORRELATION 4 12 4 13
- HETEROSKEDASTICITY :
. DELTAS 0 0 0 0
. BOX-COX 0 0 0 0
. ASSOCIATED DUMMIES 0 0 0 0
=========================================================================================
Appendix II: UCM Estimation
The SAS System
The UCM Procedure
Input Data Set
Name UCMFURGO.ACCMOR
Time ID Variable DATE
Estimation Span Summary
First Last Standard
Variable Type Obs Obs NObs NMiss Min Max Mean Deviation
ACCMOR Dependent JAN2000 DEC2009 120 0 2.48491 4.02535 3.36946 0.28973
x24 Predictor JAN2000 DEC2009 120 0 8.86954 9.82831 9.44891 0.25055
X36 Predictor JAN2000 DEC2009 120 0 7.51833 7.98036 7.79684 0.09299
x25 Predictor JAN2000 DEC2009 120 0 2.89037 3.13549 3.04092 0.05751
X38 Predictor JAN2000 DEC2009 120 0 8.00000 13.00000 9.48333 1.27010
CONALC Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.25503 0.44519
x7 Predictor JAN2000 DEC2009 120 0 13.88097 14.62248 14.09828 0.17516
Forecast Span Summary
First Last Standard
Variable Type Obs Obs NObs NMiss Min Max Mean Deviation
ACCMOR Dependent JAN2000 DEC2008 108 0 2.83321 4.02535 3.42113 0.24571
x24 Predictor JAN2000 DEC2009 120 0 8.86954 9.82831 9.44891 0.25055
X36 Predictor JAN2000 DEC2009 120 0 7.51833 7.98036 7.79684 0.09299
x25 Predictor JAN2000 DEC2009 120 0 2.89037 3.13549 3.04092 0.05751
X38 Predictor JAN2000 DEC2009 120 0 8.00000 13.00000 9.48333 1.27010
CONALC Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.25503 0.44519
x7 Predictor JAN2000 DEC2009 120 0 13.88097 14.62248 14.09828 0.17516
Preliminary Estimates of the Free Parameters
Component Parameter Estimate
Irregular Error Variance 0.02467
Likelihood Based Fit Statistics
Statistic Value
Full Log Likelihood 24.806
Diffuse Part of Log Likelihood 6.9992
Non-Missing Observations Used 120
Estimated Parameters 1
Initialized Diffuse State Elements 6
Normalized Residual Sum of Squares 114
The SAS System
The UCM Procedure
Likelihood Based Fit Statistics
Statistic Value
AIC (smaller is better) -47.61
BIC (smaller is better) -44.88
AICC (smaller is better) -47.58
HQIC (smaller is better) -46.5
CAIC (smaller is better) -43.88
Final Estimates of the Free Parameters
Approx Approx
Component Parameter Estimate Std Error t Value Pr > |t|
Irregular Error Variance 0.03247 0.0043003 7.55 <.0001
SUSP Coefficient -0.31080 0.11805 -2.63 0.0085
COMTOT Coefficient 0.97622 0.22713 4.30 <.0001
DLAB Coefficient 2.03588 0.47335 4.30 <.0001
SDF Coefficient 0.07559 0.02179 3.47 0.0005
CONALC Coefficient -0.38317 0.05612 -6.83 <.0001
PARSER Coefficient -0.24949 0.10274 -2.43 0.0152
Fit Statistics Based on Residuals
Mean Squared Error 0.15874
Root Mean Squared Error 0.39842
Mean Absolute Percentage Error 5.66279
Maximum Percent Error 91.67443
R-Square -0.85276
Adjusted R-Square -0.85276
Random Walk R-Square -0.72931
Amemiya’s Adjusted R-Square -0.88555
Number of non-missing residuals used for
computing the fit statistics = 114
The UCM Procedure
Significance Analysis of Components
(Based on the Final State)
Component DF Chi-Square Pr > ChiSq
Irregular 1 11.40 0.0007
Outlier Summary
Standard
Obs DATE Break Type Estimate Error Chi-Square DF Pr > ChiSq
28 APR2002 Additive Outlier -0.57946 0.1826786 10.06 1 0.0015
62 FEB2005 Additive Outlier 0.52371 0.1858743 7.94 1 0.0048
Forecasts for Variable accmorlog
Standard
Obs DATE Forecast Error 95% Confidence Limits
109 JAN2009 2.845549 0.20159 2.450449 3.240649
110 FEB2009 2.795925 0.20825 2.387761 3.204090
111 MAR2009 3.035446 0.19257 2.658023 3.412869
112 APR2009 2.946081 0.19667 2.560614 3.331547
113 MAY2009 2.996205 0.19336 2.617219 3.375190
114 JUN2009 3.010762 0.19570 2.627203 3.394321
115 JUL2009 3.194268 0.18940 2.823046 3.565490
116 AUG2009 2.981562 0.19963 2.590295 3.372829
117 SEP2009 2.959570 0.20199 2.563671 3.355468
118 OCT2009 3.028555 0.19340 2.649500 3.407609
119 NOV2009 2.864803 0.20304 2.466857 3.262748
120 DEC2009 2.989988 0.19893 2.600099 3.379878
Post Sample Predictions for accmorlog
Sum of Sum of
Prediction Squared Absolute
Obs DATE Actual Forecast Error Errors Errors
109 JAN2009 2.708050201 2.845549196 -0.13749899 0.018905973 0.137498995
110 FEB2009 2.708050201 2.795925238 -0.08787504 0.026627996 0.225374031
111 MAR2009 3.258096538 3.035446363 0.222650175 0.076201096 0.448024206
112 APR2009 2.48490665 2.94608071 -0.46117406 0.288882609 0.909198266
113 MAY2009 3.091042453 2.996204641 0.094837813 0.29787682 1.004036078
114 JUN2009 2.890371758 3.010762128 -0.12039037 0.312370661 1.124426448
115 JUL2009 3.044522438 3.194267706 -0.14974527 0.334794307 1.274171717
116 AUG2009 3.218875825 2.981561909 0.237313916 0.391112201 1.511485633
117 SEP2009 2.833213344 2.959569572 -0.12635623 0.407078098 1.63784186
The SAS System 15:07 Wednesday, October 12, 2011
The UCM Procedure
Post Sample Predictions for accmorlog
Sum of Sum of
Prediction Squared Absolute
Obs DATE Actual Forecast Error Errors Errors
118 OCT2009 3.135494216 3.028554665 0.106939551 0.418514165 1.744781411
119 NOV2009 2.708050201 2.864802551 -0.15675235 0.443085464 1.901533761
120 DEC2009 2.772588722 2.989988266 -0.21739954 0.490348026 2.118933304
The SAS System
The UCM Procedure
Input Data Set
Name UCMFURGO.MORHER
Time ID Variable DATE
Estimation Span Summary
First Last Standard
Variable Type Obs Obs NObs NMiss Min Max Mean Deviation
MORHERlog Dependent JAN2000 DEC2009 120 0 4.43082 5.47646 5.09374 0.21659
x6 Predictor JAN2000 DEC2009 120 0 7.28033 7.93627 7.44128 0.15883
x2 Predictor JAN2000 DEC2009 120 0 4.44679 4.65966 4.57494 0.05713
x9 Predictor JAN2000 DEC2009 120 0 2.23544 4.11625 3.58513 0.48892
x22 Predictor JAN2000 DEC2009 120 0 8.31752 9.43382 8.98953 0.29287
x28 Predictor JAN2000 DEC2009 120 0 7.46107 7.83653 7.66493 0.13712
X36 Predictor JAN2000 DEC2009 120 0 7.51833 7.98036 7.79684 0.09299
X38 Predictor JAN2000 DEC2009 120 0 8.00000 13.00000 9.48333 1.27010
Forecast Span Summary
First Last Standard
Variable Type Obs Obs NObs NMiss Min Max Mean Deviation
MORHERlog Dependent JAN2000 DEC2008 108 0 4.63473 5.47646 5.14318 0.16164
x6 Predictor JAN2000 DEC2009 120 0 7.28033 7.93627 7.44128 0.15883
x2 Predictor JAN2000 DEC2009 120 0 4.44679 4.65966 4.57494 0.05713
x9 Predictor JAN2000 DEC2009 120 0 2.23544 4.11625 3.58513 0.48892
x22 Predictor JAN2000 DEC2009 120 0 8.31752 9.43382 8.98953 0.29287
x28 Predictor JAN2000 DEC2009 120 0 7.46107 7.83653 7.66493 0.13712
X36 Predictor JAN2000 DEC2009 120 0 7.51833 7.98036 7.79684 0.09299
X38 Predictor JAN2000 DEC2009 120 0 8.00000 13.00000 9.48333 1.27010
Fixed Parameters in the Model
Component Parameter Value
Season Error Variance 0
The SAS System
The UCM Procedure
Preliminary Estimates of the Free Parameters
Component Parameter Estimate
Irregular Error Variance 0.00572
Likelihood Based Fit Statistics
Statistic Value
Full Log Likelihood 83.078
Diffuse Part of Log Likelihood 1.6134
Non-Missing Observations Used 120
Estimated Parameters 1
Initialized Diffuse State Elements 18
Normalized Residual Sum of Squares 102
AIC (smaller is better) -164.2
BIC (smaller is better) -161.5
AICC (smaller is better) -164.1
HQIC (smaller is better) -163.1
CAIC (smaller is better) -160.5
Final Estimates of the Free Parameters
Approx Approx
Component Parameter Estimate Std Error t Value Pr > |t|
Irregular Error Variance 0.00652 0.0009131 7.14 <.0001
PARO Coefficient -0.21785 0.06804 -3.20 0.0014
INDACT Coefficient 1.63687 0.65715 2.49 0.0127
AIRBAG Coefficient -0.15995 0.04038 -3.96 <.0001
PRLSUSP Coefficient -0.16287 0.08228 -1.98 0.0478
LONRED Coefficient -1.61663 0.21602 -7.48 <.0001
COMTOT Coefficient 1.72907 0.32675 5.29 <.0001
SDF Coefficient 0.01833 0.01002 1.83 0.0675
Fit Statistics Based on Residuals
Mean Squared Error 0.01479
Root Mean Squared Error 0.12163
Mean Absolute Percentage Error 1.77218
Maximum Percent Error 7.22753
R-Square 0.69391
Number of non-missing residuals used for
computing the fit statistics = 102
The SAS System
The UCM Procedure
Fit Statistics Based on Residuals
Adjusted R-Square 0.69391
Random Walk R-Square 0.21988
Amemiya’s Adjusted R-Square 0.68785
Number of non-missing residuals used for
computing the fit statistics = 102
Significance Analysis of Components
(Based on the Final State)
Component DF Chi-Square Pr > ChiSq
Irregular 1 11.40 0.0007
Season 11 29.60 0.0018
Summary of Seasons
Season Error
Name Type Length Variance
Season TRIG 12 0
Outlier Summary
Standard
Obs DATE Break Type Estimate Error Chi-Square DF Pr > ChiSq
1 JAN2000 Additive Outlier 0.21977 0.0928905 5.60 1 0.0180
75 MAR2006 Additive Outlier 0.19197 0.08796 4.76 1 0.0291
Forecasts for Variable MORHERlog
Standard
Obs DATE Forecast Error 95% Confidence Limits
109 JAN2009 4.610003 0.09892 4.416125 4.803880
110 FEB2009 4.560335 0.10161 4.361179 4.759491
111 MAR2009 4.592575 0.10479 4.387181 4.797969
112 APR2009 4.539348 0.11205 4.319736 4.758960
113 MAY2009 4.576851 0.11445 4.352536 4.801166
114 JUN2009 4.678371 0.11541 4.452170 4.904571
115 JUL2009 4.768373 0.11642 4.540202 4.996544
116 AUG2009 4.598594 0.11563 4.371972 4.825217
117 SEP2009 4.509347 0.11562 4.282735 4.735959
118 OCT2009 4.646332 0.12262 4.406004 4.886661
The SAS System
The UCM Procedure
Forecasts for Variable MORHERlog
Standard
Obs DATE Forecast Error 95% Confidence Limits
119 NOV2009 4.498467 0.11589 4.271327 4.725608
120 DEC2009 4.502763 0.12009 4.267399 4.738128
Post Sample Predictions for MORHERlog
Sum of Sum of
Prediction Squared Absolute
Obs DATE Actual Forecast Error Errors Errors
109 JAN2009 4.574710979 4.610002608 -0.03529163 0.001245499 0.03529163
110 FEB2009 4.510859507 4.560335128 -0.04947562 0.003693336 0.084767251
111 MAR2009 4.779123493 4.592575057 0.186548436 0.038493655 0.271315688
112 APR2009 4.624972813 4.539348008 0.085624805 0.045825263 0.356940493
113 MAY2009 4.744932128 4.57685125 0.168080879 0.074076444 0.525021372
114 JUN2009 4.744932128 4.678370594 0.066561534 0.078506882 0.591582906
115 JUL2009 4.804021045 4.768372955 0.035648089 0.079777669 0.627230995
116 AUG2009 4.663439094 4.598594136 0.064844958 0.083982537 0.692075953
117 SEP2009 4.430816799 4.509346825 -0.07853003 0.090149502 0.770605979
118 OCT2009 4.663439094 4.646332317 0.017106777 0.090442144 0.787712757
119 NOV2009 4.543294782 4.498467107 0.044827675 0.092451664 0.832540432
120 DEC2009 4.700480366 4.502763248 0.197717118 0.131543723 1.03025755
The SAS System
The UCM Procedure
Input Data Set
Name UCMFURGO.MUER
Time ID Variable DATE
Estimation Span Summary
First Last Standard
Variable Type Obs Obs NObs NMiss Min Max Mean Deviation
MUERlog Dependent JAN2000 DEC2009 120 0 2.56495 4.17439 3.52044 0.31583
x7 Predictor JAN2000 DEC2009 120 0 13.88097 14.62248 14.09828 0.17516
lagx19 Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.25503 0.44519
X36 Predictor JAN2000 DEC2009 120 0 7.51833 7.98036 7.79684 0.09299
X38 Predictor JAN2000 DEC2009 120 0 8.00000 13.00000 9.48333 1.27010
x25 Predictor JAN2000 DEC2009 120 0 2.89037 3.13549 3.04092 0.05751
Forecast Span Summary
First Last Standard
Variable Type Obs Obs NObs NMiss Min Max Mean Deviation
MUERlog Dependent JAN2000 DEC2008 108 0 2.89037 4.17439 3.57575 0.26781
x7 Predictor JAN2000 DEC2009 120 0 13.88097 14.62248 14.09828 0.17516
lagx19 Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.25503 0.44519
X36 Predictor JAN2000 DEC2009 120 0 7.51833 7.98036 7.79684 0.09299
X38 Predictor JAN2000 DEC2009 120 0 8.00000 13.00000 9.48333 1.27010
x25 Predictor JAN2000 DEC2009 120 0 2.89037 3.13549 3.04092 0.05751
Preliminary Estimates of the Free Parameters
Component Parameter Estimate
Irregular Error Variance 0.03414
Likelihood Based Fit Statistics
Statistic Value
Full Log Likelihood 7.3494
Diffuse Part of Log Likelihood 3.3765
Non-Missing Observations Used 120
Estimated Parameters 1
Initialized Diffuse State Elements 5
Normalized Residual Sum of Squares 115
AIC (smaller is better) -12.7
BIC (smaller is better) -9.954
The SAS System
The UCM Procedure
Likelihood Based Fit Statistics
Statistic Value
AICC (smaller is better) -12.66
HQIC (smaller is better) -11.58
CAIC (smaller is better) -8.954
Final Estimates of the Free Parameters
Approx Approx
Component Parameter Estimate Std Error t Value Pr > |t|
Irregular Error Variance 0.04454 0.0058732 7.58 <.0001
PARSER Coefficient -0.40790 0.10770 -3.79 0.0002
CONALC Coefficient -0.45524 0.06034 -7.54 <.0001
COMTOT Coefficient 0.73966 0.23849 3.10 0.0019
SDF Coefficient 0.11664 0.02239 5.21 <.0001
DLAB Coefficient 2.62313 0.52146 5.03 <.0001
Fit Statistics Based on Residuals
Mean Squared Error 0.05981
Root Mean Squared Error 0.24455
Mean Absolute Percentage Error 5.37328
Maximum Percent Error 24.70217
R-Square 0.41437
Adjusted R-Square 0.41437
Random Walk R-Square 0.51710
Amemiya’s Adjusted R-Square 0.40410
Number of non-missing residuals used for
computing the fit statistics = 115
Significance Analysis of Components
(Based on the Final State)
Component DF Chi-Square Pr > ChiSq
Irregular 1 8.33 0.0039
The SAS System
The UCM Procedure
Outlier Summary
Standard
Obs DATE Break Type Estimate Error Chi-Square DF Pr > ChiSq
28 APR2002 Additive Outlier -0.68394 0.2138883 10.23 1 0.0014
62 FEB2005 Additive Outlier 0.67209 0.2176265 9.54 1 0.0020
Forecasts for Variable MUERlog
Standard
Obs DATE Forecast Error 95% Confidence Limits
109 JAN2009 2.998799 0.23595 2.536342 3.461256
110 FEB2009 2.874368 0.24308 2.397936 3.350799
111 MAR2009 3.192832 0.22543 2.750991 3.634674
112 APR2009 3.038320 0.22961 2.588287 3.488352
113 MAY2009 3.176286 0.22604 2.733256 3.619317
114 JUN2009 3.075144 0.22771 2.628836 3.521453
115 JUL2009 3.263243 0.22022 2.831611 3.694875
116 AUG2009 3.081502 0.23344 2.623971 3.539032
117 SEP2009 3.000561 0.23418 2.541580 3.459542
118 OCT2009 3.162418 0.22650 2.718492 3.606344
119 NOV2009 2.987256 0.23778 2.521214 3.453298
120 DEC2009 3.092564 0.23249 2.636894 3.548234
Post Sample Predictions for MUERlog
Sum of Sum of
Prediction Squared Absolute
Obs DATE Actual Forecast Error Errors Errors
109 JAN2009 2.890371758 2.998799075 -0.10842732 0.011756483 0.108427318
110 FEB2009 2.708050201 2.874367583 -0.16631738 0.039417955 0.274744699
111 MAR2009 3.33220451 3.19283247 0.13937204 0.05884252 0.414116739
112 APR2009 2.564949357 3.038319811 -0.47337045 0.282922107 0.887487193
113 MAY2009 3.218875825 3.176286347 0.042589477 0.28473597 0.930076671
114 JUN2009 2.944438979 3.075144413 -0.13070543 0.301819881 1.060782105
115 JUL2009 3.044522438 3.263243185 -0.21872075 0.349658646 1.279502852
116 AUG2009 3.555348061 3.081501689 0.473846373 0.574189031 1.753349225
117 SEP2009 3.091042453 3.000561198 0.090481256 0.582375889 1.843830481
118 OCT2009 3.258096538 3.162417762 0.095678776 0.591530317 1.939509257
119 NOV2009 2.772588722 2.987256097 -0.21466737 0.637612399 2.154176631
120 DEC2009 2.890371758 3.092563779 -0.20219202 0.678494012 2.356368652
The SAS System
The UCM Procedure
Input Data Set
Name UCMFURGO.HERGRA
Time ID Variable DATE
Estimation Span Summary
First Last Standard
Variable Type Obs Obs NObs NMiss Min Max Mean Deviation
HERGRA Dependent JAN2000 DEC2009 120 0 4.57471 5.68358 5.24099 0.25212
x2 Predictor JAN2000 DEC2009 120 0 7.28033 7.93627 7.44128 0.15883
x10 Predictor JAN2000 DEC2009 120 0 7.51833 7.98036 7.79684 0.09299
x4 Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.2664 0.45249
x6 Predictor JAN2000 DEC2009 120 0 8.86954 9.82831 9.44891 0.25055
x7 Predictor JAN2000 DEC2009 120 0 1.38629 6.60534 5.26472 1.19463
x11 Predictor JAN2000 DEC2009 120 0 0 1 0.20833 0.40782
Forecast Span Summary
First Last Standard
Variable Type Obs Obs NObs NMiss Min Max Mean Deviation
HERGRA Dependent JAN2000 DEC2009 120 0 4.57471 5.68358 5.24099 0.25212
x2 Predictor JAN2000 DEC2009 120 0 7.28033 7.93627 7.44128 0.15883
x10 Predictor JAN2000 DEC2009 120 0 7.51833 7.98036 7.79684 0.09299
x4 Predictor JAN2000 DEC2009 120 0 11.60084 13.27341 12.2664 0.45249
x6 Predictor JAN2000 DEC2009 120 0 8.86954 9.82831 9.44891 0.25055
x7 Predictor JAN2000 DEC2009 120 0 1.38629 6.60534 5.26472 1.19463
x11 Predictor JAN2000 DEC2009 120 0 0 1 0.20833 0.40782
Fixed Parameters in the Model
Component Parameter Estimate
Irregular Error Variance 0
RPC Error Variance 0
Preliminary Estimates of the Free Parameters
Component Parameter Estimate
Irregular Error Variance 0.01517
Likelihood Based Fit Statistics
Statistic Value
Full Log Likelihood -8.156
Diffuse Part of Log Likelihood 57.068
Non-Missing Observations Used 120
Estimated Parameters 1
Initialized Diffuse State Elements 17
Normalized Residual Sum of Squares 103
AIC (smaller is better) 18.311
BIC (smaller is better) 20.946
The SAS System
The UCM Procedure
Likelihood Based Fit Statistics
Statistic Value
AICC (smaller is better) 18.351
HQIC (smaller is better) 19.379
CAIC (smaller is better) 21.946
Final Estimates of the Free Parameters
Approx Approx
Component Parameter Estimate Std Error t Value Pr > |t|
Season Error Variance 0.00068677 0.0000957 7.18 <.0001
PARO Coefficient -0.18544 0.07713 -2.4 0.0162
COMTOT Coefficient 1.86861 0.11425 16.36 <.0001
CONALC Coefficient -0.28821 0.045 -6.4 <.0001
SUSP Coefficient -0.43721 0.09072 -4.82 <.0001
RUIDO Coefficient -0.05168 0.0154 -3.36 0.0008
RPC Coefficient -0.05596 0.0388 -1.44 0.1493
Fit Statistics Based on Residuals
Mean Squared Error 0.0222
Root Mean Squared Error 0.14899
Mean Absolute Percentage Error 0.14899
Maximum Percent Error 4.43671
R-Square 0.3758
Adjusted R-Square 0.3758
Random Walk R-Square 0.32948
Amemiya’s Adjusted R-Square 0.32152
Number of non-missing residuals used for
computing the fit statistics = 24
Significance Analysis of Components
(Based on the Final State)
Component DF Chi-Square Pr > ChiSq
Irregular 0 . .
Season 11 38.66 <.0001
Summary of Seasons
Name Type Season Length Error Variance
Season TRIG 12 0.00068677
The SAS System
The UCM Procedure
Outlier Summary
Standard
Obs DATE Break Type Estimate Error Chi-Square DF Pr > ChiSq
75 MAR2006 Additive Outlier 0.6893 0.1473719 21.88 1 <.0001
74 FEB2006 Additive Outlier 0.63582 0.1462865 18.89 1 <.0001
Forecasts for Variable HERGRA
Standard
Obs DATE Forecast Error 95% Confidence Limits
109 JAN2009 4.888183 0.25566 4.387095 5.389271
109 JAN2009 4.785545 0.25839 4.279106 5.291985
111 MAR2009 4.652695 0.25443 4.154012 5.151379
112 APR2009 4.77492 0.25593 4.273314 5.276525
113 MAY2009 4.77492 0.25593 4.273314 5.276525
114 JUN2009 5.09988 0.23237 4.644445 5.555315
115 JUL2009 5.141305 0.25327 4.644913 5.637697
116 AUG2009 4.738095 0.23929 4.26909 5.207101
117 SEP2009 4.713624 0.23978 4.243668 5.18358
118 OCT2009 4.886632 0.23748 4.421171 5.352093
119 NOV2009 4.612448 0.23189 4.157953 5.066943
120 DEC2009 4.834177 0.22969 4.383997 5.284357
Post Sample Predictions for HERGRA
Sum of Sum of
Prediction Squared Absolute
Obs DATE Actual Forecast Error Errors Errors
109 JAN2009 4.59511985 4.888182981 -0.29306313 0.085885999 0.293063131
110 FEB2009 4.605170186 4.785545441 -0.18037525 0.118421231 0.473438386
111 MAR2009 4.812184355 4.811209575 0.000974781 0.118422182 0.474413167
112 APR2009 4.744932128 4.652695465 0.092236663 0.126929784 0.56664983
113 MAY2009 4.859812404 4.774919573 0.084892831 0.134136576 0.651542661
114 JUN2009 4.934473933 5.099880127 -0.16540619 0.161495785 0.816948855
115 JUL2009 4.912654886 5.14130519 -0.2286503 0.213776747 1.045599158
116 AUG2009 4.753590191 4.73809548 0.015494711 0.214016833 1.06109387
117 SEP2009 4.574710979 4.713623939 -0.13891296 0.233313643 1.20000683
118 OCT2009 4.682131227 4.886632151 -0.20450092 0.275134271 1.404507754
119 NOV2009 4.59511985 4.612447926 -0.01732808 0.275434534 1.42183583
120 DEC2009 4.820281566 4.834176862 -0.0138953 0.275627613 1.435731126
Appendix III: WinBUGS Codes
WinBugs Code: Structural explanatory model estimation
model {
mu[1] <- inprod( b[], X[1,])
Y[1] ~ dnorm(mu[1],tau.u)
mu[2] <- inprod( b[], X[2,])
+rho[1]*(Y[1]-inprod( b[], X[1,]))
Y[2] ~ dnorm(mu[2],tau.e)
for (t in 3:T){
mu[t] <- inprod( b[], X[t,])
+rho[1]*(Y[t-1]-inprod( b[], X[t-1,]))
+rho[2]*(Y[t-2]-inprod( b[], X[t-2,]))
Y[t] ~ dnorm(mu[t], tau.e)
Y.pred[t]~ dnorm(mu[t], tau.e) #Prediction estimation
}
for (t in T+1:N){
mu.pred[t] <- inprod( b[], X[t,])
+rho[1]*(Y.pred[t-1]-inprod( b[], X[t-1,]))
+rho[2]*(Y.pred[t-2]-inprod( b[], X[t-2,]))
Y.pred[t]~ dnorm(mu.pred[t], tau.e)
}
sigma.e <- 1/tau.e
sigma.u <-sigma.e*(1-rho[2])/((1+rho[2])*(pow((1-rho[2]),2)
-pow(rho[1],2)))
tau.u <- 1/sigma.u
for (i in 1:2) {
rho[i]~ dunif(r0[i], R0[i])
}
b[1:n] ~ dmnorm(b0[], B0[ , ])
tau.e ~ dgamma(0.01, 0.01)
}
DATA
list(’n’,’N’,’T’,’X’,’Y’,’b0’,’B0’,’r0’,’R0’ )
INITS
list( b=c(matrix(data=0.01, nrow=1, ncol=n)),
rho=c(0.05,0.01),tau.e=.01)
Appendix IV: SE Bayesian Estimation: Vari-
able Selection
177
M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5
1 V HP VKM 0.8177146 0.8175842 0.8177526
2 V HP CONGAS 0.8633223 0.8164691 0.8110146
3 V HP PARO 0.854253 0.7985948 0.7977917
4 V HP OCUP1 0.8022488 0.8015802 0.6126772
5 V HP OCUP4 0.7936083 0.8063415 0.6618917
6 V HP PRCRN 0.7604337 0.788923 0.6724536
7 V HP IPI 0.8024817 0.8023117 0.6131628
8 V HP PCONCEM 0.7903066 0.7904969 0.6626231
9 V HP MANT 0.5815363 0.7470997 0.6725995
10 V HP PRECOML 0.8016426 0.8040959 0.8392632
11 V HP PREC 0.8022192 0.7996903 0.7984826
12 V HP HSOL 0.8005376 0.7712959 0.7729773
13 V HP DNIEB 0.802471 0.8186242 0.6133427
14 V HP DLAB 0.7937751 0.8077033 0.6620008
15 V HP COND 0.6985997 0.7623451 0.6727231
16 V HP CONALC 0.8029933 0.8148661 0.6130014
17 V HP RADAR 0.7956255 0.813858 0.6618806
18 V HP SUSP 0.7408465 0.7431765 0.6722548
19 V HP V EH10 0.8200421 0.8123648 0.8166806
20 V HP ABS 0.8365977 0.7980062 0.8124503
21 V HP LONRAC 0.8189307 0.6895311 0.7674998
22 V HP LONRED 0.8023182 0.8035284 0.8195032
23 V HP PPS 0.8154297 0.7952132 0.7994828
24 V HP PCR 0.7908286 0.7205856 0.7315893
25 V HP SDF 0.8018307 0.8031048 0.8148504
26 V HP SEMSAN 0.7948011 0.8041271 0.8201274
27 V HP DSCN 0.7739817 0.7958927 0.8193945
28 V KM CONGAS 0.8042948 0.8029049 0.8149373
29 V KM PARO 0.8010769 0.8003293 0.8291742
30 V KM OCUP1 0.7956938 0.7685242 0.7783732
M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5
31 V KM OCUP4 0.8177369 0.8024944 0.8142447
32 V KM PRCRN 0.8068281 0.7997772 0.799153
33 V KM IPI 0.7281825 0.7443171 0.7457771
34 V KM PCONCEM 0.8150335 0.8019097 0.8158791
35 V KM MANT 0.8110105 0.8525853 0.662618
36 V KM PRECOML 0.7509789 0.8417006 0.6869132
37 V KM PREC 0.8122344 0.8016743 0.8158597
38 V KM HSOL 0.7934893 0.7943238 0.8186473
39 V KM DNIEB 0.6930369 0.7911324 0.819957
40 V KM DLAB 0.8039932 0.8184131 0.8227307
41 V KM COND 0.7926421 0.8253475 0.8419418
42 V KM CONALC 0.7024982 0.8332624 0.8472065
43 V KM RADAR 0.8029414 0.8421648 0.8328259
44 V KM SUSP 0.80169 0.8263395 0.8242046
45 V KM V EH10 0.7964532 0.8149253 0.8279104
46 V KM ABS 0.8025811 0.8026719 0.8147169
47 V KM LONRAC 0.8045783 0.7912803 0.8186206
48 V KM LONRED 0.7542224 0.7771379 0.8126447
49 V KM PPS 0.8024775 0.8077896 0.8164252
50 V KM PCR 0.7942209 0.8007252 0.8084237
51 V KM SDF 0.7018674 0.7161553 0.7477667
52 V KM SEMSAN 0.8015026 0.8028268 0.8129071
53 V KM DSCN 0.8596083 0.79339 0.804531
54 CONGAS PARO 0.810767 0.7143458 0.748188
55 CONGAS OCUP1 0.8019279 0.8333313 0.8387111
56 CONGAS OCUP4 0.7988748 0.8301117 0.8582663
57 CONGAS PRCRN 0.7953983 0.8191112 0.8424202
58 CONGAS IPI 0.8181123 0.8024005 0.8117343
59 CONGAS PCONCEM 0.8237281 0.7928198 0.8051074
60 CONGAS MANT 0.8292634 0.7248405 0.7485408
61 CONGAS PRECOML 0.8426114 0.8029551 0.8121599
62 CONGAS PREC 0.8214007 0.7933023 0.8119313
63 CONGAS HSOL 0.8081024 0.7169706 0.7549123
64 CONGAS DNIEB 0.8026749 0.8186196 0.8013039
65 CONGAS DLAB 0.7975095 0.8176019 0.7279907
66 CONGAS COND 0.7874491 0.7214555 0.6721187
67 CONGAS CONALC 0.8072548 0.8019044 0.8134041
68 CONGAS RADAR 0.7995603 0.79893 0.8072544
69 CONGAS SUSP 0.7117075 0.6943242 0.8002756
70 CONGAS V EH10 0.8021846 0.8018988 0.8131273
71 CONGAS ABS 0.7896054 0.7971026 0.8115512
72 CONGAS LONRAC 0.7057952 0.7761258 0.710728
73 CONGAS LONRED 0.8337116 0.803909 0.8135646
74 CONGAS PPS 0.8339543 0.8016799 0.6754979
75 CONGAS PCR 0.8260382 0.7972781 0.6657882
76 CONGAS SDF 0.8015085 0.8191803 0.8110915
77 CONGAS SEMSAN 0.7909441 0.810806 0.4786969
78 CONGAS DSCN 0.7084325 0.7536537 0.606624
79 PARO OCUP1 0.8027989 0.81485 0.8119726
80 PARO OCUP4 0.7900512 0.8204957 0.8041709
M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5
81 PARO PRCRN 0.709393 0.8112935 0.799443
82 PARO IPI 0.817981 0.813485 0.8096414
83 PARO PCONCEM 0.8657481 0.8068974 0.815507
84 PARO MANT 0.8485372 0.7591413 0.8244092
85 PARO PRECOML 0.8193548 0.8039355 0.8326634
86 PARO PREC 0.8603456 0.7994843 0.8173454
87 PARO HSOL 0.8379193 0.7234451 0.8106285
88 PARO DNIEB 0.8171518 0.8015966 0.8121349
89 PARO DLAB 0.8593346 0.8016541 0.8045158
90 PARO COND 0.8590953 0.7954139 0.7919884
91 PARO CONALC 0.8186303 0.8033172 0.6662796
92 PARO RADAR 0.8599243 0.8059517 0.66751
93 PARO SUSP 0.845686 0.7687274 0.6691402
94 PARO V EH10 0.8167623 0.8032978 0.6653
95 PARO ABS 0.8619321 0.8023057 0.6654278
96 PARO LONRAC 0.862701 0.7337906 0.667138
97 PARO LONRED 0.8325585 0.8031045 0.8457149
98 PARO PPS 0.867736 0.8483223 0.8002327
99 PARO PCR 0.8496205 0.7554901 0.7671273
100 PARO SDF 0.8206047 0.8022563 0.6661761
101 PARO SEMSAN 0.8706911 0.7992259 0.6672496
102 PARO DSCN 0.8270232 0.7957522 0.668268
103 OCUP1 OCUP4 0.8181561 0.8183737 0.6669999
104 OCUP1 PRCRN 0.8604405 0.8230952 0.6683062
105 OCUP1 IPI 0.8477729 0.8262305 0.6694916
106 OCUP1 PCONCEM 0.8085033 0.8427564 0.8039146
107 OCUP1 MANT 0.8671118 0.83703 0.8020617
108 OCUP1 PRECOML 0.8447033 0.8090556 0.7960699
109 OCUP1 PREC 0.8252275 0.8027668 0.8039556
110 OCUP1 HSOL 0.8706435 0.7971233 0.8044677
111 OCUP1 DNIEB 0.8418557 0.7877588 0.7453765
112 OCUP1 DLAB 0.8116384 0.8077051 0.8043248
113 OCUP1 COND 0.8723929 0.8018738 0.7291518
114 OCUP1 CONALC 0.8375506 0.732387 0.6787788
115 OCUP1 RADAR 0.8190067 0.8034062 0.8010043
116 OCUP1 SUSP 0.8715686 0.7970314 0.5361637
117 OCUP1 V EH10 0.8507222 0.7261359 0.7308758
118 OCUP1 ABS 0.8151765 0.8342945 0.8013602
119 OCUP1 LONRAC 0.8702629 0.8348999 0.7998687
120 OCUP1 LONRED 0.8326637 0.8283952 0.7962436
121 OCUP1 PPS 0.816782 0.8025501 0.8165366
122 OCUP1 PCR 0.8584543 0.7968542 0.8191087
123 OCUP1 SDF 0.8545053 0.7361098 0.8229729
124 OCUP1 SEMSAN 0.8163241 0.8018586 0.842477
125 OCUP1 DSCN 0.8693568 0.7966464 0.8181047
126 OCUP4 PRCRN 0.8449012 0.7319608 0.8099033
127 OCUP4 IPI 0.8164593 0.8164723 0.8035007
128 OCUP4 PCONCEM 0.8748668 0.7091916 0.7992298
129 OCUP4 MANT 0.8370542 0.6231448 0.7863793
130 OCUP4 PRECOML 0.8231295 0.8159253 0.798784
M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5
131 OCUP4 PREC 0.8712107 0.8076577 0.7358418
132 OCUP4 HSOL 0.8085898 0.7780075 0.6752643
133 OCUP4 DNIEB 0.818318 0.8053004 0.7920324
134 OCUP4 DLAB 0.8599455 0.806879 0.7248855
135 OCUP4 COND 0.8552877 0.7985435 0.673356
136 OCUP4 CONALC 0.8204952 0.784465 0.8377942
137 OCUP4 RADAR 0.8651884 0.5655491 0.8486993
138 OCUP4 SUSP 0.8799376 0.6208145 0.853941
139 OCUP4 V EH10 0.8383208 0.8267241 0.7920708
140 OCUP4 ABS 0.8556648 0.7446674 0.7364794
141 OCUP4 LONRAC 0.8589986 0.6961203 0.6674088
142 OCUP4 LONRED 0.8175199 0.7877541 0.7919534
143 OCUP4 PPS 0.8600844 0.5632836 0.7280612
144 OCUP4 PCR 0.8477131 0.6144382 0.6776355
145 OCUP4 SDF 0.8127813 0.7850196 0.8032572
146 OCUP4 SEMSAN 0.8713335 0.6786676 0.8058785
147 OCUP4 DSCN 0.838255 0.6575677 0.8004544
148 PRCRN IPI 0.809005 0.8174156 0.8026858
149 PRCRN PCONCEM 0.8718846 0.8185809 0.8071421
150 PRCRN MANT 0.8376584 0.812004 0.8007521
151 PRCRN PRECOML 0.8364227 0.8183428 0.8019024
152 PRCRN PREC 0.8774896 0.7966366 0.849601
153 PRCRN HSOL 0.8628281 0.6618719 0.8422259
154 PRCRN DNIEB 0.8090952 0.8179866 0.8021276
155 PRCRN DLAB 0.8752892 0.5316843 0.800468
156 PRCRN COND 0.8487674 0.6117747 0.7968869
157 PRCRN CONALC 0.808623 0.8123097 0.8184171
158 PRCRN RADAR 0.8720834 0.4364196 0.8241593
159 PRCRN SUSP 0.8403805 0.5993511 0.8293394
160 PRCRN V EH10 0.8026666 0.8113697 0.8425349
161 PRCRN ABS 0.7954464 0.8153706 0.8308879
162 PRCRN LONRAC 0.7285878 0.8113417 0.8097642
163 PRCRN LONRED 0.8028518 0.8144649 0.802761
164 PRCRN PPS 0.8007795 0.8062329 0.8030566
165 PRCRN PCR 0.7988766 0.8224995 0.7976037
166 PRCRN SDF 0.8023547 0.8500317 0.8072577
167 PRCRN SEMSAN 0.7884496 0.8362918 0.8047019
168 PRCRN DSCN 0.7339607 0.827002 0.7986949
169 IPI PCONCEM 0.8027135 0.8172644 0.8029824
170 IPI MANT 0.7944165 0.8138492 0.8012297
171 IPI PRECOML 0.76845 0.7995465 0.796285
172 IPI PREC 0.8189657 0.7787061 0.8341185
173 IPI HSOL 0.8352812 0.5610755 0.8323098
174 IPI DNIEB 0.814536 0.6193843 0.8284105
175 IPI DLAB 0.8019226 0.7473589 0.8022876
176 IPI COND 0.823622 0.5644437 0.8013616
177 IPI CONALC 0.814046 0.6205317 0.7966963
178 IPI RADAR 0.8026382 0.8304521 0.8026443
179 IPI SUSP 0.7974025 0.7906591 0.8016385
180 IPI V EH10 0.7819428 0.7464324 0.7958521
M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5
181 IPI ABS 0.804043 0.7581114 0.8024189
182 IPI LONRAC 0.8040253 0.5585804 0.8067381
183 IPI LONRED 0.7992863 0.6167365 0.7187955
184 IPI PPS 0.8188207 0.7513783 0.803302
185 IPI PCR 0.8112056 0.5579529 0.7815464
186 IPI SDF 0.780273 0.6191529 0.6471709
187 IPI SEMSAN 0.8147661 0.8015906 0.8027459
188 IPI DSCN 0.8178912 0.7960677 0.805073
189 PCONCEM MANT 0.7958295 0.7726824 0.7988621
190 PCONCEM PRECOML 0.8125099 0.8034616 0.8184416
191 PCONCEM PREC 0.8018711 0.8002722 0.8278837
192 PCONCEM HSOL 0.7712741 0.8006085 0.8295076
193 PCONCEM DNIEB 0.8037809 0.8159733 0.8426265
194 PCONCEM DLAB 0.8029221 0.59225 0.8084854
195 PCONCEM COND 0.7664897 0.6201463 0.8074731
196 PCONCEM CONALC 0.8027254 0.8157316 0.8020523
197 PCONCEM RADAR 0.7999521 0.7132975 0.806531
198 PCONCEM SUSP 0.7961661 0.6932914 0.7912557
199 PCONCEM V EH10 0.8025988 0.811743 0.8076371
200 PCONCEM ABS 0.8084887 0.5918014 0.8113267
201 PCONCEM LONRAC 0.780903 0.6081571 0.719124
202 PCONCEM LONRED 0.8022382 0.8030331 0.8031865
203 PCONCEM PPS 0.802995 0.6575 0.809543
204 PCONCEM PCR 0.777027 0.6777468 0.7183791
205 PCONCEM SDF 0.8024647 0.8022493 0.8337897
206 PCONCEM SEMSAN 0.8571991 0.8088987 0.8314761
207 PCONCEM DSCN 0.8300805 0.8034591 0.7791769
208 MANT PRECOML 0.8025315 0.8029373 0.8031629
209 MANT PREC 0.799095 0.7964026 0.8088327
210 MANT HSOL 0.7945355 0.6804436 0.71785
211 MANT DNIEB 0.8185302 0.8018515 0.8027029
212 MANT DLAB 0.8262494 0.6325564 0.8085434
213 MANT COND 0.8341029 0.6247462 0.718098
214 MANT CONALC 0.8421848 0.801266 0.8018244
215 MANT RADAR 0.8195827 0.5295981 0.4570613
216 MANT SUSP 0.8037528 0.6330832 0.6117017
217 MANT V EH10 0.8020468 0.8013577 0.802367
218 MANT ABS 0.7983169 0.8046625 0.8062233
219 MANT LONRAC 0.7892269 0.8022003 0.8021456
220 MANT LONRED 0.8072559 0.8182096 0.8185569
221 MANT PPS 0.803381 0.8252102 0.818127
222 MANT PCR 0.776737 0.8326215 0.8217059
223 MANT SDF 0.804149 0.8427287 0.8427956
224 MANT SEMSAN 0.7993248 0.8249284 0.8255273
225 MANT DSCN 0.7739915 0.8172542 0.8128662
226 PRECOML PREC 0.8335713 0.8018802 0.8026256
227 PRECOML HSOL 0.840189 0.8034711 0.8042399
228 PRECOML DNIEB 0.8430549 0.7925271 0.7940023
229 PRECOML DLAB 0.80299 0.8067066 0.8081479
230 PRECOML COND 0.8007227 0.6220574 0.6832529
M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5
231 PRECOML CONALC 0.7748959 0.6271633 0.6755643
232 PRECOML RADAR 0.8027776 0.8020155 0.8038543
233 PRECOML SUSP 0.7995724 0.6342282 0.6826434
234 PRECOML V EH10 0.7766107 0.6326462 0.6751984
235 PRECOML ABS 0.802318 0.8336061 0.8343619
236 PRECOML LONRAC 0.8342743 0.8325257 0.8098646
237 PRECOML LONRED 0.8271725 0.8175785 0.7711921
238 PRECOML PPS 0.8018639 0.8020362 0.802144
239 PRECOML PCR 0.7950026 0.5869677 0.6901301
240 PRECOML SDF 0.3463804 0.6217626 0.6757403
241 PRECOML SEMSAN 0.8024319 0.8010321 0.8026746
242 PRECOML DSCN 0.8017316 0.5982199 0.6853769
243 PREC HSOL 0.6089112 0.6226696 0.6752623
244 PREC DNIEB 0.8141246 0.8041385 0.8010191
245 PREC DLAB 0.7789798 0.8015598 0.8482312
246 PREC COND 0.389691 0.7961804 0.8460647
247 PREC CONALC 0.8021586 0.8173462 0.8178381
248 PREC RADAR 0.7655609 0.8067594 0.8137785
249 PREC SUSP 0.3868807 0.7852026 0.8421694
250 PREC V EH10 0.8016922 0.8154004 0.8435518
251 PREC ABS 0.8003895 0.816497 0.8700421
252 PREC LONRAC 0.7648491 0.80605 0.8599413
253 PREC LONRED 0.804109 0.812376 0.8023709
254 PREC PPS 0.7983945 0.7997876 0.8454726
255 PREC PCR 0.7808899 0.7807682 0.8352669
256 PREC SDF 0.8171735 0.8022594 0.8061961
257 PREC SEMSAN 0.7970394 0.7947252 0.4387541
258 PREC DSCN 0.6428801 0.7753979 0.6134612
259 HSOL DNIEB 0.814799 0.8028456 0.8015362
260 HSOL DLAB 0.813954 0.8097876 0.4400104
261 HSOL COND 0.7865152 0.8014919 0.6121818
262 HSOL CONALC 0.8119278 0.8030266 0.8331818
263 HSOL RADAR 0.7908942 0.8043954 0.7621032
264 HSOL SUSP 0.6154104 0.7859217 0.7168892
265 HSOL V EH10 0.8031204 0.8025347 0.8005233
266 HSOL ABS 0.7781173 0.7985959 0.417049
267 HSOL LONRAC 0.5328157 0.7771499 0.6044848
268 HSOL LONRED 0.8025323 0.8022483 0.8007875
269 HSOL PPS 0.8220255 0.8393333 0.4426737
270 HSOL PCR 0.8097165 0.823342 0.6105403
271 HSOL SDF 0.8033353 0.8011687 0.818186
272 HSOL SEMSAN 0.795472 0.8022975 0.8233175
273 HSOL DSCN 0.6633954 0.8044716 0.8283526
274 DNIEB DLAB 0.802295 0.8180137 0.8426477
275 DNIEB COND 0.7840268 0.8217409 0.839265
276 DNIEB CONALC 0.6002579 0.8252991 0.8248309
277 DNIEB RADAR 0.8011525 0.8430021 0.8020027
278 DNIEB SUSP 0.8166035 0.8470611 0.7983913
279 DNIEB V EH10 0.6704432 0.845627 0.8011711
280 DNIEB ABS 0.8013855 0.8025935 0.8054063
M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5
281 DNIEB LONRAC 0.8328708 0.8005556 0.8019902
282 DNIEB LONRED 0.8408698 0.7884685 0.7980442
283 DNIEB PPS 0.8178589 0.8066005 0.802572
284 DNIEB PCR 0.8203434 0.7973721 0.7984923
285 DNIEB SDF 0.8095639 0.7767379 0.7960865
286 DNIEB SEMSAN 0.8437495 0.8034665 0.833557
287 DNIEB DSCN 0.8535188 0.7935704 0.8315013
288 DLAB COND 0.8443313 0.7700073 0.8285805
289 DLAB CONALC 0.8023017 0.83411 0.8012303
290 DLAB RADAR 0.8205853 0.831187 0.7985719
291 DLAB SUSP 0.8076937 0.8203379 0.7950395
292 DLAB V EH10 0.8064329 0.801958 0.8012164
293 DLAB ABS 0.7825408 0.7943072 0.7991429
294 DLAB LONRAC 0.5154273 0.7742683 0.7954598
295 DLAB LONRED 0.8018405 0.8012321 0.826621
296 DLAB PPS 0.7773717 0.7955405 0.8264926
297 DLAB PCR 0.4799133 0.7742258 0.8299019
298 DLAB SDF 0.8332608 0.8155321 0.8184026
299 DLAB SEMSAN 0.8202554 0.8096874 0.8230121
300 DLAB DSCN 0.6480552 0.7997965 0.8279362
301 COND CONALC 0.8019845 0.8122241 0.7970354
302 COND RADAR 0.7802844 0.8163128 0.8134748
303 COND SUSP 0.5371699 0.8075223 0.820856
304 COND V EH10 0.8017459 0.8096658 0.79607
305 COND ABS 0.7795558 0.8025701 0.8120152
306 COND LONRAC 0.5022017 0.7949075 0.8201797
307 COND LONRED 0.8020302 0.8044701 0.8436118
308 COND PPS 0.8088196 0.8008472 0.8480323
309 COND PCR 0.812897 0.7961977 0.8515208
310 COND SDF 0.8026744 0.8038579 0.7983258
311 COND SEMSAN 0.8014651 0.8040571 0.8107866
312 COND DSCN 0.7993778 0.8020434 0.8209671
313 CONALC RADAR 0.8183627 0.804085 0.7939811
314 CONALC SUSP 0.8228468 0.8120772 0.8109269
315 CONALC V EH10 0.8227236 0.8023296 0.8209948
316 CONALC ABS 0.8023917 0.8040464 0.8427443
317 CONALC LONRAC 0.8120209 0.8091219 0.8421057
318 CONALC LONRED 0.81337 0.805031 0.8377355
319 CONALC PPS 0.8028692 0.803712 0.8332441
320 CONALC PCR 0.8354772 0.8137141 0.8220741
321 CONALC SDF 0.8148162 0.8297172 0.8149056
322 CONALC SEMSAN 0.8044048 0.8039758 0.8335598
323 CONALC DSCN 0.8040421 0.8030754 0.816103
324 RADAR SUSP 0.8027946 0.800414 0.809433
325 RADAR V EH10 0.8187281 0.8192675 0.8347794
326 RADAR ABS 0.8150761 0.8238789 0.8373343
327 RADAR LONRAC 0.8096017 0.8284216 0.8355959
328 RADAR LONRED 0.8142254 0.8374016 0.821199
329 RADAR PPS 0.8199405 0.8104663 0.8110525
330 RADAR PCR 0.8218945 0.8067558 0.806878
M X1 X2 λX = −0.5 λX = 0.1 λX = 0.5
331 RADAR SDF 0.8133328 0.8043737 0.8211055
332 RADAR SEMSAN 0.8080674 0.8027013 0.8113551
333 RADAR DSCN 0.8034381 0.7983248 0.8069341
334 SUSP V EH10 0.8036057 0.8097748 0.8073548
335 SUSP ABS 0.8039292 0.8082205 0.8013315
336 SUSP LONRAC 0.8008538 0.8029621 0.7909047
337 SUSP LONRED 0.8029065 0.8048129 0.8028127
338 SUSP PPS 0.8015424 0.8034583 0.7978693
339 SUSP PCR 0.7984759 0.7980875 0.7876263
340 SUSP SDF 0.8024696 0.8361496 0.8336978
341 SUSP SEMSAN 0.8080495 0.8376428 0.831532
342 SUSP DSCN 0.8034414 0.8366434 0.8234911
343 V EH10 ABS 0.8024877 0.8041964 0.8020142
344 V EH10 LONRAC 0.8092256 0.8029364 0.798101
345 V EH10 LONRED 0.8032036 0.797426 0.7882843
346 V EH10 PPS 0.8027529 0.8036126 0.8017914
347 V EH10 PCR 0.855589 0.8019825 0.7985028
348 V EH10 SDF 0.8530131 0.7978273 0.7876679
349 V EH10 SEMSAN 0.8024791 0.8221404 0.6769551
350 V EH10 DSCN 0.8067071 0.8018141 0.6769551
351 ABS LONRAC 0.8007792 0.7589147 0.6769551
352 ABS LONRED 0.8185386 0.6185572 0.8375151
353 ABS PPS 0.8243669 0.6565701 0.8020374
354 ABS PCR 0.8310752 0.6659081 0.772318
355 ABS SDF 0.8426902 0.8003165 0.6771796
356 ABS SEMSAN 0.8366697 0.7331786 0.6771796
357 ABS DSCN 0.8103501 0.6737012 0.6771796
358 LONRAC LONRED 0.8022304 0.8180917 0.6773342
359 LONRAC PPS 0.8303597 0.813956 0.6773342
360 LONRAC PCR 0.815368 0.8059941 0.6773342
361 LONRAC SDF 0.807937 0.818143 0.8370532
362 LONRAC SEMSAN 0.8064075 0.8133426 0.8013598
363 LONRAC DSCN 0.801271 0.714338 0.7711194
364 LONRED PPS 0.8038055 0.8187184 0.6770562
365 LONRED PCR 0.8022871 0.6769864 0.6770562
366 LONRED SDF 0.7992827 0.6711104 0.6770562
367 LONRED SEMSAN 0.8339847 0.8156877 0.6770441
368 LONRED DSCN 0.8329483 0.4582689 0.6770441
369 PPS PCR 0.8318461 0.6119364 0.6770441
370 PPS SDF 0.8035692 0.8163935 0.8445552
371 PPS SEMSAN 0.8019062 0.8118677 0.8230756
372 PPS DSCN 0.7988585 0.806015 0.7910318
373 PCR SDF 0.8027218 0.7893519 0.8364614
374 PCR SEMSAN 0.8020762 0.8113378 0.8031359
375 PCR DSCN 0.8000596 0.8223714 0.7722329
376 SDF SEMSAN 0.8028954 0.8495689 0.6770119
377 SDF DSCN 0.7964628 0.8251071 0.6770119
378 SEMSAN DSCN 0.7370984 0.8171374 0.6770119
Appendix V: SE Bayesian Estimation: Model
Selection
M DIC β1 β2 β3 β4 β5 β6 β7 β8 β9 β10 β11
1 93 -115.708 -25.241 17.424 -368.619 57.754 6.029 -79.059 169.543 98.314 2.833 -0.206
2 100 5.409 -0.070 -59.985 -806.879 -38.496 -3.222 -34.261 461.951 212.396 4.460 -0.132
3 87 0.056 0.102 -11.121 -663.105 26.163 2.215 21.618 309.252 133.747 2.847 -0.201
4 88 -82.098 -67.031 4.820 -561.965 30.528 2.394 7.157 259.959 127.351 2.833 -0.132
5 90 6.121 5.192 -13.603 -447.450 73.678 4.463 1.839 236.600 110.671 1.839 -0.405
6 86 0.064 0.087 -1.637 -582.138 51.217 3.739 -8.615 278.786 118.514 2.536 -0.258
7 90 -95.596 -42.909 0.553 -558.288 7.587 3.106 -43.645 272.609 129.515 3.725 -0.010
8 104 6.387 0.563 -1.445 -405.467 85.757 2.509 -26.578 271.031 146.527 1.140 -0.682
9 86 0.060 0.098 -0.228 -575.527 57.614 3.457 7.211 282.380 115.225 2.213 -0.315
10 87 -68.120 -83.532 -4.300 11.667 -8.176 -5.756 33.468 194.936 141.601 2.181 -0.145
11 91 6.816 3.334 15.861 6.846 -13.131 -9.111 -6.384 357.494 113.671 1.638 -0.285
12 86 0.061 0.090 3.754 10.540 -10.695 -7.680 13.054 309.545 128.581 1.994 -0.231
13 87 -69.234 -81.049 -1.442 11.694 -7.704 -5.246 31.384 167.352 141.428 2.109 -0.200
14 88 5.710 5.829 -10.300 9.380 -9.915 -8.050 7.876 221.839 123.017 1.801 -0.313
15 86 0.057 0.101 -4.701 11.596 -8.846 -7.297 16.807 231.506 130.142 2.098 -0.252
16 87 -68.076 -82.125 0.011 11.582 -8.279 -5.777 27.188 192.572 142.101 2.091 -0.183
17 91 6.370 4.463 -0.544 7.605 -11.843 -8.836 1.825 286.360 116.388 1.603 -0.321
18 86 0.061 0.091 -0.200 10.710 -9.992 -7.661 12.981 288.326 125.172 1.999 -0.262
19 85 -55.114 -86.257 -29.657 0.066 -0.037 -0.260 29.781 152.211 173.093 3.372 -0.017
20 105 8.206 -4.477 0.121 0.024 -0.225 -0.758 -19.783 577.875 163.574 1.800 -0.347
21 86 0.054 0.110 -4.265 0.042 -0.157 -0.518 59.067 396.768 139.463 1.698 -0.233
22 86 -59.162 -89.265 2.114 0.052 -0.079 -0.410 39.753 149.978 151.222 2.341 -0.182
23 90 5.492 6.016 -13.001 0.039 -0.122 -0.648 18.470 193.459 125.818 1.745 -0.365
24 85 0.054 0.110 -3.424 0.049 -0.099 -0.583 20.651 207.209 132.282 2.248 -0.271
25 85 -57.897 -92.016 0.313 0.056 -0.080 -0.368 45.238 167.039 157.219 2.486 -0.131
26 96 6.869 2.203 -1.073 0.021 -0.188 -0.814 -3.375 315.853 116.848 0.999 -0.493
27 86 0.055 0.106 -0.271 0.043 -0.127 -0.600 41.440 260.030 133.581 1.818 -0.308
28 97 -118.214 -23.467 19.181 -312.421 61.388 5.824 0.649 -0.115 -1.009 3.068 -0.213
29 90 5.405 4.506 -23.480 -544.419 43.846 0.153 -0.279 -0.369 -3.320 2.528 -0.161
30 90 0.069 0.074 4.478 -455.090 63.819 4.187 0.297 -0.208 -1.553 2.675 -0.213
187
M DIC β1 β2 β3 β4 β5 β6 β7 β8 β9 β10 β11
31 91 -82.733 -60.597 11.108 -509.968 40.290 1.048 -0.045 -0.283 -2.561 2.780 -0.085
32 91 5.972 5.121 -6.802 -421.800 80.403 2.910 -0.080 -0.240 -2.471 1.747 -0.349
33 89 0.062 0.085 4.773 -516.963 59.205 2.125 -0.030 -0.303 -2.387 2.413 -0.208
34 96 -106.780 -25.636 0.871 -449.762 15.498 2.310 0.517 -0.309 -1.711 4.244 0.084
35 93 5.672 3.468 -0.076 -483.558 78.851 1.001 -0.354 -0.330 -3.407 1.602 -0.375
36 89 0.065 0.076 0.484 -497.092 42.124 2.407 0.180 -0.311 -1.997 3.085 -0.094
37 88 -60.058 -82.295 -21.493 13.231 -6.221 -2.609 -0.146 -0.173 -3.158 2.585 -0.061
38 90 5.811 4.404 -7.732 8.519 -11.193 -4.485 -0.157 -0.344 -2.925 1.853 -0.180
39 87 0.054 0.097 -16.912 11.875 -8.504 -3.926 -0.124 -0.263 -2.916 2.386 -0.123
40 88 -68.102 -78.047 3.410 11.646 -7.000 -4.358 -0.121 -0.138 -2.918 2.243 -0.159
41 90 5.550 5.563 -4.335 9.117 -10.033 -6.012 -0.061 -0.216 -2.646 1.786 -0.273
42 87 0.055 0.102 0.731 11.015 -8.590 -5.319 -0.061 -0.197 -2.648 2.131 -0.218
43 88 -63.315 -80.659 0.384 12.164 -6.888 -3.457 -0.160 -0.176 -3.016 2.338 -0.110
44 90 5.801 4.744 -0.025 8.314 -11.288 -5.427 -0.122 -0.290 -2.787 1.712 -0.231
45 87 0.055 0.099 0.242 10.948 -8.806 -4.534 -0.117 -0.252 -2.815 2.167 -0.169
46 91 -62.472 -66.865 -38.643 0.079 0.027 -0.270 0.306 0.013 -2.982 4.823 0.079
47 90 4.957 4.258 -32.502 0.049 -0.114 -0.101 -0.395 -0.386 -3.966 2.400 -0.094
48 86 0.043 0.119 -34.439 0.068 -0.031 -0.273 0.027 -0.144 -3.177 3.681 -0.015
49 88 -59.449 -85.442 8.187 0.054 -0.065 -0.300 -0.182 -0.105 -3.147 2.588 -0.125
50 90 5.248 5.954 -6.387 0.039 -0.121 -0.499 -0.087 -0.182 -2.769 1.791 -0.316
51 87 0.050 0.112 2.584 0.050 -0.090 -0.418 -0.083 -0.164 -2.879 2.356 -0.216
52 87 -56.293 -80.994 0.977 0.065 -0.037 -0.197 -0.106 -0.143 -3.385 3.451 0.024
53 92 5.724 3.710 -0.067 0.034 -0.152 -0.373 -0.289 -0.326 -3.403 1.463 -0.317
54 86 0.047 0.114 0.519 0.054 -0.084 -0.309 -0.172 -0.221 -3.187 2.587 -0.136
55 97 -120.645 -18.407 19.761 -312.102 64.572 6.261 0.001 0.000 -0.007 2.875 -0.228
56 97 5.259 2.190 -47.466 -606.423 28.779 -2.881 0.000 0.000 -0.018 3.095 -0.106
57 90 0.063 0.087 -3.396 -481.118 55.281 3.168 0.000 0.000 -0.010 2.538 -0.200
58 91 -79.274 -69.005 7.276 -477.877 46.989 1.389 0.000 0.000 -0.012 2.468 -0.130
59 92 5.885 5.419 -11.624 -417.062 82.947 3.763 0.000 0.000 -0.011 1.684 -0.390
60 90 0.060 0.097 0.555 -483.024 58.327 2.689 0.000 0.000 -0.011 2.234 -0.258
61 93 -98.746 -36.730 0.859 -475.595 18.431 1.883 0.000 0.000 -0.011 3.739 0.062
62 103 6.210 0.942 -0.952 -373.656 95.433 1.894 0.000 0.000 -0.015 1.059 -0.636
63 89 0.058 0.099 0.182 -519.722 55.979 2.180 0.000 0.000 -0.012 2.323 -0.219
64 89 -66.042 -80.309 -12.939 11.124 -6.961 -3.458 0.000 0.000 -0.013 2.353 -0.105
65 93 6.137 4.124 -0.949 6.603 -12.468 -5.371 0.000 0.000 -0.012 1.708 -0.195
66 88 0.055 0.100 -8.997 9.938 -9.399 -4.791 0.000 0.000 -0.012 2.147 -0.152
67 90 -66.944 -80.837 0.566 10.957 -7.033 -4.841 0.000 0.000 -0.013 2.168 -0.179
68 91 5.493 6.021 -8.039 8.733 -10.054 -6.682 0.000 0.000 -0.011 1.752 -0.301
69 89 0.055 0.102 -2.435 10.783 -8.643 -6.221 0.000 0.000 -0.012 2.112 -0.250
70 89 -66.737 -80.612 0.220 10.691 -7.441 -4.030 0.000 0.000 -0.013 2.179 -0.148
71 92 5.976 4.742 -0.235 6.840 -11.877 -6.195 0.000 0.000 -0.011 1.599 -0.264
72 89 0.056 0.100 0.036 9.805 -9.467 -5.454 0.000 0.000 -0.012 2.021 -0.202
73 89 -58.241 -78.622 -31.289 0.069 -0.005 -0.294 0.000 0.000 -0.015 3.942 0.024
74 99 6.404 0.178 -22.704 0.026 -0.189 -0.145 0.000 0.000 -0.017 1.787 -0.162
75 88 0.046 0.115 -25.326 0.050 -0.089 -0.259 0.000 0.000 -0.015 2.600 -0.099
76 90 -60.878 -86.720 3.771 0.050 -0.067 -0.364 0.000 0.000 -0.013 2.500 -0.151
77 92 5.293 6.096 -11.263 0.037 -0.116 -0.621 0.000 0.000 -0.012 1.837 -0.352
78 88 0.050 0.117 -1.967 0.048 -0.087 -0.540 0.000 0.000 -0.012 2.342 -0.263
79 88 -54.659 -91.084 0.557 0.056 -0.060 -0.266 0.000 0.000 -0.015 2.746 -0.073
80 97 6.411 2.701 -0.674 0.020 -0.187 -0.585 0.000 0.000 -0.013 0.988 -0.420
M DIC β1 β2 β3 β4 β5 β6 β7 β8 β9 β10 β11
81 88 0.157 0.245 0.005 0.497 -0.276 -0.105 -0.005 -0.010 -0.129 0.636 -0.011
82 97 -0.158 -0.340 0.555 -0.207 0.463 0.120 0.022 0.023 0.084 0.472 -0.025
83 90 0.884 1.432 0.294 -0.259 0.290 0.111 0.012 0.021 0.080 -1.840 -0.017
84 93 0.184 0.265 0.510 -0.236 0.417 0.139 0.016 0.025 0.076 -0.362 -0.025
85 103 -0.079 -0.449 1.934 -0.290 0.348 -0.017 0.041 0.037 0.134 -0.632 -0.013
86 90 0.659 1.869 0.630 -0.328 0.241 0.038 0.024 0.029 0.101 -2.242 -0.011
87 99 0.116 0.363 1.469 -0.311 0.329 0.016 0.038 0.041 0.123 -1.153 -0.014
88 100 -0.139 -0.384 -0.545 -0.202 0.543 0.108 0.031 0.026 0.093 1.506 -0.027
89 90 0.805 1.627 -0.250 -0.272 0.317 0.099 0.017 0.023 0.085 -1.425 -0.017
90 96 0.163 0.307 -0.494 -0.222 0.477 0.121 0.026 0.030 0.084 0.546 -0.026
91 94 -0.019 -0.498 -0.170 4.397 -0.833 0.269 0.037 0.013 0.162 -2.339 -0.013
92 86 0.456 1.861 -0.255 3.612 -0.610 -0.092 0.017 0.012 0.131 -4.121 -0.006
93 90 0.063 0.406 -0.151 4.208 -0.746 0.073 0.031 0.016 0.146 -3.027 -0.013
94 88 -0.077 -0.375 2.892 4.050 -0.266 0.073 0.014 0.013 0.149 -5.469 0.002
95 85 0.694 1.304 1.746 3.343 -0.421 -0.284 0.005 0.014 0.126 -5.519 -0.001
96 86 0.109 0.292 2.689 3.905 -0.198 -0.053 0.010 0.016 0.140 -5.904 0.001
97 91 -0.011 -0.492 0.554 4.831 -0.363 0.353 0.034 0.014 0.174 -4.084 -0.004
98 85 0.503 1.726 0.401 3.757 -0.414 -0.117 0.013 0.014 0.135 -5.012 -0.002
99 89 0.060 0.388 0.502 4.687 -0.256 0.203 0.028 0.017 0.156 -4.775 -0.005
100 98 -0.072 -0.477 0.404 0.474 -0.461 -0.070 0.039 0.021 0.121 1.054 -0.024
101 88 0.493 2.025 0.043 0.563 -0.279 -0.059 0.026 0.018 0.114 -1.925 -0.013
102 94 0.106 0.394 0.359 0.497 -0.404 -0.089 0.034 0.023 0.110 0.003 -0.023
103 94 0.000 -0.527 4.250 0.941 -0.145 0.077 0.040 0.024 0.178 -3.828 0.000
104 86 0.420 1.904 2.648 0.775 -0.102 -0.002 0.018 0.018 0.141 -4.810 -0.001
105 90 0.053 0.411 3.926 0.909 -0.125 0.052 0.037 0.028 0.165 -4.446 -0.001
106 99 -0.016 -0.569 -0.133 0.613 -0.464 -0.002 0.053 0.026 0.147 1.379 -0.022
107 88 0.375 2.235 0.121 0.641 -0.253 -0.035 0.029 0.018 0.125 -2.239 -0.010
108 96 0.067 0.462 -0.145 0.600 -0.418 -0.029 0.046 0.027 0.129 0.293 -0.021
109 101 -0.161 -0.328 0.532 -0.133 0.548 0.088 -0.114 -0.115 -0.437 1.148 -0.025
110 93 0.841 1.474 0.236 -0.207 0.366 0.075 -0.072 -0.105 -0.468 -1.120 -0.016
111 97 0.174 0.274 0.431 -0.168 0.506 0.096 -0.078 -0.128 -0.416 0.337 -0.023
112 105 -0.100 -0.389 2.598 -0.193 0.474 -0.101 -0.220 -0.245 -0.663 -0.144 -0.008
113 93 0.685 1.689 1.450 -0.258 0.312 -0.024 -0.124 -0.166 -0.560 -1.991 -0.007
114 105 -0.127 -0.387 -0.393 -0.123 0.634 0.032 -0.167 -0.157 -0.488 2.208 -0.025
115 94 0.774 1.640 -0.146 -0.204 0.394 0.042 -0.107 -0.126 -0.465 -0.781 -0.015
116 101 0.160 0.296 -0.328 -0.147 0.593 0.051 -0.124 -0.169 -0.450 1.147 -0.023
117 103 0.005 -0.532 -0.050 5.037 -0.781 0.387 -0.180 -0.026 -0.852 -1.987 -0.016
118 90 0.313 2.211 -0.208 3.531 -0.740 0.028 -0.108 -0.036 -0.731 -3.249 -0.008
119 99 0.034 0.459 -0.081 4.542 -0.693 0.315 -0.139 -0.047 -0.768 -2.603 -0.016
120 92 -0.055 -0.399 3.629 4.133 -0.212 0.325 -0.098 -0.058 -0.885 -5.380 0.003
121 88 0.591 1.470 2.241 3.301 -0.459 -0.085 -0.041 -0.058 -0.737 -5.221 0.000
122 88 3.374 9.198 18.425 14.610 -2.777 -0.816 -0.139 -0.155 -3.353 -80.647 -0.005
123 89 0.028 0.157 27.304 17.531 -1.196 1.777 -0.195 -0.204 -3.689 -88.545 0.042
124 100 14.445 -158.187 1.146 23.291 -2.383 6.716 -0.678 -0.134 -4.434 -52.406 -0.172
125 89 1.957 12.862 0.879 16.500 -2.844 1.098 -0.357 -0.147 -3.547 -66.103 -0.075
126 96 0.006 0.230 1.062 21.622 -1.989 5.010 -0.542 -0.186 -3.962 -61.819 -0.168
127 105 -35.472 -131.421 37.418 0.026 -0.229 -0.168 -0.612 -0.288 -2.571 33.998 -0.628
128 92 2.831 13.070 9.366 0.038 -0.148 -0.220 -0.406 -0.202 -2.628 -14.740 -0.351
129 100 0.033 0.195 30.720 0.031 -0.213 -0.223 -0.503 -0.315 -2.344 16.865 -0.561
130 100 -1.665 -144.610 40.987 0.069 -0.102 0.649 -0.806 -0.433 -4.280 -43.614 0.017
M DIC β1 β2 β3 β4 β5 β6 β7 β8 β9 β10 β11
131 90 2.045 12.840 25.021 0.059 -0.065 0.170 -0.408 -0.261 -3.473 -62.270 0.007
132 97 0.015 0.205 38.269 0.067 -0.091 0.531 -0.656 -0.459 -3.901 -55.147 0.018
133 104 -9.943 -159.736 -0.371 0.037 -0.247 0.192 -0.900 -0.398 -3.096 46.936 -0.537
134 92 1.841 15.080 0.218 0.045 -0.138 0.010 -0.526 -0.248 -2.955 -17.268 -0.271
135 103 0.021 0.228 -0.372 0.035 -0.231 0.091 -0.773 -0.431 -2.706 27.826 -0.505
136 100 -64.283 -98.718 30.280 -239.381 164.063 2.472 -0.001 0.000 -0.011 13.009 -0.525
137 92 4.676 9.242 11.987 -355.710 111.849 2.234 0.000 0.000 -0.011 -22.975 -0.348
138 97 0.051 0.140 25.887 -292.537 151.536 2.845 0.000 0.000 -0.011 0.038 -0.501
139 101 -43.910 -110.440 18.766 -335.381 135.326 -2.715 -0.001 0.000 -0.016 -10.058 -0.143
140 92 4.001 10.100 10.562 -405.515 85.025 -0.181 -0.001 0.000 -0.013 -37.221 -0.164
141 98 0.041 0.152 18.254 -363.593 123.636 -1.902 -0.001 0.000 -0.015 -23.458 -0.153
142 103 -54.229 -110.129 -0.512 -220.706 185.320 0.779 -0.001 0.000 -0.013 23.983 -0.493
143 93 4.278 10.281 -0.136 -355.745 112.006 1.478 -0.001 0.000 -0.012 -20.209 -0.320
144 99 0.047 0.151 -0.467 -253.765 169.958 1.475 -0.001 0.000 -0.012 8.968 -0.483
145 100 0.952 -152.575 -6.427 18.641 -4.520 2.722 -0.001 0.000 -0.019 -28.823 -0.362
146 91 2.162 12.762 -15.399 14.744 -3.814 -0.463 0.000 0.000 -0.016 -56.701 -0.159
147 96 0.011 0.225 -8.515 17.941 -3.600 1.725 -0.001 0.000 -0.017 -43.143 -0.322
148 92 -28.220 -111.875 25.520 16.591 -1.516 1.854 0.000 0.000 -0.018 -79.164 0.047
149 88 3.541 9.230 15.312 13.643 -2.650 -1.939 0.000 0.000 -0.015 -80.962 -0.008
150 89 0.094 0.323 2.870 3.653 -0.198 0.042 -0.011 -0.008 -0.165 -5.598 0.001
151 98 0.013 -0.544 0.553 4.497 -0.355 0.516 -0.040 -0.005 -0.206 -3.421 -0.006
152 90 0.416 1.912 0.414 3.459 -0.378 0.009 -0.015 -0.006 -0.159 -4.648 -0.002
153 94 0.034 0.448 0.503 4.354 -0.293 0.336 -0.029 -0.007 -0.186 -4.151 -0.005
154 102 -0.068 -0.484 0.377 0.327 -0.487 -0.038 -0.043 -0.013 -0.148 1.604 -0.024
155 92 0.461 2.106 0.042 0.463 -0.295 -0.043 -0.026 -0.009 -0.138 -1.546 -0.013
156 99 0.098 0.402 0.326 0.386 -0.445 -0.049 -0.032 -0.014 -0.135 0.489 -0.022
157 97 -0.020 -0.489 4.254 0.708 -0.212 0.111 -0.047 -0.019 -0.205 -3.077 0.001
158 90 0.422 1.905 2.638 0.644 -0.137 0.009 -0.021 -0.011 -0.164 -4.281 0.000
159 95 0.057 0.400 4.028 0.699 -0.179 0.091 -0.035 -0.022 -0.185 -3.851 0.001
160 103 -0.021 -0.564 -0.042 0.401 -0.514 0.049 -0.061 -0.020 -0.174 1.971 -0.019
161 92 0.341 2.307 0.174 0.527 -0.260 -0.005 -0.030 -0.011 -0.152 -1.876 -0.010
162 99 0.061 0.464 -0.005 0.431 -0.456 0.028 -0.049 -0.021 -0.160 0.731 -0.018
163 101 -93.952 -62.678 54.961 -195.217 165.091 6.263 65.870 272.379 96.467 1.597 -0.591
164 87 5.427 6.473 -3.838 -424.376 28.994 2.381 -11.284 242.350 130.135 -41.724 -0.143
165 92 0.063 0.110 33.684 -321.038 118.653 5.328 48.194 276.551 98.966 -13.008 -0.454
166 90 -69.226 -72.728 22.819 -503.951 -2.989 -0.093 27.816 322.431 163.093 -53.042 0.095
167 87 5.651 5.899 -0.333 -427.796 34.125 2.765 -14.179 235.058 127.130 -40.875 -0.167
168 86 0.054 0.104 15.411 -531.713 10.167 1.264 2.256 320.391 146.315 -50.507 -0.002
169 126 -59.114 -73.408 2.815 -27.819 81.631 3.391 82.620 343.908 175.479 -24.558 -0.094
170 87 5.462 6.069 0.221 -435.914 20.746 2.194 -11.900 238.974 132.530 -45.072 -0.111
171 102 0.052 0.155 -0.219 -267.150 169.543 4.608 176.198 534.729 126.685 0.574 -0.396
172 87 -45.547 -95.200 -25.406 13.793 -2.345 -0.806 50.789 142.125 185.570 -45.151 -0.016
173 88 5.774 4.507 -9.127 8.510 -6.287 -5.958 -32.644 255.969 143.462 -44.209 -0.058
174 85 0.047 0.116 -18.823 12.091 -3.617 -3.491 18.869 206.585 163.380 -46.321 -0.047
175 87 -59.865 -85.596 6.377 11.149 -4.744 -3.227 36.127 155.422 160.737 -38.963 -0.077
176 87 5.316 6.097 -3.408 8.795 -7.161 -5.931 -7.708 206.177 135.022 -35.142 -0.183
177 86 0.052 0.107 2.731 10.745 -5.305 -4.785 7.757 211.701 147.996 -39.911 -0.139
178 86 -53.927 -88.050 0.565 12.299 -3.603 -2.109 38.561 179.412 171.139 -43.352 -0.024
179 87 5.765 4.966 -0.037 7.979 -7.060 -6.352 -33.451 238.497 133.311 -38.753 -0.137
180 85 0.050 0.109 0.347 11.299 -4.972 -4.424 3.717 217.470 153.335 -43.039 -0.091
M DIC β1 β2 β3 β4 β5 β6 β7 β8 β9 β10 β11
181 113 -38.232 -84.029 40.850 0.124 -0.007 0.027 59.829 189.670 201.728 -33.259 -0.314
182 87 4.063 7.372 -25.966 0.052 -0.026 -0.204 14.996 184.969 174.461 -52.039 0.010
183 94 0.026 0.203 19.049 0.059 -0.095 -0.221 187.094 192.628 168.123 -13.321 -0.465
184 86 -51.427 -89.960 15.202 0.052 -0.038 -0.155 31.933 165.380 181.055 -46.548 0.008
185 87 5.129 6.196 -2.371 0.037 -0.073 -0.478 -10.174 193.861 142.269 -38.034 -0.196
186 85 0.046 0.120 8.887 0.049 -0.048 -0.285 23.437 198.978 164.813 -44.399 -0.093
187 98 -5.363 -118.215 2.297 0.106 0.043 0.517 169.758 228.806 272.700 -64.781 0.140
188 88 5.498 3.953 0.358 0.041 -0.045 -0.406 -54.264 199.602 155.281 -52.403 -0.042
189 88 0.024 0.179 1.320 0.073 0.004 0.132 116.625 234.402 207.325 -53.318 0.058
190 106 -102.861 -55.473 61.645 -50.622 185.860 6.663 0.302 -0.189 -0.642 -0.420 -0.578
191 89 5.142 7.710 1.921 -349.130 71.063 2.191 -0.015 -0.227 -2.120 -29.593 -0.200
192 98 0.066 0.107 39.009 -202.481 152.779 5.353 0.231 -0.233 -0.953 -9.816 -0.480
193 95 -67.749 -69.901 28.853 -399.880 24.989 -1.877 -0.052 -0.393 -2.873 -48.898 0.152
194 89 5.429 6.010 5.476 -404.972 47.223 1.395 0.005 -0.231 -2.503 -39.082 -0.119
195 90 0.053 0.100 21.009 -433.532 32.125 -0.418 0.036 -0.370 -2.633 -46.535 0.031
196 128 -75.761 -59.213 3.573 52.946 111.430 3.298 0.289 -0.449 -1.662 -20.666 -0.120
197 90 5.034 8.107 0.231 -370.816 67.066 1.505 -0.044 -0.268 -2.184 -32.084 -0.137
198 110 0.060 0.145 -0.269 -38.030 231.496 2.948 0.331 -0.554 0.137 -0.613 -0.301
199 93 -32.572 -105.281 -30.208 15.826 0.632 1.225 -0.102 -0.007 -3.587 -50.395 -0.022
200 89 4.548 6.880 -20.014 9.745 -5.218 -2.535 -0.058 -0.204 -3.099 -41.344 -0.042
201 88 0.034 0.146 -26.021 13.927 -1.767 -0.588 -0.046 -0.109 -3.299 -47.647 -0.037
202 89 -52.771 -89.431 11.285 11.397 -3.982 -1.632 -0.142 -0.122 -3.224 -39.873 -0.046
203 90 4.988 6.327 1.736 8.652 -6.743 -4.469 -0.011 -0.174 -2.806 -35.177 -0.154
204 88 0.049 0.108 8.916 10.349 -5.328 -2.752 -0.009 -0.198 -3.010 -40.162 -0.092
205 90 -42.193 -96.886 0.903 13.776 -1.427 0.166 -0.166 -0.116 -3.565 -47.160 0.023
206 88 5.033 6.010 0.375 8.794 -6.565 -3.298 -0.027 -0.224 -2.921 -38.645 -0.080
207 87 0.041 0.129 0.697 12.368 -3.806 -1.410 -0.037 -0.177 -3.175 -44.950 -0.025
208 122 -46.156 -71.743 72.545 0.153 0.029 -0.062 0.133 -0.099 -3.296 -32.009 -0.203
209 89 3.307 10.764 -10.636 0.045 -0.060 -0.198 -0.068 -0.112 -2.795 -35.857 -0.133
210 103 0.029 0.180 48.978 0.087 -0.052 -0.258 0.220 -0.047 -2.014 -23.990 -0.439
211 91 -45.613 -90.187 23.362 0.053 -0.026 0.067 -0.171 -0.161 -3.541 -49.058 0.086
212 89 4.654 6.804 3.911 0.039 -0.069 -0.329 -0.025 -0.139 -2.984 -38.827 -0.138
213 88 0.040 0.131 16.350 0.050 -0.041 -0.097 -0.087 -0.175 -3.258 -46.332 -0.019
214 118 -36.222 -79.414 4.127 0.203 0.062 0.031 -0.016 -0.200 -3.708 -104.716 0.053
215 88 3.789 8.362 0.759 0.049 -0.037 -0.126 -0.068 -0.166 -3.241 -46.678 -0.023
216 107 0.018 0.178 2.846 0.139 0.062 0.334 0.035 -0.215 -3.203 -87.021 0.103
217 105 -94.443 -60.153 56.491 -106.844 181.108 6.173 0.000 0.000 -0.008 4.517 -0.605
218 90 5.111 7.286 -5.923 -375.598 47.095 1.667 0.000 0.000 -0.012 -35.784 -0.142
219 97 0.061 0.113 33.633 -233.594 137.005 5.041 0.000 0.000 -0.008 -8.619 -0.467
220 93 -68.080 -73.241 22.488 -394.577 32.356 -1.171 0.000 0.000 -0.014 -43.509 0.081
221 90 5.436 5.969 1.149 -390.189 41.417 2.288 0.000 0.000 -0.011 -39.076 -0.160
222 90 0.052 0.106 15.368 -429.556 35.823 0.290 0.000 0.000 -0.013 -42.718 -0.022
223 123 -72.469 -65.638 1.588 78.592 217.247 1.718 -0.001 0.000 -0.013 1.625 -0.156
224 90 5.191 6.580 0.314 -397.264 38.297 1.279 0.000 0.000 -0.012 -39.982 -0.111
225 105 0.049 0.155 0.308 -152.312 195.362 1.181 -0.001 0.000 -0.010 0.929 -0.220
226 92 -38.684 -103.586 -24.858 14.007 -0.622 -0.540 0.000 0.000 -0.016 -46.564 -0.025
227 90 5.158 5.705 -13.439 8.202 -6.373 -3.669 0.000 0.000 -0.013 -40.740 -0.054
228 89 0.040 0.135 -19.911 11.991 -2.632 -2.259 0.000 0.000 -0.014 -45.701 -0.055
229 91 -57.067 -85.851 8.212 10.553 -4.148 -2.190 0.000 0.000 -0.014 -39.553 -0.060
230 90 5.066 6.598 -1.738 8.123 -6.829 -5.212 0.000 0.000 -0.012 -34.390 -0.186
M DIC β1 β2 β3 β4 β5 β6 β7 β8 β9 β10 β11
231 89 0.047 0.121 4.651 10.092 -4.957 -3.898 0.000 0.000 -0.013 -39.603 -0.114
232 90 -48.779 -94.532 0.662 12.205 -2.298 -1.126 0.000 0.000 -0.015 -44.665 -0.003
233 90 5.327 5.566 0.150 7.602 -6.952 -4.743 0.000 0.000 -0.013 -37.710 -0.107
234 88 0.045 0.123 0.482 10.860 -4.117 -2.958 0.000 0.000 -0.014 -43.391 -0.072
235 120 -40.263 -82.021 51.911 0.145 0.018 -0.116 0.000 0.000 -0.017 -37.029 -0.217
236 89 3.723 8.823 -20.937 0.046 -0.037 -0.171 0.000 0.000 -0.014 -45.761 -0.043
237 102 0.021 0.218 34.572 0.066 -0.071 -0.289 0.000 0.000 -0.013 -15.496 -0.506
238 91 -46.233 -94.930 17.647 0.049 -0.032 -0.034 0.000 0.000 -0.016 -45.070 0.019
239 90 4.751 6.868 -0.783 0.037 -0.065 -0.444 0.000 0.000 -0.013 -38.922 -0.174
240 88 0.041 0.134 11.185 0.047 -0.038 -0.222 0.000 0.000 -0.014 -45.225 -0.065
241 114 -18.948 -99.670 3.180 0.153 0.065 0.330 0.000 0.000 -0.020 -90.068 0.147
242 90 4.969 5.465 0.419 0.040 -0.043 -0.343 0.000 0.000 -0.014 -49.163 -0.052
243 96 0.010 0.219 1.743 0.076 0.016 0.440 -0.001 0.000 -0.018 -53.444 0.098
App
endix
VI:
DR
AG
Est
imati
on
===============================================================================================================================
I.
BETA
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
ELASTICITY
S(y)
(EP)
VARIANT
=M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
(COND.
T-STATISTIC)
VERSION
=0
11
11
11
11
1
DEP.VAR.
=AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
===============================================================================================================================
comtot
.10E+01
.96E+00
.95E+00
.98E+00
.13E+01
.89E+00
.88E+00
.91E+00
.12E+01
.83E+00
.284
.285
.278
.286
.282
.201
.279
.287
.283
.202
(1.63)
(1.63)
(1.60)
(1.64)
(1.61)
(1.15)
(1.60)
(1.65)
(1.62)
(1.16)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
conalc
-.53E+01
-.50E+01
-.48E+01
-.51E+01
-.67E+01
-.64E+01
-.46E+01
-.48E+01
-.63E+01
-.61E+01
-.341
-.341
-.306
-.341
-.341
-.341
-.306
-.341
-.341
-.342
(-6.75)
(-6.75)
(-6.04)
(-6.76)
(-6.72)
(-6.77)
(-6.04)
(-6.76)
(-6.72)
(-6.77)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
dlab
.65E+00
.59E+00
.56E+00
.60E+00
.60E+00
.80E+00
.51E+00
.54E+00
.55E+00
.73E+00
.812
.812
.815
.809
.633
.810
.815
.809
.633
.810
(5.35)
(5.35)
(5.36)
(5.33)
(4.17)
(5.33)
(5.35)
(5.33)
(4.17)
(5.33)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
parser
-.17E+02
-.15E+02
-.18E+02
-.16E+02
-.22E+02
-.20E+02
-.16E+02
-.15E+02
-.20E+02
-.19E+02
-.624
-.600
-.625
-.624
-.628
-.622
-.601
-.599
-.604
-.597
(-5.04)
(-4.84)
(-5.04)
(-5.04)
(-5.09)
(-5.03)
(-4.84)
(-4.83)
(-4.89)
(-4.83)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
rcp
-.29E-01
-.26E-01
-.23E-01
-.26E-01
-.33E-01
-.36E-01
-.21E-01
-.23E-01
-.30E-01
-.32E-01
===
-.094
-.094
-.093
-.094
-.095
-.094
-.094
-.094
-.095
-.095
(-2.16)
(-2.16)
(-2.15)
(-2.14)
(-2.17)
(-2.17)
(-2.15)
(-2.15)
(-2.18)
(-2.17)
susp
-.12E+01
-.11E+01
-.11E+01
-.94E+00
-.14E+01
-.14E+01
-.10E+01
-.88E+00
-.13E+01
-.13E+01
-.187
-.187
-.188
-.161
-.185
-.187
-.188
-.161
-.185
-.187
(-2.83)
(-2.84)
(-2.84)
(-2.44)
(-2.80)
(-2.84)
(-2.85)
(-2.44)
(-2.80)
(-2.84)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
-------------------------------------------------------------------------------------------------------------------------------
REGRESSION
CONSTANT
CONSTANT
.70E+02
.64E+02
.68E+02
.66E+02
.88E+02
.85E+02
.62E+02
.61E+02
.80E+02
.78E+02
--
--
--
--
--
(7.17)
(6.96)
(6.96)
(7.11)
(7.17)
(7.18)
(6.76)
(6.91)
(6.96)
(6.97)
===============================================================================================================================
===============================================================================================================================
II.
PARAMETERS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
(COND.
T-STATISTIC)
VERSION
=0
11
11
11
11
1
DEP.VAR.
=AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
===============================================================================================================================
------------------------------------------------------------------
BOX-COX
TRANSFORMATIONS:
UNCOND:
[T-STATISTIC=0]
/[T-STATISTIC=1]
------------------------------------------------------------------
LAMBDA(Y)
-GROUP
1LAM
1-.317
-.321
-.335
-.322
-.324
-.316
-.340
-.326
-.329
-.320
[-1.73]
[-1.73]
[-1.67]
[-1.75]
[-1.69]
[-1.72]
[-1.67]
[-1.75]
[-1.69]
[-1.72]
[-7.19]
[-7.11]
[-6.67]
[-7.18]
[-6.92]
[-7.17]
[-6.59]
[-7.10]
[-6.84]
[-7.09]
LAMBDA(X)
-GROUP
1LAM
1-.317
-.321
-.335
-.322
-.324
-.316
-.340
-.326
-.329
-.320
[-1.73]
[-1.73]
[-1.67]
[-1.75]
[-1.69]
[-1.72]
[-1.67]
[-1.75]
[-1.69]
[-1.72]
[-7.19]
[-7.11]
[-6.67]
[-7.18]
[-6.92]
[-7.17]
[-6.59]
[-7.10]
[-6.84]
[-7.09]
---------------
AUTOCORRELATION
---------------
ORDER
1RHO
1.303
.303
.302
.303
.303
.302
.302
.303
.303
.303
(2.99)
(2.99)
(3.00)
(2.98)
(3.01)
(2.99)
(2.99)
(2.98)
(3.01)
(2.99)
ORDER
2RHO
2.168
.169
.166
.170
.166
.168
.166
.170
.167
.168
(1.57)
(1.57)
(1.55)
(1.58)
(1.55)
(1.56)
(1.55)
(1.59)
(1.55)
(1.56)
===============================================================================================================================
III.GENERAL
STATISTICS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
VERSION
=0
11
11
11
11
1
DEP.VAR.
=AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
===============================================================================================================================
LOG-LIKELIHOOD
-291.727
-326.398
-339.667
-321.721
-228.495
-214.177
-374.340
-356.392
-263.167
-248.849
PSEUDO-R2
:-
(E)
.933
.933
.928
.932
.932
.935
.927
.931
.932
.934
-(L)
.945
.944
.940
.943
.944
.947
.939
.942
.944
.946
-(E)
ADJUSTED
FOR
D.F.
.928
.927
.922
.926
.927
.930
.921
.925
.926
.929
-(L)
ADJUSTED
FOR
D.F.
.941
.940
.935
.939
.940
.943
.934
.938
.939
.942
AVERAGE
PROBABILITY
(Y=LIMIT
OBSERV.)
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
SAMPLE
:-
NUMBER
OF
OBSERVATIONS
118
118
118
118
118
118
118
118
118
118
-FIRST
OBSERVATION
33
33
33
33
33
-LAST
OBSERVATION
120
120
120
120
120
120
120
120
120
120
NUMBER
OF
ESTIMATED
PARAMETERS
:
-FIXED
PART
:
.BETAS
77
77
77
77
77
.BOX-COX
11
11
11
11
11
.ASSOCIATED
DUMMIES
00
00
00
00
00
-AUTOCORRELATION
22
22
22
22
22
-HETEROSKEDASTICITY
:
.DELTAS
00
00
00
00
00
.BOX-COX
00
00
00
00
00
.ASSOCIATED
DUMMIES
00
00
00
00
00
===============================================================================================================================
=================================================================================================================================================
I.
BETA
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
ELASTICITY
S(y)
(EP)
VARIANT
=M11
M12
M13
M14
M15
M16
M17
M18
M19
M20
M21
M22
(COND.
T-STATISTIC)
VERSION
=1
11
11
11
11
11
1
DEP.VAR.
=AC11
AC12
AC13
AC14
AC15
AC16
AC17
AC18
AC19
AC20
AC21
AC22
=================================================================================================================================================
-----------
INDEPENDENT
-----------
comtot
.90E+00
.12E+01
.83E+00
.12E+01
.86E+00
.11E+01
.83E+00
.11E+01
.77E+00
.11E+01
.10E+01
.80E+00
.281
.276
.196
.285
.204
.198
.282
.277
.197
.286
.200
.205
(1.61)
(1.58)
(1.12)
(1.63)
(1.17)
(1.13)
(1.62)
(1.58)
(1.12)
(1.63)
(1.14)
(1.17)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
conalc
-.47E+01
-.62E+01
-.60E+01
-.65E+01
-.62E+01
-.82E+01
-.44E+01
-.59E+01
-.57E+01
-.61E+01
-.78E+01
-.59E+01
-.307
-.306
-.307
-.341
-.342
-.341
-.307
-.306
-.307
-.341
-.342
-.342
(-6.05)
(-6.02)
(-6.07)
(-6.73)
(-6.79)
(-6.74)
(-6.05)
(-6.02)
(-6.07)
(-6.73)
(-6.74)
(-6.79)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
dlab
.51E+00
.53E+00
.70E+00
.55E+00
.74E+00
.74E+00
.46E+00
.47E+00
.63E+00
.50E+00
.68E+00
.67E+00
.812
.637
.814
.630
.807
.632
.812
.637
.814
.630
.632
.807
(5.34)
(4.18)
(5.34)
(4.15)
(5.32)
(4.16)
(5.34)
(4.18)
(5.34)
(4.15)
(4.15)
(5.31)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
parser
-.17E+02
-.23E+02
-.22E+02
-.21E+02
-.20E+02
-.26E+02
-.16E+02
-.21E+02
-.20E+02
-.19E+02
-.24E+02
-.18E+02
-.625
-.630
-.623
-.628
-.621
-.626
-.601
-.605
-.599
-.604
-.602
-.597
(-5.04)
(-5.09)
(-5.03)
(-5.09)
(-5.02)
(-5.08)
(-4.83)
(-4.89)
(-4.82)
(-4.88)
(-4.87)
(-4.82)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
rcp
-.21E-01
-.27E-01
-.29E-01
-.30E-01
-.32E-01
-.42E-01
-.18E-01
-.24E-01
-.26E-01
-.27E-01
-.38E-01
-.29E-01
===
-.093
-.094
-.094
-.094
-.094
-.095
-.093
-.094
-.094
-.094
-.095
-.094
(-2.13)
(-2.16)
(-2.16)
(-2.16)
(-2.15)
(-2.18)
(-2.14)
(-2.17)
(-2.16)
(-2.16)
(-2.19)
(-2.16)
susp
-.92E+00
-.14E+01
-.14E+01
-.12E+01
-.12E+01
-.17E+01
-.85E+00
-.13E+01
-.13E+01
-.11E+01
-.16E+01
-.11E+01
-.162
-.185
-.188
-.158
-.161
-.185
-.162
-.186
-.188
-.158
-.185
-.161
(-2.44)
(-2.81)
(-2.84)
(-2.40)
(-2.44)
(-2.80)
(-2.45)
(-2.81)
(-2.85)
(-2.41)
(-2.81)
(-2.44)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
-------------------------------------------------------------------------------------------------------------------------------------------------
REGRESSION
CONSTANT
CONSTANT
.65E+02
.87E+02
.85E+02
.84E+02
.82E+02
.11E+03
.59E+02
.80E+02
.77E+02
.77E+02
.99E+02
.75E+02
--
--
--
--
--
--
(6.91)
(6.96)
(6.97)
(7.11)
(7.12)
(7.20)
(6.70)
(6.75)
(6.76)
(6.90)
(6.99)
(6.91)
=================================================================================================================================================
=================================================================================================================================================
II.
PARAMETERS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M11
M12
M13
M14
M15
M16
M17
M18
M19
M20
M21
M22
(COND.
T-STATISTIC)
VERSION
=1
11
11
11
11
11
1
DEP.VAR.
=AC11
AC12
AC13
AC14
AC15
AC16
AC17
AC18
AC19
AC20
AC21
AC22
=================================================================================================================================================
------------------------------------------------------------------
BOX-COX
TRANSFORMATIONS:
UNCOND:
[T-STATISTIC=0]
/[T-STATISTIC=1]
------------------------------------------------------------------
LAMBDA(Y)
-GROUP
1LAM
1-.341
-.344
-.334
-.330
-.321
-.323
-.346
-.349
-.339
-.335
-.327
-.325
[-1.69]
[-1.64]
[-1.66]
[-1.72]
[-1.74]
[-1.68]
[-1.69]
[-1.64]
[-1.66]
[-1.71]
[-1.68]
[-1.74]
[-6.65]
[-6.41]
[-6.65]
[-6.91]
[-7.16]
[-6.90]
[-6.58]
[-6.33]
[-6.57]
[-6.83]
[-6.82]
[-7.08]
LAMBDA(X)
-GROUP
1LAM
1-.341
-.344
-.334
-.330
-.321
-.323
-.346
-.349
-.339
-.335
-.327
-.325
[-1.69]
[-1.64]
[-1.66]
[-1.72]
[-1.74]
[-1.68]
[-1.69]
[-1.64]
[-1.66]
[-1.71]
[-1.68]
[-1.74]
[-6.65]
[-6.41]
[-6.65]
[-6.91]
[-7.16]
[-6.90]
[-6.58]
[-6.33]
[-6.57]
[-6.83]
[-6.82]
[-7.08]
---------------
AUTOCORRELATION
---------------
ORDER
1RHO
1.302
.303
.302
.303
.303
.303
.302
.303
.302
.303
.303
.303
(2.99)
(3.01)
(2.99)
(3.00)
(2.98)
(3.01)
(2.99)
(3.01)
(2.99)
(3.00)
(3.01)
(2.98)
ORDER
2RHO
2.167
.164
.165
.168
.169
.166
.168
.164
.166
.169
.166
.170
(1.56)
(1.53)
(1.54)
(1.56)
(1.57)
(1.54)
(1.57)
(1.53)
(1.54)
(1.57)
(1.55)
(1.58)
=================================================================================================================================================
III.GENERAL
STATISTICS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M11
M12
M13
M14
M15
M16
M17
M18
M19
M20
M21
M22
VERSION
=1
11
11
11
11
11
1
DEP.VAR.
=AC11
AC12
AC13
AC14
AC15
AC16
AC17
AC18
AC19
AC20
AC21
AC22
=================================================================================================================================================
LOG-LIKELIHOOD
-369.659
-276.433
-262.116
-258.485
-244.170
-150.950
-404.331
-311.107
-296.790
-293.157
-185.623
-278.842
PSEUDO-R2
:-
(E)
.926
.927
.930
.930
.933
.934
.925
.926
.929
.930
.933
.932
-(L)
.938
.939
.942
.942
.945
.946
.937
.938
.941
.941
.945
.944
-(E)
ADJUSTED
FOR
D.F.
.920
.921
.924
.925
.928
.929
.919
.920
.923
.924
.928
.927
-(L)
ADJUSTED
FOR
D.F.
.933
.934
.937
.938
.941
.942
.931
.933
.936
.937
.941
.940
AVERAGE
PROBABILITY
(Y=LIMIT
OBSERV.)
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
SAMPLE
:-
NUMBER
OF
OBSERVATIONS
118
118
118
118
118
118
118
118
118
118
118
118
-FIRST
OBSERVATION
33
33
33
33
33
33
-LAST
OBSERVATION
120
120
120
120
120
120
120
120
120
120
120
120
NUMBER
OF
ESTIMATED
PARAMETERS
:
-FIXED
PART
:
.BETAS
77
77
77
77
77
77
.BOX-COX
11
11
11
11
11
11
.ASSOCIATED
DUMMIES
00
00
00
00
00
00
-AUTOCORRELATION
22
22
22
22
22
22
-HETEROSKEDASTICITY
:
.DELTAS
00
00
00
00
00
00
.BOX-COX
00
00
00
00
00
00
.ASSOCIATED
DUMMIES
00
00
00
00
00
00
=================================================================================================================================================
===============================================================================================================================
I.
BETA
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
ELASTICITY
S(y)
(EP)
VARIANT
=M23
M24
M25
M26
M27
M28
M29
M30
M31
M32
(COND.
T-STATISTIC)
VERSION
=1
11
11
21
11
1
DEP.VAR.
=AC23
AC24
AC25
AC27
AC27
AC28
AC29
AC30
AC31
AC32
===============================================================================================================================
-----------
INDEPENDENT
-----------
comtot
.11E+01
.79E+00
.10E+01
.10E+01
.10E+01
.74E+00
.98E+00
.97E+00
.95E+00
.91E+00
.279
.199
.193
.280
.280
.200
.196
.203
.194
.197
(1.60)
(1.14)
(1.10)
(1.60)
(1.60)
(1.14)
(1.12)
(1.16)
(1.11)
(1.13)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
conalc
-.61E+01
-.58E+01
-.77E+01
-.57E+01
-.57E+01
-.55E+01
-.76E+01
-.76E+01
-.73E+01
-.72E+01
-.307
-.307
-.307
-.307
-.307
-.307
-.307
-.342
-.307
-.308
(-6.03)
(-6.08)
(-6.04)
(-6.03)
(-6.03)
(-6.08)
(-6.05)
(-6.75)
(-6.04)
(-6.05)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
dlab
.48E+00
.64E+00
.66E+00
.43E+00
.43E+00
.58E+00
.60E+00
.62E+00
.59E+00
.54E+00
.633
.811
.635
.633
.633
.810
.632
.629
.635
.632
(4.16)
(5.33)
(4.17)
(4.16)
(4.16)
(5.32)
(4.15)
(4.14)
(4.17)
(4.15)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
parser
-.23E+02
-.21E+02
-.29E+02
-.21E+02
-.21E+02
-.20E+02
-.28E+02
-.24E+02
-.26E+02
-.26E+02
-.630
-.623
-.627
-.606
-.606
-.598
-.627
-.602
-.603
-.603
(-5.09)
(-5.02)
(-5.08)
(-4.89)
(-4.89)
(-4.82)
(-5.07)
(-4.87)
(-4.87)
(-4.87)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
rcp
-.24E-01
-.26E-01
-.34E-01
-.21E-01
-.21E-01
-.23E-01
-.31E-01
-.34E-01
-.31E-01
-.27E-01
===
-.093
-.093
-.094
-.094
-.094
-.093
-.094
-.095
-.094
-.094
(-2.15)
(-2.14)
(-2.17)
(-2.15)
(-2.15)
(-2.15)
(-2.16)
(-2.17)
(-2.18)
(-2.16)
susp
-.11E+01
-.11E+01
-.17E+01
-.11E+01
-.11E+01
-.11E+01
-.14E+01
-.13E+01
-.16E+01
-.13E+01
-.159
-.162
-.185
-.159
-.159
-.162
-.159
-.159
-.186
-.159
(-2.41)
(-2.45)
(-2.81)
(-2.41)
(-2.41)
(-2.45)
(-2.41)
(-2.41)
(-2.81)
(-2.42)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
-------------------------------------------------------------------------------------------------------------------------------
REGRESSION
CONSTANT
CONSTANT
.84E+02
.81E+02
.11E+03
.76E+02
.76E+02
.74E+02
.10E+03
.95E+02
.99E+02
.95E+02
--
--
--
--
--
(6.90)
(6.91)
(6.98)
(6.69)
(6.69)
(6.70)
(6.92)
(6.92)
(6.76)
(6.70)
===============================================================================================================================
===============================================================================================================================
II.
PARAMETERS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M23
M24
M25
M26
M27
M28
M29
M30
M31
M32
(COND.
T-STATISTIC)
VERSION
=1
11
11
21
11
1
DEP.VAR.
=AC23
AC24
AC25
AC27
AC27
AC28
AC29
AC30
AC31
AC32
===============================================================================================================================
------------------------------------------------------------------
BOX-COX
TRANSFORMATIONS:
UNCOND:
[T-STATISTIC=0]
/[T-STATISTIC=1]
------------------------------------------------------------------
LAMBDA(Y)
-GROUP
1LAM
1-.351
-.340
-.342
-.356
-.356
-.345
-.349
-.333
-.347
-.354
[-1.66]
[-1.68]
[-1.63]
[-1.66]
[-1.66]
[-1.68]
[-1.65]
[-1.70]
[-1.63]
[-1.65]
[-6.40]
[-6.63]
[-6.39]
[-6.33]
[-6.33]
[-6.56]
[-6.38]
[-6.81]
[-6.32]
[-6.30]
LAMBDA(X)
-GROUP
1LAM
1-.351
-.340
-.342
-.356
-.356
-.345
-.349
-.333
-.347
-.354
[-1.66]
[-1.68]
[-1.63]
[-1.66]
[-1.66]
[-1.68]
[-1.65]
[-1.70]
[-1.63]
[-1.65]
[-6.40]
[-6.63]
[-6.39]
[-6.33]
[-6.33]
[-6.56]
[-6.38]
[-6.81]
[-6.32]
[-6.30]
---------------
AUTOCORRELATION
---------------
ORDER
1RHO
1.303
.302
.303
.303
.303
.302
.303
.303
.303
.303
(3.00)
(2.98)
(3.01)
(3.00)
(3.00)
(2.98)
(3.00)
(3.00)
(3.01)
(3.00)
ORDER
2RHO
2.166
.167
.163
.166
.166
.167
.165
.168
.164
.166
(1.54)
(1.56)
(1.52)
(1.55)
(1.55)
(1.56)
(1.54)
(1.56)
(1.52)
(1.54)
===============================================================================================================================
III.GENERAL
STATISTICS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M23
M24
M25
M26
M27
M28
M29
M30
M31
M32
VERSION
=1
11
11
21
11
1
DEP.VAR.
=AC23
AC24
AC25
AC27
AC27
AC28
AC29
AC30
AC31
AC32
===============================================================================================================================
LOG-LIKELIHOOD
-306.421
-292.107
-198.888
-341.094
-341.094
-326.780
-228.874
-215.612
-233.562
-263.548
PSEUDO-R2
:-
(E)
.925
.928
.929
.924
.924
.927
.927
.931
.928
.926
-(L)
.937
.940
.941
.936
.936
.939
.939
.943
.940
.938
-(E)
ADJUSTED
FOR
D.F.
.919
.922
.923
.917
.917
.921
.921
.926
.922
.919
-(L)
ADJUSTED
FOR
D.F.
.931
.935
.936
.930
.930
.934
.934
.939
.935
.932
AVERAGE
PROBABILITY
(Y=LIMIT
OBSERV.)
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
SAMPLE
:-
NUMBER
OF
OBSERVATIONS
118
118
118
118
118
118
118
118
118
118
-FIRST
OBSERVATION
33
33
33
33
33
-LAST
OBSERVATION
120
120
120
120
120
120
120
120
120
120
NUMBER
OF
ESTIMATED
PARAMETERS
:
-FIXED
PART
:
.BETAS
77
77
77
77
77
.BOX-COX
11
11
11
11
11
.ASSOCIATED
DUMMIES
00
00
00
00
00
-AUTOCORRELATION
22
22
22
22
22
-HETEROSKEDASTICITY
:
.DELTAS
00
00
00
00
00
.BOX-COX
00
00
00
00
00
.ASSOCIATED
DUMMIES
00
00
00
00
00
===============================================================================================================================
===============================================================================================================================
I.
BETA
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
ELASTICITY
S(y)
(EP)
VARIANT
=M33
M34
M35
M36
M37
M38
M39
M40
M41
M42
(COND.
T-STATISTIC)
VERSION
=1
11
11
11
11
1
DEP.VAR.
=AC33
AC34
AC35
AC36
AC37
AC38
AC39
AC40
AC41
AC42
===============================================================================================================================
-----------
INDEPENDENT
-----------
comtot
.40E+00
.41E+00
.38E+00
.43E+00
.34E+00
.31E+00
.39E+00
.44E+00
.35E+00
.32E+00
.629
.629
.630
.630
.627
.543
.630
.630
.627
.543
(3.80)
(3.80)
(3.83)
(3.80)
(3.81)
(3.29)
(3.83)
(3.80)
(3.81)
(3.29)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
conalc
-.72E-01
-.72E-01
-.50E-01
-.82E-01
-.56E-01
-.63E-01
-.49E-01
-.82E-01
-.56E-01
-.63E-01
-.200
-.200
-.167
-.200
-.199
-.200
-.167
-.200
-.199
-.199
(-4.28)
(-4.28)
(-3.60)
(-4.27)
(-4.29)
(-4.27)
(-3.61)
(-4.27)
(-4.29)
(-4.27)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
dlab
.90E+00
.94E+00
.99E+00
.91E+00
.66E+00
.83E+00
.11E+01
.95E+00
.69E+00
.87E+00
.779
.779
.779
.777
.606
.781
.780
.777
.606
.781
(5.31)
(5.31)
(5.32)
(5.29)
(4.13)
(5.32)
(5.33)
(5.29)
(4.14)
(5.33)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
parser
-.29E-01
-.24E-01
-.22E-01
-.35E-01
-.22E-01
-.25E-01
-.18E-01
-.28E-01
-.17E-01
-.20E-01
-.102
-.081
-.099
-.103
-.099
-.101
-.079
-.083
-.079
-.081
(-1.05)
(-.84)
(-1.03)
(-1.07)
(-1.03)
(-1.05)
(-.82)
(-.86)
(-.82)
(-.84)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
rcp
-.75E-01
-.80E-01
-.92E-01
-.74E-01
-.76E-01
-.71E-01
-.99E-01
-.78E-01
-.81E-01
-.75E-01
===
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
(-1.15)
(-1.15)
(-1.16)
(-1.15)
(-1.15)
(-1.15)
(-1.16)
(-1.15)
(-1.15)
(-1.15)
susp
-.55E-01
-.56E-01
-.50E-01
-.44E-01
-.47E-01
-.49E-01
-.51E-01
-.45E-01
-.47E-01
-.50E-01
-.107
-.107
-.108
-.079
-.109
-.107
-.108
-.079
-.109
-.108
(-1.84)
(-1.84)
(-1.86)
(-1.35)
(-1.87)
(-1.85)
(-1.86)
(-1.35)
(-1.87)
(-1.85)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
-------------------------------------------------------------------------------------------------------------------------------
REGRESSION
CONSTANT
CONSTANT
.11E+01
.12E+01
.11E+01
.12E+01
.12E+01
.10E+01
.12E+01
.13E+01
.13E+01
.11E+01
--
--
--
--
--
(.80)
(.84)
(.76)
(.84)
(.92)
(.81)
(.78)
(.87)
(.99)
(.87)
===============================================================================================================================
===============================================================================================================================
II.
PARAMETERS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M33
M34
M35
M36
M37
M38
M39
M40
M41
M42
(COND.
T-STATISTIC)
VERSION
=1
11
11
11
11
1
DEP.VAR.
=AC33
AC34
AC35
AC36
AC37
AC38
AC39
AC40
AC41
AC42
===============================================================================================================================
------------------------------------------------------------------
BOX-COX
TRANSFORMATIONS:
UNCOND:
[T-STATISTIC=0]
/[T-STATISTIC=1]
------------------------------------------------------------------
LAMBDA(Y)
-GROUP
1LAM
1.125
.129
.156
.113
.145
.130
.162
.117
.150
.134
[.35]
[.35]
[.37]
[.31]
[.38]
[.36]
[.38]
[.32]
[.39]
[.37]
[-2.43]
[-2.38]
[-2.01]
[-2.46]
[-2.26]
[-2.41]
[-1.95]
[-2.41]
[-2.22]
[-2.37]
LAMBDA(X)
-GROUP
1LAM
1.125
.129
.156
.113
.145
.130
.162
.117
.150
.134
[.35]
[.35]
[.37]
[.31]
[.38]
[.36]
[.38]
[.32]
[.39]
[.37]
[-2.43]
[-2.38]
[-2.01]
[-2.46]
[-2.26]
[-2.41]
[-1.95]
[-2.41]
[-2.22]
[-2.37]
---------------
AUTOCORRELATION
---------------
ORDER
1RHO
1.157
.156
.157
.157
.156
.156
.156
.157
.156
.156
(1.46)
(1.46)
(1.46)
(1.47)
(1.46)
(1.46)
(1.46)
(1.47)
(1.45)
(1.46)
ORDER
2RHO
2.247
.247
.248
.248
.247
.247
.248
.248
.247
.247
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
===============================================================================================================================
III.GENERAL
STATISTICS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M33
M34
M35
M36
M37
M38
M39
M40
M41
M42
VERSION
=1
11
11
11
11
1
DEP.VAR.
=AC33
AC34
AC35
AC36
AC37
AC38
AC39
AC40
AC41
AC42
===============================================================================================================================
LOG-LIKELIHOOD
-344.630
-379.310
-392.413
-374.689
-281.329
-267.066
-427.091
-409.370
-316.009
-301.746
PSEUDO-R2
:-
(E)
.772
.766
.744
.765
.759
.774
.736
.758
.751
.767
-(L)
.775
.768
.747
.767
.761
.776
.739
.760
.754
.769
-(E)
ADJUSTED
FOR
D.F.
.753
.746
.723
.745
.739
.755
.715
.738
.730
.747
-(L)
ADJUSTED
FOR
D.F.
.756
.749
.726
.748
.741
.757
.717
.740
.733
.750
AVERAGE
PROBABILITY
(Y=LIMIT
OBSERV.)
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
SAMPLE
:-
NUMBER
OF
OBSERVATIONS
118
118
118
118
118
118
118
118
118
118
-FIRST
OBSERVATION
33
33
33
33
33
-LAST
OBSERVATION
120
120
120
120
120
120
120
120
120
120
NUMBER
OF
ESTIMATED
PARAMETERS
:
-FIXED
PART
:
.BETAS
77
77
77
77
77
.BOX-COX
11
11
11
11
11
.ASSOCIATED
DUMMIES
00
00
00
00
00
-AUTOCORRELATION
22
22
22
22
22
-HETEROSKEDASTICITY
:
.DELTAS
00
00
00
00
00
.BOX-COX
00
00
00
00
00
.ASSOCIATED
DUMMIES
00
00
00
00
00
===============================================================================================================================
===============================================================================================================================
I.
BETA
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
ELASTICITY
S(y)
(EP)
VARIANT
=M43
M44
M45
M46
M47
M48
M49
M50
M51
M52
(COND.
T-STATISTIC)
VERSION
=1
12
11
11
11
1
DEP.VAR.
=AC43
AC44
AC45
AC46
AC47
AC48
AC49
AC50
AC51
AC52
===============================================================================================================================
-----------
INDEPENDENT
-----------
comtot
.41E+00
.32E+00
.29E+00
.37E+00
.34E+00
.26E+00
.42E+00
.33E+00
.30E+00
.38E+00
.631
.629
.544
.629
.545
.541
.631
.628
.544
.628
(3.82)
(3.84)
(3.31)
(3.80)
(3.29)
(3.29)
(3.83)
(3.84)
(3.32)
(3.81)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
conalc
-.57E-01
-.37E-01
-.42E-01
-.65E-01
-.72E-01
-.48E-01
-.57E-01
-.37E-01
-.41E-01
-.65E-01
-.167
-.166
-.167
-.200
-.200
-.199
-.167
-.166
-.166
-.200
(-3.60)
(-3.61)
(-3.60)
(-4.28)
(-4.27)
(-4.28)
(-3.60)
(-3.62)
(-3.60)
(-4.28)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
dlab
.10E+01
.73E+00
.90E+00
.68E+00
.85E+00
.60E+00
.11E+01
.77E+00
.95E+00
.71E+00
.778
.606
.781
.604
.779
.608
.778
.606
.782
.604
(5.30)
(4.14)
(5.34)
(4.11)
(5.30)
(4.15)
(5.31)
(4.15)
(5.35)
(4.12)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
parser
-.27E-01
-.16E-01
-.18E-01
-.26E-01
-.30E-01
-.18E-01
-.21E-01
-.12E-01
-.15E-01
-.21E-01
-.101
-.097
-.099
-.101
-.103
-.099
-.081
-.077
-.078
-.081
(-1.05)
(-1.01)
(-1.03)
(-1.05)
(-1.07)
(-1.03)
(-.84)
(-.80)
(-.82)
(-.84)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
rcp
-.90E-01
-.93E-01
-.86E-01
-.75E-01
-.70E-01
-.71E-01
-.97E-01
-.10E+00
-.93E-01
-.80E-01
===
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
(-1.16)
(-1.16)
(-1.16)
(-1.16)
(-1.15)
(-1.16)
(-1.16)
(-1.16)
(-1.16)
(-1.16)
susp
-.41E-01
-.41E-01
-.44E-01
-.38E-01
-.40E-01
-.41E-01
-.42E-01
-.42E-01
-.44E-01
-.39E-01
-.080
-.110
-.109
-.080
-.079
-.109
-.080
-.110
-.109
-.080
(-1.37)
(-1.89)
(-1.87)
(-1.38)
(-1.36)
(-1.88)
(-1.37)
(-1.89)
(-1.87)
(-1.38)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
-------------------------------------------------------------------------------------------------------------------------------
REGRESSION
CONSTANT
CONSTANT
.12E+01
.13E+01
.11E+01
.13E+01
.11E+01
.10E+01
.13E+01
.14E+01
.12E+01
.14E+01
--
--
--
--
--
(.78)
(.95)
(.80)
(.95)
(.86)
(.90)
(.79)
(1.01)
(.85)
(1.00)
===============================================================================================================================
===============================================================================================================================
II.
PARAMETERS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M43
M44
M45
M46
M47
M48
M49
M50
M51
M52
(COND.
T-STATISTIC)
VERSION
=1
12
11
11
11
1
DEP.VAR.
=AC43
AC44
AC45
AC46
AC47
AC48
AC49
AC50
AC51
AC52
===============================================================================================================================
------------------------------------------------------------------
BOX-COX
TRANSFORMATIONS:
UNCOND:
[T-STATISTIC=0]
/[T-STATISTIC=1]
------------------------------------------------------------------
LAMBDA(Y)
-GROUP
1LAM
1.143
.179
.164
.132
.118
.152
.149
.186
.170
.137
[.34]
[.40]
[.39]
[.35]
[.33]
[.40]
[.35]
[.41]
[.40]
[.36]
[-2.03]
[-1.85]
[-1.98]
[-2.30]
[-2.45]
[-2.25]
[-1.98]
[-1.81]
[-1.93]
[-2.25]
LAMBDA(X)
-GROUP
1LAM
1.143
.179
.164
.132
.118
.152
.149
.186
.170
.137
[.34]
[.40]
[.39]
[.35]
[.33]
[.40]
[.35]
[.41]
[.40]
[.36]
[-2.03]
[-1.85]
[-1.98]
[-2.30]
[-2.45]
[-2.25]
[-1.98]
[-1.81]
[-1.93]
[-2.25]
---------------
AUTOCORRELATION
---------------
ORDER
1RHO
1.157
.156
.156
.157
.157
.155
.157
.156
.156
.156
(1.47)
(1.46)
(1.46)
(1.46)
(1.47)
(1.45)
(1.47)
(1.45)
(1.46)
(1.46)
ORDER
2RHO
2.248
.248
.247
.247
.247
.247
.248
.248
.247
.247
(2.65)
(2.65)
(2.65)
(2.65)
(2.64)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
===============================================================================================================================
III.GENERAL
STATISTICS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M43
M44
M45
M46
M47
M48
M49
M50
M51
M52
VERSION
=1
12
11
11
11
1
DEP.VAR.
=AC43
AC44
AC45
AC46
AC47
AC48
AC49
AC50
AC51
AC52
===============================================================================================================================
LOG-LIKELIHOOD
-422.474
-329.113
-314.847
-311.392
-297.127
-203.763
-457.153
-363.791
-349.525
-346.072
PSEUDO-R2
:-
(E)
.736
.727
.744
.750
.765
.761
.728
.718
.736
.742
-(L)
.738
.730
.746
.752
.767
.763
.730
.721
.738
.744
-(E)
ADJUSTED
FOR
D.F.
.714
.705
.722
.729
.746
.741
.706
.695
.714
.720
-(L)
ADJUSTED
FOR
D.F.
.717
.707
.725
.731
.748
.744
.708
.698
.716
.723
AVERAGE
PROBABILITY
(Y=LIMIT
OBSERV.)
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
SAMPLE
:-
NUMBER
OF
OBSERVATIONS
118
118
118
118
118
118
118
118
118
118
-FIRST
OBSERVATION
33
33
33
33
33
-LAST
OBSERVATION
120
120
120
120
120
120
120
120
120
120
NUMBER
OF
ESTIMATED
PARAMETERS
:
-FIXED
PART
:
.BETAS
77
77
77
77
77
.BOX-COX
11
11
11
11
11
.ASSOCIATED
DUMMIES
00
00
00
00
00
-AUTOCORRELATION
22
22
22
22
22
-HETEROSKEDASTICITY
:
.DELTAS
00
00
00
00
00
.BOX-COX
00
00
00
00
00
.ASSOCIATED
DUMMIES
00
00
00
00
00
===============================================================================================================================
=================================================================================================================================================
I.
BETA
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
ELASTICITY
S(y)
(EP)
VARIANT
=M53
M54
M55
M56
M57
M58
M59
M60
M61
M62
M63
M64
(COND.
T-STATISTIC)
VERSION
=1
11
11
11
11
11
1
DEP.VAR.
=AC53
AC54
AC55
AC56
AC57
AC58
AC59
AC60
AC61
AC62
AC63
AC64
=================================================================================================================================================
-----------
INDEPENDENT
-----------
comtot
.27E+00
.35E+00
.35E+00
.32E+00
.24E+00
.29E+00
.36E+00
.32E+00
.26E+00
.29E+00
.29E+00
.27E+00
.541
.545
.630
.545
.543
.543
.629
.545
.544
.543
.543
.543
(3.29)
(3.29)
(3.83)
(3.31)
(3.32)
(3.29)
(3.83)
(3.31)
(3.32)
(3.29)
(3.29)
(3.32)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
conalc
-.48E-01
-.73E-01
-.44E-01
-.49E-01
-.30E-01
-.56E-01
-.44E-01
-.49E-01
-.36E-01
-.56E-01
-.56E-01
-.36E-01
-.199
-.200
-.167
-.167
-.166
-.199
-.167
-.167
-.166
-.199
-.199
-.166
(-4.28)
(-4.27)
(-3.61)
(-3.59)
(-3.61)
(-4.28)
(-3.61)
(-3.60)
(-3.60)
(-4.28)
(-4.28)
(-3.60)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
dlab
.63E+00
.88E+00
.74E+00
.93E+00
.65E+00
.62E+00
.79E+00
.98E+00
.67E+00
.65E+00
.65E+00
.71E+00
.608
.779
.605
.780
.608
.606
.605
.780
.607
.606
.606
.607
(4.15)
(5.30)
(4.13)
(5.32)
(4.17)
(4.13)
(4.13)
(5.32)
(4.15)
(4.13)
(4.13)
(4.15)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
parser
-.14E-01
-.24E-01
-.20E-01
-.22E-01
-.13E-01
-.22E-01
-.15E-01
-.18E-01
-.16E-01
-.18E-01
-.18E-01
-.12E-01
-.079
-.083
-.099
-.101
-.096
-.101
-.079
-.080
-.098
-.081
-.081
-.078
(-.82)
(-.86)
(-1.03)
(-1.05)
(-1.00)
(-1.05)
(-.82)
(-.84)
(-1.02)
(-.84)
(-.84)
(-.82)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
rcp
-.75E-01
-.74E-01
-.92E-01
-.85E-01
-.86E-01
-.70E-01
-.99E-01
-.91E-01
-.85E-01
-.74E-01
-.74E-01
-.92E-01
===
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
-.045
(-1.16)
(-1.15)
(-1.16)
(-1.16)
(-1.16)
(-1.16)
(-1.16)
(-1.16)
(-1.16)
(-1.16)
(-1.16)
(-1.16)
susp
-.41E-01
-.41E-01
-.35E-01
-.36E-01
-.35E-01
-.34E-01
-.35E-01
-.37E-01
-.30E-01
-.35E-01
-.35E-01
-.30E-01
-.109
-.079
-.081
-.080
-.111
-.081
-.081
-.080
-.082
-.081
-.081
-.082
(-1.88)
(-1.36)
(-1.40)
(-1.38)
(-1.90)
(-1.39)
(-1.40)
(-1.38)
(-1.41)
(-1.39)
(-1.39)
(-1.41)
LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1LAM
1
-------------------------------------------------------------------------------------------------------------------------------------------------
REGRESSION
CONSTANT
CONSTANT
.12E+01
.12E+01
.14E+01
.11E+01
.12E+01
.11E+01
.15E+01
.13E+01
.13E+01
.13E+01
.13E+01
.14E+01
--
--
--
--
--
--
(.99)
(.91)
(.96)
(.83)
(.98)
(.95)
(1.01)
(.87)
(1.00)
(1.02)
(1.02)
(1.08)
=================================================================================================================================================
=================================================================================================================================================
II.
PARAMETERS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M53
M54
M55
M56
M57
M58
M59
M60
M61
M62
M63
M64
(COND.
T-STATISTIC)
VERSION
=1
11
11
11
11
11
1
DEP.VAR.
=AC53
AC54
AC55
AC56
AC57
AC58
AC59
AC60
AC61
AC62
AC63
AC64
=================================================================================================================================================
------------------------------------------------------------------
BOX-COX
TRANSFORMATIONS:
UNCOND:
[T-STATISTIC=0]
/[T-STATISTIC=1]
------------------------------------------------------------------
LAMBDA(Y)
-GROUP
1LAM
1.156
.122
.165
.151
.189
.139
.172
.156
.175
.143
.143
.181
[.41]
[.33]
[.37]
[.36]
[.43]
[.37]
[.38]
[.36]
[.39]
[.37]
[.37]
[.40]
[-2.20]
[-2.40]
[-1.88]
[-2.00]
[-1.82]
[-2.28]
[-1.83]
[-1.96]
[-1.85]
[-2.24]
[-2.24]
[-1.81]
LAMBDA(X)
-GROUP
1LAM
1.156
.122
.165
.151
.189
.139
.172
.156
.175
.143
.143
.181
[.41]
[.33]
[.37]
[.36]
[.43]
[.37]
[.38]
[.36]
[.39]
[.37]
[.37]
[.40]
[-2.20]
[-2.40]
[-1.88]
[-2.00]
[-1.82]
[-2.28]
[-1.83]
[-1.96]
[-1.85]
[-2.24]
[-2.24]
[-1.81]
---------------
AUTOCORRELATION
---------------
ORDER
1RHO
1.155
.157
.157
.157
.155
.156
.156
.157
.156
.156
.156
.156
(1.45)
(1.47)
(1.46)
(1.47)
(1.45)
(1.46)
(1.46)
(1.46)
(1.46)
(1.46)
(1.46)
(1.46)
ORDER
2RHO
2.247
.247
.248
.248
.247
.247
.248
.247
.247
.247
.247
.247
(2.65)
(2.64)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
(2.65)
=================================================================================================================================================
III.GENERAL
STATISTICS
TYPE
=LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
LEVEL-1
VARIANT
=M53
M54
M55
M56
M57
M58
M59
M60
M61
M62
M63
M64
VERSION
=1
11
11
11
11
11
1
DEP.VAR.
=AC53
AC54
AC55
AC56
AC57
AC58
AC59
AC60
AC61
AC62
AC63
AC64
=================================================================================================================================================
LOG-LIKELIHOOD
-238.443
-331.808
-359.178
-344.910
-251.544
-233.828
-393.856
-379.590
-281.611
-268.508
-268.508
-316.290
PSEUDO-R2
:-
(E)
.753
.758
.718
.735
.728
.751
.708
.726
.717
.743
.743
.707
-(L)
.756
.760
.720
.737
.730
.753
.711
.729
.719
.745
.745
.709
-(E)
ADJUSTED
FOR
D.F.
.733
.738
.694
.713
.705
.730
.684
.704
.693
.722
.722
.683
-(L)
ADJUSTED
FOR
D.F.
.735
.740
.696
.715
.707
.733
.686
.706
.695
.724
.724
.685
AVERAGE
PROBABILITY
(Y=LIMIT
OBSERV.)
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
SAMPLE
:-
NUMBER
OF
OBSERVATIONS
118
118
118
118
118
118
118
118
118
118
118
118
-FIRST
OBSERVATION
33
33
33
33
33
33
-LAST
OBSERVATION
120
120
120
120
120
120
120
120
120
120
120
120
NUMBER
OF
ESTIMATED
PARAMETERS
:
-FIXED
PART
:
.BETAS
77
77
77
77
77
77
.BOX-COX
11
11
11
11
11
11
.ASSOCIATED
DUMMIES
00
00
00
00
00
00
-AUTOCORRELATION
22
22
22
22
22
22
-HETEROSKEDASTICITY
:
.DELTAS
00
00
00
00
00
00
.BOX-COX
00
00
00
00
00
00
.ASSOCIATED
DUMMIES
00
00
00
00
00
00
=================================================================================================================================================
Appendix VII:Analysis of Variance
211
Table 6.9: Analysis of variance: ηPARSER
Effects Sum Sq.a Mean Sq.b Df F test Pr(>F) Percentage Cont.
F 4. 3759 4. 3759 1 7. 19E+05 < 2. 20E-16 99. 822
A 0. 0075 0. 0075 1 1. 23E+03 4. 03E-09 0. 171
DF 0. 0001 0. 0001 1 1. 94E+01 0. 003127 0. 002
CE 0. 0001 0. 0001 1 1. 68E+01 0. 004551 0. 002
E 0. 0001 0. 0001 1 1. 08E+01 0. 013244 0. 002
BF 0 0 1 7. 21E+00 0. 031301
EF 0 0 1 6. 68E+00 0. 036265
BC 0 0 1 5. 20E+00 0. 056643
AD 0 0 1 1. 60E+00 0. 245807
BD 0 0 1 1. 36E+00 0. 282069
ABE 0 0 1 1. 36E+00 0. 282069
BCE 0 0 1 1. 36E+00 0. 282069
BDF 0 0 1 1. 36E+00 0. 282069
CEF 0 0 1 1. 36E+00 0. 282069
ABCE 0 0 1 1. 36E+00 0. 282069
ABCF 0 0 1 1. 36E+00 0. 282069
ACDF 0 0 1 1. 36E+00 0. 282069
AB 0 0 1 1. 13E+00 0. 322666
AC 0 0 1 1. 13E+00 0. 322666
AF 0 0 1 1. 13E+00 0. 322666
CF 0 0 1 1. 13E+00 0. 322666
ABC 0 0 1 1. 13E+00 0. 322666
ABD 0 0 1 1. 13E+00 0. 322666
ADE 0 0 1 1. 13E+00 0. 322666
CDE 0 0 1 1. 13E+00 0. 322666
ADF 0 0 1 1. 13E+00 0. 322666
BCF 0 0 1 1. 13E+00 0. 322666
BEF 0 0 1 1. 13E+00 0. 322666
ADEF 0 0 1 1. 13E+00 0. 322666
ACEF 0 0 1 1. 13E+00 0. 322666
BCDF 0 0 1 1. 13E+00 0. 322666
BCEF 0 0 1 1. 13E+00 0. 322666
AE 0 0 1 9. 27E-01 0. 367799
BE 0 0 1 9. 27E-01 0. 367799
ACD 0 0 1 9. 27E-01 0. 367799
ACE 0 0 1 9. 27E-01 0. 367799
BCD 0 0 1 9. 27E-01 0. 367799
BDE 0 0 1 9. 27E-01 0. 367799
ABF 0 0 1 9. 27E-01 0. 367799
DEF 0 0 1 9. 27E-01 0. 367799
BCDE 0 0 1 9. 27E-01 0. 367799
ABEF 0 0 1 9. 27E-01 0. 367799
BDEF 0 0 1 9. 27E-01 0. 367799
CDEF 0 0 1 9. 27E-01 0. 367799
ABDE 0 0 1 9. 27E-01 0. 367799
D 0 0 1 7. 42E-01 0. 417596
ACF 0 0 1 7. 42E-01 0. 417596
CDF 0 0 1 7. 42E-01 0. 417596
ABCD 0 0 1 7. 42E-01 0. 417596
ABDF 0 0 1 7. 42E-01 0. 417596
DE 0 0 1 5. 78E-01 0. 472086
ACDE 0 0 1 5. 78E-01 0. 472086
CD 0 0 1 4. 34E-01 0. 531184
AEF 0 0 1 4. 34E-01 0. 531184
C 0 0 1 2. 08E-01 0. 662211
B 0 0 1 2. 31E-02 0. 883479
a<0.0001 values are approximated to 0.b<0.0001 values are approximated to 0.
Table 6.10: Analysis of variance: ηCONALC
Effects Sum Sq.a Mean Sq.b Df F test Pr(>F) Percentage Cont.
F 0. 31332 0. 31332 1 16734. 3095 4. 35E-13 94. 543
B 0. 017096 0. 017096 1 913. 0677 1. 12E-08 5. 159
D 0. 00003 0. 00003 1 1. 6156 0. 2443 0. 009
BC 0. 000025 0. 000025 1 1. 3352 0. 2858 0. 008
CDE 0. 000025 0. 000025 1 1. 3352 0. 2858 0. 008
BEF 0. 000025 0. 000025 1 1. 3352 0. 2858 0. 008
AD 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007
BD 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007
AF 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007
BCE 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007
ADF 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007
ACDF 0. 000023 0. 000023 1 1. 2051 0. 3086 0. 007
A 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
AB 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
AC 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
AE 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
BE 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
CF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
ABE 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
ACD 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
ACE 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
ABF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
AEF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
BCF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
CDF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
ABDF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
BCDF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
BCEF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
CDEF 0. 00002 0. 00002 1 1. 0815 0. 3329 0. 006
CD 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
BF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
ABD 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
ADE 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
BDE 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
BDF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
CEF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
ABCD 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
ACDE 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
ABCF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
ABEF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
ACEF 0. 000018 0. 000018 1 0. 9647 0. 3587 0. 005
DE 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005
ABC 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005
BCD 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005
DEF 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005
ABCE 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005
BCDE 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005
ADEF 0. 000016 0. 000016 1 0. 8546 0. 386 0. 005
E 0. 000014 0. 000014 1 0. 7511 0. 4149 0. 004
ACF 0. 000014 0. 000014 1 0. 7511 0. 4149 0. 004
BDEF 0. 000014 0. 000014 1 0. 7511 0. 4149 0. 004
ABDE 0. 000012 0. 000012 1 0. 6543 0. 4452 0. 004
DF 0. 000009 0. 000009 1 0. 4807 0. 5105 0. 003
C 0. 000008 0. 000008 1 0. 4039 0. 5453 0. 002
EF 0. 000005 0. 000005 1 0. 2704 0. 6191 0. 002
CE 0. 000002 0. 000002 1 0. 0835 0. 781 0. 001
a<0.0001 values are approximated to 0.b<0.0001 values are approximated to 0.
Table 6.11: Analysis of variance: ηSUSP
Effects Sum Sq.a Mean Sq.b Df F test Pr(>F) Percentage Cont.
F 0. 099146 0. 099146 1 6345361 < 2. 20E-16 89. 097
C 0. 012018 0. 012018 1 769129 2. 20E-16 10. 800
DF 0. 00007 0. 00007 1 4489 4. 34E-11 0. 063
BF 0. 000021 0. 000021 1 1369 2. 74E-09 0. 019
B 0. 000015 0. 000015 1 961 9. 39E-09 0. 013
D 0. 000003 0. 000003 1 169 3. 71E-06 0. 003
E 0. 000002 0. 000002 1 121 1. 14E-05 0. 002
CE 0. 000001 0. 000001 1 49 0. 0002116 0. 001
DE 0. 000001 0. 000001 1 49 0. 0002116 0. 001
EF 0. 000001 0. 000001 1 49 0. 0002116 0. 001
BEF 0. 000001 0. 000001 1 49 0. 0002116 0. 001
CF 0 0 1 25 0. 0015653
ACF 0 0 1 25 0. 0015653
BCF 0 0 1 25 0. 0015653
BDF 0 0 1 25 0. 0015653
A 0 0 1 9 0. 0199421
AC 0 0 1 9 0. 0199421
BD 0 0 1 9 0. 0199421
BE 0 0 1 9 0. 0199421
ABD 0 0 1 9 0. 0199421
ACD 0 0 1 9 0. 0199421
BDE 0 0 1 9 0. 0199421
ADF 0 0 1 9 0. 0199421
CEF 0 0 1 9 0. 0199421
ABCD 0 0 1 9 0. 0199421
BCDE 0 0 1 9 0. 0199421
ACDF 0 0 1 9 0. 0199421
BCDF 0 0 1 9 0. 0199421
CDEF 0 0 1 9 0. 0199421
ABDE 0 0 1 9 0. 0199421
AB 0 0 1 1 0. 3506167
AD 0 0 1 1 0. 3506167
AE 0 0 1 1 0. 3506167
BC 0 0 1 1 0. 3506167
CD 0 0 1 1 0. 3506167
AF 0 0 1 1 0. 3506167
ABC 0 0 1 1 0. 3506167
ABE 0 0 1 1 0. 3506167
ADE 0 0 1 1 0. 3506167
ACE 0 0 1 1 0. 3506167
BCD 0 0 1 1 0. 3506167
BCE 0 0 1 1 0. 3506167
CDE 0 0 1 1 0. 3506167
ABF 0 0 1 1 0. 3506167
AEF 0 0 1 1 0. 3506167
CDF 0 0 1 1 0. 3506167
DEF 0 0 1 1 0. 3506167
ABCE 0 0 1 1 0. 3506167
ACDE 0 0 1 1 0. 3506167
ABCF 0 0 1 1 0. 3506167
ABDF 0 0 1 1 0. 3506167
ABEF 0 0 1 1 0. 3506167
ADEF 0 0 1 1 0. 3506167
ACEF 0 0 1 1 0. 3506167
BCEF 0 0 1 1 0. 3506167
BDEF 0 0 1 1 0. 3506167
a<0.0001 values are approximated to 0.b<0.0001 values are approximated to 0.
Table 6.12: Analysis of variance: ηDLAB
Effects Sum Sq.a Mean Sq.b Df F test Pr(>F) Percentage Cont.
D 0. 49386 0. 49386 1 2. 13E+06 < 2. 20E-16 97. 251
F 0. 01363 0. 01363 1 5. 87E+04 5. 38E-15 2. 684
DF 0. 00011 0. 00011 1 4. 75E+02 1. 08E-07 0. 022
C 0. 00009 0. 00009 1 3. 69E+02 2. 59E-07 0. 018
B 0. 00006 0. 00006 1 2. 42E+02 1. 09E-06 0. 012
EF 0. 00004 0. 00004 1 1. 82E+02 2. 89E-06 0. 008
CE 0. 00002 0. 00002 1 9. 72E+01 2. 35E-05 0. 004
BF 0. 00001 0. 00001 1 2. 69E+01 0. 001269 0. 002
E 0 0 1 1. 32E+01 0. 008374
ADF 0 0 1 9. 69E+00 0. 017004
CDEF 0 0 1 6. 73E+00 0. 035717
AC 0 0 1 4. 31E+00 0. 076593
BC 0 0 1 4. 31E+00 0. 076593
CF 0 0 1 4. 31E+00 0. 076593
AEF 0 0 1 4. 31E+00 0. 076593
ABDE 0 0 1 4. 31E+00 0. 076593
AB 0 0 1 2. 42E+00 0. 163515
BE 0 0 1 2. 42E+00 0. 163515
ACE 0 0 1 2. 42E+00 0. 163515
CDE 0 0 1 2. 42E+00 0. 163515
BEF 0 0 1 2. 42E+00 0. 163515
CEF 0 0 1 2. 42E+00 0. 163515
DEF 0 0 1 2. 42E+00 0. 163515
ABCD 0 0 1 2. 42E+00 0. 163515
BCDE 0 0 1 2. 42E+00 0. 163515
ACDE 0 0 1 2. 42E+00 0. 163515
ABCF 0 0 1 2. 42E+00 0. 163515
BCEF 0 0 1 2. 42E+00 0. 163515
AD 0 0 1 1. 08E+00 0. 333899
AE 0 0 1 1. 08E+00 0. 333899
DE 0 0 1 1. 08E+00 0. 333899
AF 0 0 1 1. 08E+00 0. 333899
ABD 0 0 1 1. 08E+00 0. 333899
ABE 0 0 1 1. 08E+00 0. 333899
ABF 0 0 1 1. 08E+00 0. 333899
ACF 0 0 1 1. 08E+00 0. 333899
BCF 0 0 1 1. 08E+00 0. 333899
BDF 0 0 1 1. 08E+00 0. 333899
ABEF 0 0 1 1. 08E+00 0. 333899
ACDF 0 0 1 1. 08E+00 0. 333899
ADEF 0 0 1 1. 08E+00 0. 333899
ACEF 0 0 1 1. 08E+00 0. 333899
A 0 0 1 2. 69E-01 0. 619844
BD 0 0 1 2. 69E-01 0. 619844
CD 0 0 1 2. 69E-01 0. 619844
ADE 0 0 1 2. 69E-01 0. 619844
BCD 0 0 1 2. 69E-01 0. 619844
BCE 0 0 1 2. 69E-01 0. 619844
BDE 0 0 1 2. 69E-01 0. 619844
CDF 0 0 1 2. 69E-01 0. 619844
ABCE 0 0 1 2. 69E-01 0. 619844
ABDF 0 0 1 2. 69E-01 0. 619844
BCDF 0 0 1 2. 69E-01 0. 619844
BDEF 0 0 1 2. 69E-01 0. 619844
ABC 0 0 1 0. 00E+00 1
ACD 0 0 1 0. 00E+00 1
a<0.0001 values are approximated to 0.b<0.0001 values are approximated to 0.
Table 6.13: Analysis of variance: ηCOMTOT
Effects Sum Sq.a Mean Sq.b Df F test Pr(>F) Percentage Cont.
F 1. 88582 1. 88582 1 19405. 6728 2. 59E-13 94. 331
E 0. 10709 0. 10709 1 1102. 0183 5. 83E-09 5. 357
CE 0. 00052 0. 00052 1 5. 3259 0. 05436 0. 026
B 0. 00036 0. 00036 1 3. 7148 0. 09529 0. 018
C 0. 00033 0. 00033 1 3. 4273 0. 10656 0. 017
EF 0. 00026 0. 00026 1 2. 6343 0. 14861 0. 013
BF 0. 00017 0. 00017 1 1. 7391 0. 22876 0. 009
BCF 0. 00012 0. 00012 1 1. 1892 0. 3116 0. 006
AF 0. 00011 0. 00011 1 1. 1345 0. 32217 0. 006
ACF 0. 00011 0. 00011 1 1. 1345 0. 32217 0. 006
AD 0. 00011 0. 00011 1 1. 0811 0. 33302 0. 006
BD 0. 00011 0. 00011 1 1. 0811 0. 33302 0. 006
DE 0. 00011 0. 00011 1 1. 0811 0. 33302 0. 006
ABF 0. 00011 0. 00011 1 1. 0811 0. 33302 0. 006
AC 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
BE 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
ABC 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
ACD 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
ADE 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
CDF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
ABCD 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
ABCF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
ADEF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
BCEF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
CDEF 0. 0001 0. 0001 1 1. 029 0. 34416 0. 005
CD 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
ACE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
BCD 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
CDE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
AEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
CEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
ABCE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
BCDE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
ABDF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
ABEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
ACDF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
ACEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
BDEF 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
ABDE 0. 0001 0. 0001 1 0. 9782 0. 35558 0. 005
AE 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005
ABE 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005
BCE 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005
BEF 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005
ACDE 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005
BCDF 0. 00009 0. 00009 1 0. 9287 0. 3673 0. 005
AB 0. 00009 0. 00009 1 0. 8805 0. 37931 0. 005
ABD 0. 00009 0. 00009 1 0. 8805 0. 37931 0. 005
BDE 0. 00008 0. 00008 1 0. 8335 0. 39162 0. 004
ADF 0. 00008 0. 00008 1 0. 8335 0. 39162 0. 004
BDF 0. 00008 0. 00008 1 0. 8335 0. 39162 0. 004
DEF 0. 00008 0. 00008 1 0. 8335 0. 39162 0. 004
CF 0. 00008 0. 00008 1 0. 7879 0. 40421 0. 004
DF 0. 00008 0. 00008 1 0. 7879 0. 40421 0. 004
A 0. 00007 0. 00007 1 0. 7004 0. 43029 0. 004
BC 0. 00005 0. 00005 1 0. 5042 0. 50061 0. 003
D 0 0 1 0. 0412 0. 845
a<0.0001 values are approximated to 0.b<0.0001 values are approximated to 0.
Table 6.14: Analysis of variance: ρ1
Effects Sum Sq.a Mean Sq.b Df F test Pr(>F) Percentage Cont.
F 0. 34325 0. 34325 1 1. 03E+07 < 2. 20E-16 99. 997
DF 0. 00001 0. 00001 1 2. 06E+02 1. 90E-06 0. 003
C 0 0 1 7. 89E+01 4. 65E-05
BF 0 0 1 5. 65E+01 0. 0001356
E 0 0 1 3. 78E+01 0. 0004684
B 0 0 1 2. 29E+01 0. 0020078
BE 0 0 1 2. 29E+01 0. 0020078
CE 0 0 1 2. 29E+01 0. 0020078
EF 0 0 1 2. 29E+01 0. 0020078
BCF 0 0 1 2. 29E+01 0. 0020078
AE 0 0 1 1. 17E+01 0. 0112014
BC 0 0 1 1. 17E+01 0. 0112014
AF 0 0 1 1. 17E+01 0. 0112014
DEF 0 0 1 1. 17E+01 0. 0112014
ABEF 0 0 1 1. 17E+01 0. 0112014
ACDF 0 0 1 1. 17E+01 0. 0112014
A 0 0 1 4. 20E+00 0. 079602
D 0 0 1 4. 20E+00 0. 079602
CF 0 0 1 4. 20E+00 0. 079602
ADE 0 0 1 4. 20E+00 0. 079602
CDE 0 0 1 4. 20E+00 0. 079602
CEF 0 0 1 4. 20E+00 0. 079602
AB 0 0 1 4. 67E-01 0. 5164896
AC 0 0 1 4. 67E-01 0. 5164896
AD 0 0 1 4. 67E-01 0. 5164896
BD 0 0 1 4. 67E-01 0. 5164896
CD 0 0 1 4. 67E-01 0. 5164896
DE 0 0 1 4. 67E-01 0. 5164896
ABC 0 0 1 4. 67E-01 0. 5164896
ABD 0 0 1 4. 67E-01 0. 5164896
ABE 0 0 1 4. 67E-01 0. 5164896
ACD 0 0 1 4. 67E-01 0. 5164896
ACE 0 0 1 4. 67E-01 0. 5164896
BCD 0 0 1 4. 67E-01 0. 5164896
BCE 0 0 1 4. 67E-01 0. 5164896
BDE 0 0 1 4. 67E-01 0. 5164896
ABF 0 0 1 4. 67E-01 0. 5164896
ACF 0 0 1 4. 67E-01 0. 5164896
ADF 0 0 1 4. 67E-01 0. 5164896
AEF 0 0 1 4. 67E-01 0. 5164896
BDF 0 0 1 4. 67E-01 0. 5164896
BEF 0 0 1 4. 67E-01 0. 5164896
CDF 0 0 1 4. 67E-01 0. 5164896
ABCD 0 0 1 4. 67E-01 0. 5164896
ABCE 0 0 1 4. 67E-01 0. 5164896
BCDE 0 0 1 4. 67E-01 0. 5164896
ACDE 0 0 1 4. 67E-01 0. 5164896
ABCF 0 0 1 4. 67E-01 0. 5164896
ABDF 0 0 1 4. 67E-01 0. 5164896
ADEF 0 0 1 4. 67E-01 0. 5164896
ACEF 0 0 1 4. 67E-01 0. 5164896
BCDF 0 0 1 4. 67E-01 0. 5164896
BCEF 0 0 1 4. 67E-01 0. 5164896
BDEF 0 0 1 4. 67E-01 0. 5164896
CDEF 0 0 1 4. 67E-01 0. 5164896
ABDE 0 0 1 4. 67E-01 0. 5164896
a<0.0001 values are approximated to 0.b<0.0001 values are approximated to 0.
Table 6.15: Analysis of variance: ρ2
Effects Sum Sq.a Mean Sq.b Df F test Pr(>F) Percentage Cont.
F 0. 103765 0. 103765 1 6. 55E+05 < 2. 20E-16 99. 897
CE 0. 000032 0. 000032 1 2. 00E+02 2. 11E-06 0. 031
D 0. 000017 0. 000017 1 1. 07E+02 1. 69E-05 0. 016
B 0. 000015 0. 000015 1 9. 47E+01 2. 56E-05 0. 014
C 0. 000013 0. 000013 1 8. 29E+01 3. 95E-05 0. 013
DF 0. 000011 0. 000011 1 7. 19E+01 6. 28E-05 0. 011
BF 0. 000008 0. 000008 1 5. 22E+01 0. 0001741 0. 008
E 0. 000006 0. 000006 1 3. 56E+01 0. 0005611 0. 006
BC 0. 000002 0. 000002 1 1. 19E+01 0. 0106347 0. 002
A 0. 000001 0. 000001 1 7. 99E+00 0. 0255547 0. 001
BDF 0. 000001 0. 000001 1 4. 83E+00 0. 0639241 0. 001
ABCE 0. 000001 0. 000001 1 4. 83E+00 0. 0639241 0. 001
ACF 0 0 1 2. 46E+00 0. 1604145
CDF 0 0 1 2. 46E+00 0. 1604145
CDEF 0 0 1 2. 46E+00 0. 1604145
AB 0 0 1 8. 87E-01 0. 3775675
AD 0 0 1 8. 87E-01 0. 3775675
BE 0 0 1 8. 87E-01 0. 3775675
CD 0 0 1 8. 87E-01 0. 3775675
AF 0 0 1 8. 87E-01 0. 3775675
ABC 0 0 1 8. 87E-01 0. 3775675
ADE 0 0 1 8. 87E-01 0. 3775675
BCD 0 0 1 8. 87E-01 0. 3775675
BCE 0 0 1 8. 87E-01 0. 3775675
CDE 0 0 1 8. 87E-01 0. 3775675
ABF 0 0 1 8. 87E-01 0. 3775675
ADF 0 0 1 8. 87E-01 0. 3775675
DEF 0 0 1 8. 87E-01 0. 3775675
ACDE 0 0 1 8. 87E-01 0. 3775675
ABCF 0 0 1 8. 87E-01 0. 3775675
ABDF 0 0 1 8. 87E-01 0. 3775675
ABEF 0 0 1 8. 87E-01 0. 3775675
ADEF 0 0 1 8. 87E-01 0. 3775675
ABDE 0 0 1 8. 87E-01 0. 3775675
AC 0 0 1 9. 86E-02 0. 7626771
AE 0 0 1 9. 86E-02 0. 7626771
BD 0 0 1 9. 86E-02 0. 7626771
DE 0 0 1 9. 86E-02 0. 7626771
CF 0 0 1 9. 86E-02 0. 7626771
EF 0 0 1 9. 86E-02 0. 7626771
ABD 0 0 1 9. 86E-02 0. 7626771
ABE 0 0 1 9. 86E-02 0. 7626771
ACD 0 0 1 9. 86E-02 0. 7626771
ACE 0 0 1 9. 86E-02 0. 7626771
BDE 0 0 1 9. 86E-02 0. 7626771
AEF 0 0 1 9. 86E-02 0. 7626771
BCF 0 0 1 9. 86E-02 0. 7626771
BEF 0 0 1 9. 86E-02 0. 7626771
CEF 0 0 1 9. 86E-02 0. 7626771
ABCD 0 0 1 9. 86E-02 0. 7626771
BCDE 0 0 1 9. 86E-02 0. 7626771
ACDF 0 0 1 9. 86E-02 0. 7626771
ACEF 0 0 1 9. 86E-02 0. 7626771
BCDF 0 0 1 9. 86E-02 0. 7626771
BCEF 0 0 1 9. 86E-02 0. 7626771
BDEF 0 0 1 9. 86E-02 0. 7626771
a<0.0001 values are approximated to 0.b<0.0001 values are approximated to 0.
Table 6.16: Analysis of variance: λ
Effects Sum Sq.a Mean Sq.b Df F test Pr(>F) Percentage Cont.
F 3. 7893 3. 7893 1 3. 25E+05 < 2. 20E-16 99. 491
CE 0. 011 0. 011 1 9. 42E+02 1. 01E-08 0. 289
DF 0. 0042 0. 0042 1 3. 60E+02 2. 80E-07 0. 110
C 0. 0017 0. 0017 1 1. 48E+02 5. 75E-06 0. 045
B 0. 0011 0. 0011 1 9. 40E+01 2. 63E-05 0. 029
D 0. 0006 0. 0006 1 5. 19E+01 0. 0001765 0. 016
BC 0. 0003 0. 0003 1 2. 30E+01 0. 0019843 0. 008
EF 0. 0002 0. 0002 1 1. 96E+01 0. 0030579 0. 005
E 0. 0002 0. 0002 1 1. 65E+01 0. 0048065 0. 005
BF 0. 0001 0. 0001 1 1. 01E+01 0. 0154357 0. 003
CD 0 0 1 3. 76E+00 0. 0937007
ACD 0 0 1 3. 21E+00 0. 1161567
BE 0 0 1 2. 47E+00 0. 1597197
DE 0 0 1 2. 47E+00 0. 1597197
A 0 0 1 1. 83E+00 0. 2179717
DEF 0 0 1 1. 64E+00 0. 2412173
CDE 0 0 1 1. 46E+00 0. 2665681
AD 0 0 1 1. 29E+00 0. 2941266
AEF 0 0 1 1. 29E+00 0. 2941266
ACEF 0 0 1 1. 29E+00 0. 2941266
AF 0 0 1 1. 13E+00 0. 3239822
ABC 0 0 1 1. 13E+00 0. 3239822
ABE 0 0 1 1. 13E+00 0. 3239822
BCD 0 0 1 1. 13E+00 0. 3239822
ADF 0 0 1 1. 13E+00 0. 3239822
ABCE 0 0 1 1. 13E+00 0. 3239822
ABDF 0 0 1 1. 13E+00 0. 3239822
ADEF 0 0 1 1. 13E+00 0. 3239822
BDEF 0 0 1 1. 13E+00 0. 3239822
ADE 0 0 1 9. 76E-01 0. 3562073
BCE 0 0 1 9. 76E-01 0. 3562073
ABF 0 0 1 9. 76E-01 0. 3562073
BEF 0 0 1 9. 76E-01 0. 3562073
CDF 0 0 1 9. 76E-01 0. 3562073
ABCD 0 0 1 9. 76E-01 0. 3562073
ACDE 0 0 1 9. 76E-01 0. 3562073
ABCF 0 0 1 9. 76E-01 0. 3562073
ABEF 0 0 1 9. 76E-01 0. 3562073
ACDF 0 0 1 9. 76E-01 0. 3562073
BCDF 0 0 1 9. 76E-01 0. 3562073
BCEF 0 0 1 9. 76E-01 0. 3562073
CDEF 0 0 1 9. 76E-01 0. 3562073
ABDE 0 0 1 9. 76E-01 0. 3562073
AC 0 0 1 8. 36E-01 0. 3908532
AE 0 0 1 8. 36E-01 0. 3908532
ACE 0 0 1 8. 36E-01 0. 3908532
ACF 0 0 1 8. 36E-01 0. 3908532
CEF 0 0 1 8. 36E-01 0. 3908532
BCDE 0 0 1 8. 36E-01 0. 3908532
ABD 0 0 1 7. 08E-01 0. 4279468
BDE 0 0 1 4. 83E-01 0. 5094361
AB 0 0 1 3. 87E-01 0. 5537283
BD 0 0 1 1. 08E-01 0. 7516136
BCF 0 0 1 1. 08E-01 0. 7516136
CF 0 0 1 6. 56E-02 0. 8052607
BDF 0 0 1 3. 35E-02 0. 860057
a<0.0001 values are approximated to 0.b<0.0001 values are approximated to 0.