introducing latent psychological constructs in...

INTRODUCING LATENT PSYCHOLOGICAL CONSTRUCTS IN INJURY SEVERITY MODELING: A MULTI-VEHICLE AND MULTI-OCCUPANT APPROACH Patrícia Lavieri The University of Texas at Austin Department of Civil, Architectural and Environmental Engineering 301 E. Dean Keeton St. Stop C1761, Austin TX 78712 Phone: 512-471-4535, Fax: 512-475-8744, Email: [email protected] Chandra R. Bhat (corresponding author) The University of Texas at Austin Department of Civil, Architectural and Environmental Engineering 301 E. Dean Keeton St. Stop C1761, Austin TX 78712 Phone: 512-471-4535, Fax: 512-475-8744, Email: [email protected] and King Abdulaziz University, Jeddah 21589, Saudi Arabia Subodh K. Dubey The University of Texas at Austin Department of Civil, Architectural and Environmental Engineering 301 E. Dean Keeton St. Stop C1761, Austin TX 78712 Phone: 512-471-4535, Fax: 512-475-8744, Email: [email protected] Ram M. Pendyala Georgia Institute of Technology School of Civil and Environmental Engineering Mason Building, 790 Atlantic Drive, Atlanta, GA 30332-0355 Phone: 404-385-3754, Fax: 404-894-2278, Email: [email protected] Venu M. Garikapati Georgia Institute of Technology School of Civil and Environmental Engineering Mason Building, 790 Atlantic Drive, Atlanta, GA 30332-0355 Phone: 480-522-8067, Fax: 404-894-2278, Email: [email protected] Submitted for Presentation and Publication Paper #: 16-6858 Word count: 6,834 text + 4 tables/figures × 250 = 7,834 words 95th Annual Meeting of the Transportation Research Board Committee on Safety Data, Analysis, and Evaluation (ANB20) August 1, 2015

Lavieri, Bhat, Dubey, Pendyala, and Garikapati

ABSTRACT 1 This paper presents a comprehensive model of injury severity that accounts for unmeasured 2 driver behavior attributes. Using indicators of risky and distracted/careless driving present in 3 crash databases, the model system incorporates a latent variable component where latent 4 constructs describing such behaviors can be modeled as a function of observed attributes of the 5 driver. The model system also includes a measurement equation where the latent constructs of 6 driver behavior are combined with other explanatory factors to model injury severity outcomes 7 for all vehicular occupants in two-vehicle crashes. Building upon previous research, the paper 8 presents a Generalized Heterogeneous Data Model (GHDM) capable of jointly modeling injury 9 severity outcomes for all passengers in multiple vehicles by seat position. The model system is 10 found to offer key insights on how various factors differentially affect injury outcomes for 11 occupants in different seat positions. The results of the model have important implications for 12 the design of safety interventions and advanced vehicular features and technologies. 13 Engineering designs that accommodate the diminished capabilities of older drivers, include rear 14 seat safety features, and alert drivers to frontal collisions before they occur (collision warning 15 systems and automated braking systems) would contribute to substantial reductions in injury 16 severity across all vehicular occupants. 17 18 Keywords: injury severity model, Generalized Heterogeneous Data Model (GHDM), latent 19 variable modeling, driver behavior, safety interventions 20

Lavieri, Bhat, Dubey, Pendyala, and Garikapati 1

1. INTRODUCTION 1 The World Health Organization (WHO) has reported that motor vehicle crashes are one of the 2 most serious public health problems confronting both developed and developing countries 3 around the world. Globally, the annual number of deaths on roadways is a staggering 1.24 4 million. The organization has stressed the need for a greater understanding of crash causation, 5 injury severity and risky road-user behavior as important elements for preventing fatalities and 6 injuries in the future (WHO, 2013). Although the number of crashes, injuries, and fatalities per 7 million vehicle miles of travel is decreasing in the United States, the numbers are still large with 8 more than 32,000 roadway fatalities in 2013. Another two million individuals were injured in 9 roadway crashes (NHTSA, 2014). 10 Despite considerable research devoted to crash data analysis and injury severity 11 modeling, there is a paucity of literature devoted to fully accounting for driver behavior in injury 12 severity models. The aim of this paper is to fill a critical gap in the literature by presenting a 13 model system that captures the impact of driver’s behavior on the injury severities of crash 14 victims. In addition, while prior research has generally focused on the injury severity of the most 15 injured victim, the model system in the current study jointly models the injury severity of all 16 vehicle occupants associating them to their respective seat positions in the vehicles, and captures 17 the cross-effects of the driver characteristics of one vehicle over to the other vehicle (in a multi-18 vehicle crash). The model system also accounts for the endogeneity of seat-belt use and alcohol 19 consumption; inherently safe drivers are likely to use seat belts and avoid driving under the 20 influence of alcohol. Therefore, accounting for such self-selection is critical to modeling the 21 effects of various explanatory factors on injury severity. 22 One reason why driver behavior is usually not adequately considered in injury severity 23 models is because of data limitations; crash injury severity data generally do not include 24 behavioral characteristics and include virtually no psychological measurements. Data on driving 25 behavior is often self-reported, and may not be available in the context of specific crashes and 26 injury severity outcomes. Recent methodological enhancements, however, have made it possible 27 to account for unobserved heterogeneity in the driver population, as well as endogeneity in driver 28 behavior. Such methodological approaches capture the variation in driver behavior (due to 29 unobserved psychological factors) that is prevalent on the roadway system. For example, the 30 Generalized Heterogeneous Data Model (GHDM) offers the econometric tool necessary to 31 incorporate latent driver behavior constructs in injury severity models. Rather than using 32 exogenous variables to characterize attitudes and psychological characteristics, endogenous 33 variables in the crash data set (such as the use of seat belt and alcohol involvement prevalent in 34 police crash reports) can be used to develop latent constructs of driver behavior. 35 In addition to incorporating unobserved heterogeneity in the driver population in injury 36 severity models through the use of latent constructs, this study contributes to the literature by 37 presenting a model system that jointly models the injury severity of all people involved in a 38 crash. This has not been done previously due to methodological constraints; however, the 39 methodologies invoked in this paper are capable of accounting for injury severity across all 40 vehicle occupants. Finally, the proposed framework makes it possible to accommodate 41 endogeneity of specific factors in injury severity models in an easy and flexible manner. 42 The remainder of this paper is organized as follows. The next section provides an 43 overview of the literature on crash and injury modeling. The third section offers an overview of 44 the modeling framework. The fourth section provides an overview of the modeling methodology, 45 while the fifth section describes the data used in this research. The sixth section presents the 46


model estimation results. Conclusions and implications of the findings are in the seventh and 1 final section of the paper. 2 3 2. MODELING INJURY SEVERITY 4 Driver behavior is a critical determinant of road traffic crashes (Petridou and Moustaki, 2000), 5 and it is therefore of much interest and importance to account for this dimension in the study and 6 modeling of crash occurrence, crash type, and injury severity. There is a substantial body of 7 literature that attempts to link individual personality traits to driving behavior and the likelihood 8 of committing traffic violations and being involved in traffic accidents (recent examples include 9 Constantinou et al, 2011; Taubman-Ben-Ari and Yehiel, 2012; Zhao et al, 2013; and Beanland et 10 al, 2014). However, this stream of research has not explicitly linked driver behavior to the 11 analysis of injury severity. The reason for this disconnect is that studies of driver behavior and 12 studies of injury severity outcomes use different streams of data. Most driving behavior studies 13 rely on self-reported data as this is generally the most cost-effective manner of measuring 14 personality traits (through attitudinal, perception, and self-assessment statements) and behavior 15 (e.g., frequency of actions such as passing, tail-gating, speeding) simultaneously (Beanland et al, 16 2014). This data collection approach suffers from the limitation that it relies on the respondent’s 17 memory and judgement, and therefore limits the amount of information that can be obtained 18 about the relationship between situational contexts and driving behaviors, as well as the 19 consequent outcomes. The approach therefore makes it difficult to explicitly connect driver 20 personality and behavior with crash injury severity outcomes. Despite these data limitations, the 21 field of crash injury severity modeling has seen important methodological and empirical 22 developments. Savolainen et al (2011) provide a review of statistical methods used to model 23 crash injury and severity. More recently, Mannering and Bhat (2014) discussed methodological 24 frontiers in accident research. 25 Studies of injury severity have generally treated the injury severity variable as either 26 binary (injury versus non-injury) or as a multiple response variable (no apparent injury, possible 27 injury, minor injury, serious injury, and fatal injury). These outcomes may be treated as ordered 28 or unordered outcomes. Savolainen et al (2011) group studies according to their approach and 29 find that ordered probit models are the most frequently used, followed by multinomial logit, 30 nested logit, and mixed logit respectively. Yasmin and Eluru (2013) performed an empirical 31 comparison of ordered response and unordered response models in the context of driver injury 32 severity. They find that an ordered system that allows for exogenous variable effects to vary 33 across alternatives and accommodates unobserved heterogeneity offers almost equivalent results 34 to that of the corresponding unordered system. 35 A study that explicitly uses a psychological construct to moderate the impact of other 36 variables on injury severity outcomes is that by Paleti et al (2010). They jointly model, through 37 a two-equation system, the driving behavior (aggressive driving) and injury severity propensity. 38 Donmez and Liu (2015) also consider driver behavior while modeling injury severity, but they 39 use different types of distracted driving merely as additional explanatory variables in a single 40 equation ordered logit model. Our study aims to contribute to the literature by exploiting recent 41 econometric methodological advances to model injury severity outcomes while accounting for 42 unobserved driver characteristics. Endogenous variables (available in police reports, such as seat 43 belt use and alcohol involvement) may be used as indicators of latent variables; latent constructs 44 developed using these variables can then be introduced in the injury severity model through a 45 simultaneous equations model framework. 46


Another area where this study makes a contribution is the modeling of injury severity for 1 all individuals involved in a crash. Most injury severity studies model only the injury of one 2 individual in the crash – the vehicle’s driver or the most severely injured occupant. Kim et al, 3 (2013), and Donmez and Liu (2015) are examples of studies that focus on the injury severity of 4 the driver, while Castro et al (2013) model the injury severity of the most severely injured 5 occupant in the vehicle. Studies that model the injury severity of multiple occupants do not 6 account for the jointness in such injury severity outcomes across passengers; some use seat 7 position as an explanatory variable, and others compare the injury risk between front and rear 8 seats (Mayrose and Priya, 2008; Lennon et al, 2008; and Durbin et al, 2015). Simultaneously 9 modeling injury severity for multiple occupants presents methodological challenges; 10 multidimensionality in possible outcomes generates computational complexity associated with 11 specification, identification, and estimation of model parameters in simultaneous equation 12 frameworks. 13 Studies that have examined injury severity of multiple occupants are prevalent in the 14 literature. Yasmin et al (2014) modeled the injury severity of the two drivers involved in a two-15 vehicle crash. Abay et al (2013) also examined the injury severity of the two drivers involved in 16 a crash using a multivariate probit model. One study that considers injury severity of all 17 occupants is that by Eluru et al (2010) who employed a copula-based approach to model the 18 multiple occupant injury phenomenon. They find correlated unobserved factors in injury 19 outcomes across occupants and recommend that crash studies adopt approaches in which injury 20 outcomes are modeled simultaneously across all vehicle occupants. 21 Finally, some variables used to explain injury severity are treated as exogenous when in 22 fact they should be treated as endogenous. Factors that influence these variables may also 23 influence the severity of injuries sustained in a crash, rendering such variables correlated with 24 the unexplained part (error term in the model) of injury severity. Examples of such variables 25 include the decision to wear a seat belt, the decision to drive while impaired, and the decision to 26 acquire a vehicle with special safety features. Personality traits and intrinsic driver behavior 27 characteristics that make an individual wear a seat belt, purchase a vehicle with special safety 28 features, and avoid driving while impaired are also likely to impact injury severity outcomes as 29 such drivers are likely to be inherently safer and more risk-averse in their operation of a vehicle. 30 Eluru and Bhat (2007) and Abay et al (2013) are examples of studies that consider the 31 endogeneity of seat belt use; not accounting for endogeneity may lead to an overestimation or 32 underestimation of the effect of the corresponding variables on injury severity outcomes. For 33 example, a driver in a vehicle with enhanced safety features may compensate for their presence 34 by engaging in risky driving behaviors (speeding, for example); if the variables describing safety 35 features are treated as exogenous variables, their potential (beneficial) impacts will be under-36 estimated. 37 This paper makes a methodological contribution by exploiting advanced econometric 38 tools to account for three empirical considerations in injury severity modeling. First, the paper 39 introduces latent constructs to capture unobserved driver behavior and psychological traits; 40 second, the methodology jointly models the injury severity outcomes for all vehicle occupants 41 involved in a crash; and third, the methodology accounts for endogeneity of safety related 42 variables. 43 44


3. CONCEPTUAL FRAMEWORK 1 The conceptual framework adopted for the modeling effort in this paper is an adaptation of the 2 idea of a contextual model proposed by Sümer (2003) in which a vehicular crash is viewed as a 3 consequence of both distal context and proximal context variables. The proximal context 4 mediates the impact of the distal context on the outcome. In the modeling framework of this 5 paper, the injury severities are a consequence of both distal and proximal contexts of both drivers 6 involved in the crash. 7 The distal context variables in the modeling framework include characteristics of the 8 driver that are inherent to the individual such as age, gender, and personality traits. These 9 characteristics are relatively stable across time and not specific to the crash circumstances. On 10 the other hand, proximal context variables include both stable and transitory factors closely 11 related to the crash. Proximal variables include driver behavior (e.g., wearing seat belt, 12 speeding), environmental conditions, roadway characteristics and condition, vehicle 13 characteristics (which may also be viewed as distal context variables depending on the 14 circumstances of the crash), and crash outcome variables. As the injury severity of all vehicle 15 occupants is being modeled, age and gender of passengers are also proximal variables because 16 they are not directly related to the driver and can change from one trip to the next. Similarly, 17 presence of children is also a proximal variable. 18 This study is limited to an analysis of two-vehicle crashes. As such, one vehicle is part of 19 the proximal context of the other. Some variables describing the proximal context of one vehicle 20 also impact the other vehicle, representing a reciprocal effect. The behavior of the driver in one 21 vehicle can impact injury severity of occupants in the other vehicle. The driver behaviors 22 represented in the model include distracted/careless driving behavior and risky driving behavior. 23 They are assumed to be a consequence of distal factors, although some proximal factors such as 24 presence of passengers (or the interaction of proximal and distal factors) may also affect driving 25 behavior constructs. 26 Figure 1 presents an overview of the conceptual framework. Personality traits are 27 assumed to impact driving behaviors. However, such traits (such as conscientiousness trait and 28 sensation seeking in Figure 1) are not observed or measured in crash databases. The social-29 psychological literature also suggests that these personality traits influence crash risk not 30 directly, but through their impact on driving behavior characteristics. That is, the personality 31 traits are the distal context variables (see Figure 1), which themselves are affected by 32 demographic variables, and then proceed to affect the proximal context variables of driver 33 behavior (distracted/careless driving behavior and risky driving behavior in Figure 1) that then 34 impact injury severity. In this paper, we will focus primarily on the proximal driver behavior 35 context variables of distracted/careless driving behavior and risky driving behavior as the latent 36 psychological factors (or constructs). The framework in Figure 1 requires a minimum of two 37 indicators of these latent factors for identification purposes, but can accommodate as many as 38 desired. The proposed framework is quite flexible and may be used for crashes involving 39 multiple vehicles (more than two vehicles) of any type. As shown in the framework, injury 40 severities of all vehicle occupants in two-vehicle crashes are modeled and psychological 41 constructs describing both drivers involved in the crash are considered to have an influence on 42 these severities. The occupants of the vehicles are linked to their seat positions, resulting in five 43 possible injury severity outcomes associated with: 1) the driver’s seat; 2) the front passenger 44 seat; 3) the back left seat; 4) the back middle seat; and 5) the back right seat. Both the latent 45 constructs from each driver affect the injury severities of all occupants in both vehicles. Each 46


person in a vehicle is affected equally by the same construct corresponding to a specific driver. 1 The modeling framework accommodates the effects of: 1) risky behavior of the driver on his/her 2 own vehicle; 2) risky behavior of the driver on the other vehicle; 3) careless behavior of the 3 driver on his/her own vehicle; and 4) careless behavior of the driver on the other vehicle. 4

5

6 FIGURE 1 Conceptual framework of injury severity model system. 7

8 An issue that arises in this modeling effort is that the labeling of drivers is arbitrary 9

because there is no explicit information in the GES crash database about who is at fault. To 10 address this labeling issue, the loadings of the latent factors on each indicator variable and the 11 constants associated with the indicator variables are constrained to be the same across drivers. 12


The labeling issue also imposes restrictions on the correlation between the latent variables; there 1 is only one value for correlation between risky and distracted/careless driving behavior variables. 2 The parameters associated with exogenous explanatory variables (environment, road condition, 3 crash type) on injury severity are also constrained to be the same across the occupants of the two 4 vehicles seated in the same position, because the vehicles are also labeled arbitrarily. Thresholds 5 associated with the propensity of individuals seated in the same position in a vehicle to 6 experience injury severity of different levels are constrained to be the same across vehicles 7 (because vehicles are numbered arbitrarily). Both injury severities, and the indicators for latent 8 factors, are coded as ordinal variables. The injury severity levels are: 1) no apparent injury; 2) 9 possible injury; 3) minor injury; and 4) serious or fatal injury. The indicator variables are binary 10 and take on a value of one or two for notational consistency. 11 12 4. MODELING METHODOLOGY 13 A special case of the GHDM approach proposed by Bhat (2015) is used for the modeling effort 14 in this paper. It constitutes a special case because all of the variables in this study are ordinal 15 response variables, thus avoiding the necessity to deal with a mixture of dependent variable 16 types. The model system is composed of a structural equation component and a measurement 17 equation component. In the structural equation, driver age and gender, and presence of children 18 in the vehicle are used to explain distracted/careless driving behavior and risky driving behavior. 19 Correlation across these latent constructs is accommodated in the model formulation. In the 20 measurement equation, the latent variables are loaded on the four indicators (two for 21 distracted/careless driving, and two for risky driving) and also on the injury severity of every 22 vehicle occupant. All of the other explanatory variables are also loaded on the injury severity 23 outcomes, and interactions between the explanatory variables and the latent variables are 24 accommodated in the model specification. 25 26 4.1 Latent Variable Structural Equation Model Component 27 Let l be an index for latent variables (l=1,2,…,L), in the context of this study L=4. Consider the 28 latent variable *

lz and write it as a linear function of covariates: 29

,*llz wα l (1) 30

where w is a )1( D vector of observed covariates (excluding a constant), lα is a corresponding 31

)1( D vector of coefficients, and l is a random error term assumed to be standard normally 32

distributed for identification purposes (see Stapleton, 1978). Next, define the )( DL matrix 33

),...,,( 21 Lαααα , and the )1( L vectors ) ,...,,( **2

*1 Lzzz*z and )'.,,,,( 321 L η 34

In this study, denote *1z and *

2z as driver-one and driver-two non-risky behavior 35

respectively, and therefore 1α and 2 α are the coefficients for each of the drivers. Since the 36 labeling of the drivers is arbitrary, both latent variables and both parameter vectors are 37 constrained to be the same. An analogous approach was taken for the distracted/careless driving 38 behavior latent variable ( *

3z and *4z ). An MVN correlation structure for η is adopted to 39

accommodate interactions among the unobserved latent variables: ],[~ Γ0η LLMVN , where L0 40 is an )1( L column vector of zeros, and Γ is )( LL correlation matrix. 41 42


4.2 Latent Variable Measurement Equation Model Component 1 As mentioned earlier, all outcomes in this model may be considered ordinal. There are two types 2 of ordinal variables, those representing injury severity and those representing indicators. The first 3 have a four-level range while the second have two levels. The propensity equations for both are 4 similar, changing only on the number of thresholds. 5

Consider N ordinal outcomes (indicator variables) for the individual, and let n be the 6 index for the ordinal outcomes ) ..., ,2 ,1( Nn . Also, let nJ be the number of categories for the 7

nth ordinal outcome )2( nJ and let the corresponding index be nj ) ..., ,2 ,1( nn Jj . Let *ny be 8

the latent underlying variable whose horizontal partitioning leads to the observed outcome for 9 the nth ordinal variable. Assume that the individual under consideration chooses the th

na ordinal 10

category. Then, in the usual ordered response formulation, for the individual: 11 ,and, ,

*1,

*

nn annannnn yy *

n zdxγ (2) 12

where x is a vector of exogenous and possibly endogenous variables as defined earlier, nγ is a 13

corresponding vector of coefficients to be estimated, nd is an )1( L vector of latent variable 14

loadings on the nth continuous outcome, the terms represent thresholds, and n is the standard 15

normal random error for the nth ordinal outcome. For each ordinal outcome, 16

nn JnJnnnn ,1,2,1,0, ... ; 0,n , 01, n , and nJn , (note that, for the 17

binary indicators, there are no thresholds to be estimated because 2nJ ; for the injury severity 18

variables in the empirical context of the current study, there are two thresholds to be estimated 19 because )4nJ . For later use, let )...,,( 1,3,2, nJnnn nψ and .),...,,( Nψψψψ 21 Stack the 20

N underlying continuous variables *ny into an )1( N vector *y , and the N error terms n into 21

another )1( N vector ε . Define ),...,,( 21 Hγγγγ [ )( AN matrix] and N, dddd ,...,, 21 22

[ )( LN matrix], and let NIDEN be the identity matrix of dimension N representing the 23

correlation matrix of ε (so, NIDEN0 ,~ NNMVNε ; again, this is for identification purposes, 24

given the presence of the unobserved *z vector to generate covariance. Finally, stack the lower 25 thresholds for the decision-maker Nn

nan ..., ,2 ,11, into an )1( N vector lowψ and the upper 26

thresholds Nnnan ..., ,2 ,1, into another vector .upψ Then, in matrix form, the measurement 27

equation for the ordinal outcomes (indicators) for the decision-maker may be written as: 28

up*

low** ψyψεdzγxy , . (3) 29

Readers are referred to Bhat (2015) for a detailed discussion on identification issues and 30 the detailed estimation approach. The model system uses the features of the GHDM to 31 accommodate correlation across both vehicles and all occupants involved in a crash. However, 32 different from previous applications of the GHDM and previous injury severity studies, the 33 model proposed in this paper offers a versatile structure that accommodates cross-effects 34 between vehicles through mapping matrices. The mapping matrices are both used to solve the 35 arbitrary labeling issues noted previously and to accommodate cross-vehicle effects. The 36 mapping matrices can be easily expanded to accommodate additional vehicles, additional 37 occupants or seating positions, and additional latent and endogenous variables. 38 39 40


5. DATA DESCRIPTION 1 The data used in this study is derived from the National Automotive Sampling System (NASS) 2 General Estimates System. The crash database provides data on a representative sample of 3 crashes of all types involving all types of vehicles. The most recent 2013 GES crash database is 4 used in this study. The analysis and modeling effort is limited to crashes involving two 5 passenger vehicles. One of the key motivating factors underlying the exclusive attention paid to 6 two-vehicle crashes is the interest in analyzing the effects of the behavior of the driver in one 7 vehicle on the injury severity outcomes of occupants in the second vehicle (in addition to the 8 injury severity outcomes of passengers in the same vehicle). 9 10 TABLE 1 Descriptive Characteristics of the Crash Database Sample 11 Environment Variables Roadway Variables

Time of Day Speed Limit (mph) 12AM-6AM 208 6.1% 35 or less 1642 47.9% 6AM-9AM 412 12.0% 40-50 1227 35.8% 9AM-4PM 1465 42.7% 55-65 508 14.8% 4PM-7PM 897 26.2% 70-85 52 1.5% 7PM-12AM 447 13.0% Trafficway Type

Light Conditions One way 87 2.5% Daylight 2544 74.2% Two way divided 1140 33.3% Dawn/Dusk 125 3.7% Two way undivided 1675 48.9% Dark 195 5.7% Other 527 15.4% Dark-artificial light 565 16.5% Intersection Type

Weather Conditions Intersection 2047 59.7% Clear 2474 72.2% Access 424 12.4% Rain 335 9.8% Other type 874 25.5% Snowing 52 1.5% Not an intersection 84 2.5% Other 568 16.6% Injury Severity Driving Behavior Indicators No apparent injury 6107 66.6%

Risky Behavior Possible injury 1281 13.9% Alcohol/Drugs 165 2.4% Minor injury 1148 12.5% No Seat Belt 127 1.9% Serious/fatal injury 641 7.0%

Distracted/Careless Behavior Inattention 370 5.4% Soft violations: signs, lane use

1117 16.3%

12 The cleaned data set used for model estimation included 3,429 crashes. These crashes 13

involve 9,177 individuals – 6,858 drivers and 2,319 passengers. The vehicles have up to four 14 occupants (the few observations with more than four occupants in a vehicle had missing values 15 and were removed). The variable indicating whether an airbag was deployed or not could not be 16 included in the model specification because of the large prevalence of missing values. 17 Moreover, the crashes included in the estimation data set were limited to those involving 18 “automobiles” as defined in the GES analytical user’s manual. Due to a high prevalence of 19 missing values for several driver behavior indicators (e.g., if driver was speeding, different types 20 of violations, reckless driving, use of cell phone, distractions inside or outside vehicle), the set of 21 indicators was limited to the following where complete data was consistently available: 22


1) For risky driving behavior 1 a. Alcohol or drug use 2 b. Non seat belt use 3

2) For distracted/careless driving behavior 4 a. Inattention 5 b. Soft violations that can be associated with a distraction (fail to yield, fail to 6

stop, improper turn, improper use of lane, fail to obey sign or signal) 7 Seat belt use by the driver and alcohol consumption are treated as endogenous; thus they 8

serve both as indicators of the latent factors and as explanatory variables for the injury severity 9 outcomes. Descriptive statistics of the sample are presented in Table 1. A large percent of 10 crashes occur in the midday (9AM to 4PM) in the daylight hours, simply because there is more 11 travel during those periods. Similarly, most accidents occur during daylight hours (74.1%) and 12 in clear weather (72.2 percent). Very few crashes are associated with roadways with very high 13 speed limits of 70-85 mph presumably because there are fewer roadways (and hence less travel) 14 with such speed limits. Nearly 60 percent of crashes occur at intersections where there are 15 multiple conflict points. With respect to driving behaviors, soft violations are involved in 16 16 percent of the crashes. Risky behaviors are involved in small percent of crashes (about five 17 percent or less). There is no apparent injury in two-thirds of the crashes. Seven percent of the 18 crashes involve a serious or fatal injury. Additional extensive exploratory analysis of the data 19 was conducted to help inform the model specification. 20 21 6. MODEL ESTIMATION RESULTS 22 Model estimation was undertaken for all occupants jointly, accounting for correlation among 23 unobserved factors through latent variables. The model structure also accommodated cross-24 effects where the behavior of each driver affects outcomes for both vehicles involved in the 25 crash. A variety of model specifications were tested treating explanatory variables as both 26 alternative specific and generic in nature; for some variables, such as light conditions, it would 27 not be reasonable to test for different coefficients across the seat positions and hence such 28 variables were treated as generic variables. Other variables, such as side of impact, were tested 29 to determine whether a generic treatment would be appropriate. In general, the limitations of the 30 data set prevented the full exploitation of the capabilities of the model formulation. There was 31 missing data on a number of variables that could be used as key indicators of distracted driving. 32 33 6.1 Results of the Structural Equation Component 34 Table 2 presents results of the structural equation component of the model system. The table 35 first presents the loadings of different variables on the latent variables. The risky driving 36 behavior latent variable is negatively associated with alcohol use and no seat belt use. In other 37 words, this latent construct is actually capturing safe (non-risky) driving behavior. The 38 distracted and careless driving behavior latent variable has positive loadings associated with 39 inattention and soft violations (failure to yield, not obeying signs and signal). Thus this latent 40 variable is truly measuring distracted and careless driving behavior. 41 42 43


TABLE 2 Results of the Structural Equation Component – Latent Variable Model 1 Variable Coefficient t-stat

Loadings of Indicators on Latent Variables Indicators of Non-Risky Driving Behavior (NRDB) Constant in no seat belt use indicator equation -2.0057 -5.39 Constant in alcohol use indicator equation -1.9613 -2.46 Loading of NRDB on no seat-belt use indicator eqn. -0.3866 -4.92 Loading of NRDB on alcohol use indicator eqn. -0.6055 -7.47 Indicators of distracted and careless driving behavior (DCDB) Constant in inattention indicator equation -1.6039 -61.06 Constant in soft violations indicator equation -0.9891 -33.30 Loading of DCDB on inattention indicator equation 0.0655 9.34 Loading of DCDB on soft violations indicator equation 0.1776 3.91

Structural Equation Driver’s Non-Risky Behavior Female 0.7922 21.05 Presence of children in vehicle 0.3578 9.38 Age 26-35 years 0.3344 11.65 Age 36-65 years 0.5124 14.85 Age >65 years 0.6439 14.15 Driver’s Distracted and Careless Behavior Female -0.0815 -6.04 Age >65 years 0.0502 2.87 Correlation between non-risky and distracted/careless driving behavior latent constructs

-0.2600 -2.10

2 The second part of Table 2 presents results of the structural equation estimation. Being female 3 and the presence of children in the vehicle is positively associated with safe driving behavior. It 4 is likely that drivers are more careful when children are present (Fleiter et al, 2010); such drivers 5 may also be older and more experienced and mature. These findings are consistent with those 6 reported by Rhodes and Pivik (2011) and safe driving behavior is positively correlated with age; 7 as age increases, the propensity to drive safely increases as well. With respect to distracted and 8 careless behavior, females are less likely to be distracted and careless. Those greater than 65 9 years of age are, however, more likely to be distracted and careless. The correlation between 10 safe driving behavior and distracted/careless driving behavior is, as expected, negative and 11 statistically significant. These latent factors were then included as explanatory variables in the 12 measurement equation. 13 14 6.2 Results of the Measurement Equation Component 15 The measurement equation includes an extensive set of explanatory variables and latent factors 16 to capture the influence of various attributes on the injury severity of occupants seated in 17 different positions. As the estimation results are rather extensive and the entire table is too large 18 for inclusion within the scope of this paper, only selected estimation results (pertaining to the 19 latent variable impacts) are presented in Table 3. In addition to the latent constructs, the model 20 includes a number of occupant characteristics (age and gender), vehicle characteristics (vehicle 21 type and age), crash characteristics (collision type, area of impact), environmental variables 22 (time of day, light conditions, and weather conditions), and roadway characteristic variables 23


(speed limit, intersection type, trafficway descriptors). The discussion presents key findings 1 across all explanatory factors (even though the parameters are not included in Table 3). 2 Males have a lower propensity to sustain severe injuries when compared to females in all 3 seat positions, consistent with findings reported by Eluru et al (2010). Children 14 years of age 4 or younger are less prone to severe injuries in all back seat positions, reinforcing the adage that 5 children are safest when in the rear seat. Those older than 65 years of age are more susceptible 6 to severe injuries in all seat positions, an indication of the weakened physical state at an 7 advanced age. The absence of seat belt use contributes significantly to severe injury outcomes, 8 reaffirming that seat belts can reduce the impact of crashes on vehicle occupants even after 9 accounting for endogeneity. 10 Occupants are more likely to sustain severe injuries when seated in hatchbacks and 11 convertibles (as opposed to sedans and station wagons, that are likely larger and safer vehicles), 12 a finding consistent with that reported by Ju and Sohn (2011). Compared to newer vehicles, 13 occupants are likely to sustain injuries in older vehicles with the highest propensity for severe 14 injuries in vehicles over 10 years of age. The condition of the vehicles and the likelihood that 15 vehicles of such vintage do not include the latest safety features contribute to this finding 16 (Bilston et al, 2010). Alcohol use positively contributes to injury severity, a finding that is 17 consistent with expectations. 18

Rear-end crashes are associated with less severe injuries while frontal collisions result in 19 more severe injuries across all seating positions. Older individuals greater than 65 years of age 20 are likely to sustain more serious injuries when in a side-impact crash (compared to younger 21 counterparts). In terms of the environmental conditions, crashes occurring in the overnight hours 22 of 12AM to 6AM are most likely to result in severe injuries, possibly due to excessive speeding 23 (when there is no traffic on the roadways), darkness, and impaired driving. Both darkness and 24 dawn/dusk hours are associated with more severe injury outcomes compared to daylight 25 conditions or dark-with artificial light conditions, consistent with expectation. Crashes in rain 26 and snow (inclement weather) are less severe in terms of injury across occupants in all seat 27 positions. It is likely that this is a manifestation of the slower speeds and more care exercised by 28 drivers under such environmental conditions. In terms of roadway characteristics, crashes that 29 occur on roadways with a low speed limit of 35 mph or less are generally less severe for 30 passengers in all seat positions. Crashes at non-intersections (access or not a junction, other type 31 of junction) are likely to be more severe for all occupants; this is likely due to higher speeds at 32 non-intersection locations and the lack of traffic control at such locations. 33

Finally, latent variables are found to be very significant in their effects on injury severity 34 (see Table 3). An interesting finding is that non-risky driving behavior is associated with greater 35 levels of injury severity for all occupants in the driver’s vehicle. This finding is actually not that 36 counter-intuitive. Risky drivers may actually be more capable drivers in terms of their agility 37 and ability to swerve and reduce crash severity. The vehicle of the non-risky driver, who may 38 not be anticipating a crash may therefore be more prone to suffering the more severe outcomes. 39 Moreover, the non-risky drivers are likely to be older and female – and it is possible that these 40 groups are more susceptible to severe injury. However, non-risky driving behavior is associated 41 with less impact (in terms of injury severity) on the occupants of the other vehicle, which is very 42 much consistent with expectations. Distracted and careless driving behavior is associated with 43 more severe injury outcomes for both vehicles. These results illustrate the cross-effects of the 44 behavior of one driver on the injury severity outcomes of occupants in the other vehicle. 45


TABLE 3 Results of Measurement Equation – Parameters Indicating Influence of Factors on Injury Severity Propensity 1

Driver Front Passenger Back left seat Back middle seat Back right seat

Variable name Coef t-stat Coef t-stat Coef t-stat Coef t-stat Coef t-stat

Constant -0.8675 -8.15 -0.4064 -3.06 -0.2413 -3.31 -0.1417 -4.11 -0.2343 -3.4

Threshold parameters

Threshold 1 0.7802 30.12 0.9165 17.33 1.1803 7.47 1.0515 3.91 0.9199 8.00

Threshold 2 1.9356 44.50 2.0559 25.65 2.5991 9.34 2.3579 4.92 2.6204 11.02

Latent variables

Non-risky behavior on the driver's vehicle 0.5581 20.82 0.5581 20.82 0.0490 3.03 0.0490 3.03 0.0490 3.03

Non-risky behavior on the other vehicle -0.0793 -3.33 -0.0793 -3.33 -0.5409 -11.83 -0.5409 -11.83 -0.5409 -11.83 Distracted/careless behavior on the driver's vehicle

0.5527 17.71 0.5527 17.71 0.5527 17.71 0.5527 17.71 0.5527 17.71

Distracted/careless behavior on the other vehicle

1.2623 2.85 1.2623 2.85 1.2623 2.85 1.2623 2.85 1.2623 2.85

Goodness of Fit Assessment

Measure of Fit GHDM IHDM

Composite marginal log-likelihood value at convergence -140429.89 -164343

Number of parameters 63 45

Composite Likelihood Information Criterion (CLIC) -142202.47 -165818

Average probability of correct prediction based on joint prediction of all passengers in two vehicles 0.331 0.226

2


6.3 Model Goodness-of-Fit 1 The performance of the GHDM structure used in this paper can be compared to the one that does 2 not consider latent constructs, maintaining the same specification of the final model. However, 3 this would not constitute a fair specification to test the GHDM specification. Therefore, a model 4 specification that includes the determinants of the latent constructs as explanatory variables, 5 while maintaining the recursivity in the dimensions as obtained from the final GHDM model, 6 was estimated. The proof model is an independent model in which the error term correlations 7 across the dimensions are ignored, but the best specification of the explanatory variables 8 (including those used in the GHDM model in the structural equation system to explain the latent 9 constructs) is considered to explain the injury severity of the vehicle occupants. The model that 10 has no latent constructs takes the form of a multivariate probit model. This may be referred to as 11 an independent heterogeneous data model (or IHDM). The GHDM and the IHDM specifications 12 are not nested, but they may be compared using the composite likelihood information criterion 13 (CLIC) introduced by Varin and Vidoni (2005). The CLIC takes the following form: 14

1* )ˆ(ˆ)ˆ(ˆ)ˆ(log)ˆ(log θHθJθθ trLL CMLCML (4) 15

The model that provides a higher value of CLIC is preferred. The performance of the two models 16 may also be compared through the likelihood values )ˆ(θ L . The corresponding IHDM 17 predictive log-likelihood value may also be computed. The goodness of fit indicators are 18 presented at the bottom of Table 3. 19 20 7. CONCLUSIONS 21 This paper presents a comprehensive model of crash injury severity for two-vehicle crashes of all 22 types. The paper employs the GHDM and exploits its methodological capabilities to advance the 23 state of crash severity modeling in three key ways. First, the model system constitutes a 24 simultaneous equations model system capable of accounting for latent driver behavior constructs 25 that influence crash severity outcomes. Second, the model system is able to jointly model the 26 injury severity outcomes for all vehicle occupants in the context of their respective seat 27 positions. Third, the model system accounts for endogeneity in specific explanatory factors such 28 as seat belt use and alcohol involvement. Treating these variables as exogenous variables, when 29 in fact they are endogenous, may lead to inconsistent and biased parameter estimates. Moreover, 30 the model offers the ability to estimate cross-effects, i.e., the effects of the behavior of one 31 vehicle’s driver on the injury severity outcomes experienced by occupants in the second vehicle. 32 It is important to model the injury severity of multiple individuals involved in a crash as 33 different occupants may experience different levels of injury severity. Those differences may be 34 based on observed factors (seat belt use, vehicle type, position of seating) and on unobserved 35 factors (such as the vehicle condition or psychological traits of the driver). Some of these 36 unobserved factors may affect all of the individuals in the same vehicle, while others may impact 37 every person involved in the crash (even across multiple vehicles). The presence of these 38 common unobserved elements motivates the development of a joint multivariate injury-severity 39 model such as that presented in this paper. 40 It is found that older drivers are particularly susceptible to severe injury outcomes; their 41 impaired driving ability and frail physical condition likely contributes to adverse injury 42 outcomes. Safety interventions inside vehicles and on the roadway should be targeted towards 43 older drivers as their presence in the driving population increases in size. Similarly, 44 interventions that enhance safety at night (such as improved lighting) can help reduce injury 45


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