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V.A.Morgan /tt/file_convert/5a7074227f8b9ab6538bf241/document.docx5 July 2012
USING WEIGHTS WITH SHIP DATAVersion: 05 July 2012
Contents
USING WEIGHTS WITH SHIP DATA.........................................................................1General introduction...........................................................................................2Weights in Stata.................................................................................................3Weights in SPSS..................................................................................................4Weights in SAS...................................................................................................5
APPENDICES...........................................................................................................6Stata example output.........................................................................................6
Stata: Mean.....................................................................................................6Stata: Tabulate................................................................................................6Stata: Logistic regression................................................................................7
SPSS example output.........................................................................................9SPSS: Complex Samples Analysis Plan............................................................9SPSS: Complex Samples Descriptives...........................................................10SPSS: Complex Samples Tables.....................................................................11SPSS: Complex Samples Logistic regression.................................................15
SAS example output.........................................................................................17SAS: The SURVEYMEANS Procedure..............................................................17SAS: The SURVEYFREQ Procedure.................................................................18SAS: The SURVEYLOGISTIC Procedure...........................................................19
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V.A.Morgan /tt/file_convert/5a7074227f8b9ab6538bf241/document.docx5 July 2012
General introduction
1. Weighted analyses should be only be done using appropriate statistical software:
Stata svy or pweight commands SPSS Complex Samples SAS Survey Procedures
2. The weights to use in Stata, SPSS Complex Samples and SAS Survey Procedures are in the variable:
weightsa
3. Weightsa may also be used for subgroup analyses using Stata commands, SPSS Complex Samples and SAS Survey Procedures.
4. If working with the full SHIP dataset based on 1825 survey participants, using weights results in a population N of 7955. For SHIP, ‘population’ refers to the individuals ascertained in the screening phase This N will be smaller for subsamples (e.g. those meeting full ICD-10 criteria for psychosis; schizophrenia only etc.).
5. It is very important that weightsa be used only as a sampling (or probably) weight. Using it as a weight in a Stata [fweight=…] option, the SPSS “Weight by…” command or as a WEIGHT or FREQ variable in a normal SAS proc will lead the program to believe that 7955 participants were actually interviewed leading to extremely serious errors in many statistics.
6. When relevant strata information is included in a model, the ‘need’ for weighting is dramatically reduced. Site strata information is not available, but our experience to date is that when age is included in models (e.g., regression), the difference in estimates and standard errors between weighted and unweighted data is relatively small. Nevertheless, if it possible to use weighting, it should be done for accuracy and for uniformity across analyses.
7. For information only: there is a variable that Andrew has created called weightsa_nrm which gives an approximation for those using basic SPSS and basic SAS. However we are not recommending that people work in basic SPSS or basic SAS with this variable and will not be providing it unless the person requesting to use this variable can justify their request.
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Weights in Stata
In Stata, there are two approaches, depending on the procedure.
(a) For many procedures (e.g. mean; logistic), you can use the [pweight=weightsa] option
(b) Other procedures (e.g. tabulate) need to be run in conjunction with the survey (svy) feature. The survey feature can also be used with procedures that permit the [pweight=weightsa] option.
The survey structure must be first specified in svyset if you need to use the survey procedure:
* Specifying the survey structure before using the survey (svy) feature.
svyset [pweight=weightsa]
This will produce the following information outputpweight: weightsaVCE: linearizedSingle unit: missingStrata 1: <one>SU 1: <observations>FPC 1: <zero>
* Means using (a) pweight and (b) the survey feature. Note that (b) assumes you have specified the survey structure as above.
(a) mean age_calc [pweight = weightsa]
(b) svy: mean age_calc
* Tables using the survey feature. Note that this assumes you have specified the survey structure as above.
svy: tabulate sex DIAGicd10, count ci
* Logistic Regression a) pweight and (b) the survey feature. Note that (b) assumes you have specified the survey structure as above..
(a) logit anyIP_rev age_calc [pweight = weightsa]
(b) svy: logit anyIP_rev age_calc
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V.A.Morgan /tt/file_convert/5a7074227f8b9ab6538bf241/document.docx5 July 2012
Weights in SPSS
The appropriate SPSS Complex Samples analysis plan is in a file called SHIP_SPSSweighting.csaplan which is created by running the syntax below:
CSPLAN ANALYSIS /PLAN FILE='D:\SHIPdata_files\SHIP_SPSSweighting.csaplan' /PLANVARS ANALYSISWEIGHT=weightsa /SRSESTIMATOR TYPE=WR /PRINT PLAN /DESIGN /ESTIMATOR TYPE=WR.
You must use the SPSS Complex Samples battery of statistics with this plan. For example:
* Complex Samples Descriptives.
CSDESCRIPTIVES /PLAN FILE='D:\SHIPdata_files\SHIP_SPSSweighting.csaplan' /SUMMARY VARIABLES=age_calc /MEAN /STATISTICS SE COUNT POPSIZE CIN(95) /MISSING SCOPE=ANALYSIS CLASSMISSING=EXCLUDE.
* Complex Samples Tabulate.
CSTABULATE /PLAN FILE='D:\SHIPdata_files\SHIP_SPSSweighting.csaplan' /TABLES VARIABLES=sex BY DIAGicd10 /CELLS POPSIZE COLPCT /STATISTICS CIN(95) /MISSING SCOPE=TABLE CLASSMISSING=EXCLUDE.
* Complex Samples Logistic Regression.
CSLOGISTIC anyIP WITH age_calc /PLAN FILE='D:\SHIPdata_files\SHIP_SPSSweighting.csaplan' /MODEL age_calc /INTERCEPT INCLUDE=YES SHOW=YES /STATISTICS PARAMETER EXP CINTERVAL /TEST TYPE=F PADJUST=LSD /ODDSRATIOS COVARIATE=[age_calc(1)] /CRITERIA MXITER=100 MXSTEP=5 PCONVERGE=[1E-006 RELATIVE] LCONVERGE=[0] CHKSEP=20 CILEVEL=95 /PRINT SUMMARY CLASSTABLE VARIABLEINFO SAMPLEINFO.
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Weights in SAS
For SAS Complex Survey Design, SAS uses specific commands when using weight variable. For example: for Means, SAS uses Proc Surveymeans as the main command instead of 'Proc Means'. Similarly for frequency and logistic procedures, SAS uses Proc Surveyfreq and Proc Surveylogistic respectively
SAS SURVEY PROCEDURES COMMANDS. For example:
*Complex survey design: MEAN PROCEDURE.
Proc Surveymeans data=xxx.xxxxxx; weight weightsa;var age_calc;Title 'MEAN PROCEDURE FOR AGE';run;
*Complex survey design: CROSS TABULATION.
Proc Surveyfreq data=xxx.xxxxxx ; weight weightsa;tables sex*DIAGICD10;Title 'Cross tabulation of Sex by Psychotic illness';run;
*Complex survey design: LOGISTIC REGRESSION.
Proc Surveylogistic data= xxx.xxxxxx order=internal;weight weightsa; Model anyIP (ref=last order=internal)= age_calc /link=glogit; Title 'Effect of age on inpatient admission'; run;
w
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APPENDICESStata example output
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Stata: Mean
Stata: Tabulate
V.A.Morgan /tt/file_convert/5a7074227f8b9ab6538bf241/document.docx5 July 2012
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Stata: Logistic regression
V.A.Morgan /tt/file_convert/5a7074227f8b9ab6538bf241/document.docx5 July 2012
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SPSS example output
SPSS: Complex Samples Analysis Plan
* SHIP_SPSSweighting_egs.sps.
* Analysis Preparation Wizard.CSPLAN ANALYSIS /PLAN FILE='D:\SHIPdata_files\DataMain\weighting\SPSS\SHIP_SPSSweighting.csaplan' /PLANVARS ANALYSISWEIGHT=weightsa /SRSESTIMATOR TYPE=WR /PRINT PLAN /DESIGN /ESTIMATOR TYPE=WR.
Complex Samples: Plan
SummaryStage 1
Analysis Information Estimator Assumption Sampling with replacement
Plan File: D:\SHIPdata_files\DataMain\weighting\SPSS\SHIP_SPSSweighting.csaplanWeight Variable: weightsa Sampling weight by site and age stratumSRS Estimator: Sampling with replacement
CSPLAN VIEW /PLAN FILE='D:\SHIPdata_files\DataMain\weighting\SPSS\SHIP_SPSSweighting.csaplan' .
Complex Samples: PlanAnalysis Plan
SummaryStage 1
Analysis Information Estimator Assumption Sampling with replacement
Plan File: D:\SHIPdata_files\DataMain\weighting\SPSS\SHIP_SPSSweighting.csaplanWeight Variable: weightsa Sampling weight by site and age stratumSRS Estimator: Sampling with replacement
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SPSS: Complex Samples Descriptives* Complex Samples Descriptives.CSDESCRIPTIVES /PLAN FILE='D:\SHIPdata_files\DataMain\weighting\SPSS\SHIP_SPSSweighting.csaplan' /SUMMARY VARIABLES=age_calc /MEAN /STATISTICS SE COUNT POPSIZE CIN(95) /MISSING SCOPE=ANALYSIS CLASSMISSING=EXCLUDE.
Complex Samples: DescriptivesUnivariate Statistics
Estimate Standard Error 95% Confidence IntervalLower Upper
Mean age_calc Age (calculated) in years at time of interview 39.47 .273 38.93 40.00
Univariate StatisticsPopulation Size Unweighted Count
Mean age_calc Age (calculated) in years at time of interview 7955.000 1825
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SPSS: Complex Samples Tables* Complex Samples Tables.CSTABULATE /PLAN FILE='D:\SHIPdata_files\DataMain\weighting\SPSS\SHIP_SPSSweighting.csaplan' /TABLES VARIABLES=sex BY DIAGicd10 /CELLS POPSIZE COLPCT /STATISTICS CIN(95) /MISSING SCOPE=TABLE CLASSMISSING=EXCLUDE.
Complex Samples: Tablessex sex * DIAGicd10 DIP ICD-10
sex sex DIAGicd10 DIP ICD-10
1 schizophrenia
0 male
Population SizeEstimate 2650.360
95% Confidence IntervalLower 2464.343Upper 2836.378
% within DIAGicd10 DIP ICD-10Estimate 70.4%
95% Confidence IntervalLower 67.1%Upper 73.6%
1 female
Population SizeEstimate 1112.866
95% Confidence Interval Lower 974.388Upper 1251.344
% within DIAGicd10 DIP ICD-10Estimate 29.6%
95% Confidence Interval Lower 26.4%Upper 32.9%
Total
Population SizeEstimate 3763.226
95% Confidence IntervalLower 3559.907Upper 3966.545
% within DIAGicd10 DIP ICD-10Estimate 100.0%
95% Confidence IntervalLower 100.0%Upper 100.0%
sex sex * DIAGicd10 DIP ICD-10sex sex DIAGicd10 DIP
ICD-102 schizoaffective
0 male
Population SizeEstimate 623.920
95% Confidence IntervalLower 524.582Upper 723.257
% within DIAGicd10 DIP ICD-10Estimate 53.6%
95% Confidence IntervalLower 47.5%Upper 59.5%
1 female
Population SizeEstimate 540.863
95% Confidence Interval Lower 447.709Upper 634.017
% within DIAGicd10 DIP ICD-10Estimate 46.4%
95% Confidence Interval Lower 40.5%Upper 52.5%
Total
Population SizeEstimate 1164.782
95% Confidence IntervalLower 1033.930Upper 1295.635
% within DIAGicd10 DIP ICD-10Estimate 100.0%
95% Confidence IntervalLower 100.0%Upper 100.0%
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sex sex * DIAGicd10 DIP ICD-10sex sex DIAGicd10 DIP
ICD-103 bipolar, mania
0 male
Population SizeEstimate 621.156
95% Confidence IntervalLower 516.721Upper 725.591
% within DIAGicd10 DIP ICD-10Estimate 44.5%
95% Confidence IntervalLower 38.8%Upper 50.3%
1 female
Population SizeEstimate 774.091
95% Confidence Interval Lower 658.974Upper 889.208
% within DIAGicd10 DIP ICD-10Estimate 55.5%
95% Confidence Interval Lower 49.7%Upper 61.2%
Total
Population SizeEstimate 1395.247
95% Confidence IntervalLower 1246.483Upper 1544.011
% within DIAGicd10 DIP ICD-10Estimate 100.0%
95% Confidence IntervalLower 100.0%Upper 100.0%
sex sex * DIAGicd10 DIP ICD-10sex sex DIAGicd10 DIP
ICD-104 depressive
psychosis
0 male
Population SizeEstimate 146.112
95% Confidence IntervalLower 93.097Upper 199.128
% within DIAGicd10 DIP ICD-10Estimate 39.7%
95% Confidence IntervalLower 29.1%Upper 51.3%
1 female
Population SizeEstimate 221.883
95% Confidence Interval Lower 156.582Upper 287.185
% within DIAGicd10 DIP ICD-10Estimate 60.3%
95% Confidence Interval Lower 48.7%Upper 70.9%
Total
Population SizeEstimate 367.996
95% Confidence IntervalLower 284.700Upper 451.292
% within DIAGicd10 DIP ICD-10Estimate 100.0%
95% Confidence IntervalLower 100.0%Upper 100.0%
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sex sex * DIAGicd10 DIP ICD-10sex sex DIAGicd10 DIP
ICD-105 delusional
disorders and other non-organic psychosis
0 male
Population SizeEstimate 303.380
95% Confidence IntervalLower 225.754Upper 381.007
% within DIAGicd10 DIP ICD-10Estimate 72.0%
95% Confidence IntervalLower 61.4%Upper 80.7%
1 female
Population SizeEstimate 117.849
95% Confidence Interval Lower 70.240Upper 165.459
% within DIAGicd10 DIP ICD-10Estimate 28.0%
95% Confidence Interval Lower 19.3%Upper 38.6%
Total
Population SizeEstimate 421.230
95% Confidence IntervalLower 330.999Upper 511.461
% within DIAGicd10 DIP ICD-10Estimate 100.0%
95% Confidence IntervalLower 100.0%Upper 100.0%
sex sex * DIAGicd10 DIP ICD-10sex sex DIAGicd10 DIP
ICD-106 severe
depression without psychosis
0 male
Population SizeEstimate 288.228
95% Confidence IntervalLower 212.997Upper 363.459
% within DIAGicd10 DIP ICD-10Estimate 40.2%
95% Confidence IntervalLower 32.4%Upper 48.6%
1 female
Population SizeEstimate 427.942
95% Confidence Interval Lower 338.840Upper 517.044
% within DIAGicd10 DIP ICD-10Estimate 59.8%
95% Confidence Interval Lower 51.4%Upper 67.6%
Total
Population SizeEstimate 716.170
95% Confidence IntervalLower 601.809Upper 830.532
% within DIAGicd10 DIP ICD-10Estimate 100.0%
95% Confidence IntervalLower 100.0%Upper 100.0%
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sex sex * DIAGicd10 DIP ICD-10sex sex DIAGicd10 DIP
ICD-107 screen-positive for psychosis but did not meet full
criteria for ICD-10 psychosis
0 male
Population SizeEstimate 79.350
95% Confidence IntervalLower 40.256Upper 118.444
% within DIAGicd10 DIP ICD-10Estimate 62.8%
95% Confidence IntervalLower 41.5%Upper 80.1%
1 female
Population SizeEstimate 46.999
95% Confidence Interval Lower 13.491Upper 80.507
% within DIAGicd10 DIP ICD-10Estimate 37.2%
95% Confidence Interval Lower 19.9%Upper 58.5%
Total
Population SizeEstimate 126.349
95% Confidence IntervalLower 75.013Upper 177.685
% within DIAGicd10 DIP ICD-10Estimate 100.0%
95% Confidence IntervalLower 100.0%Upper 100.0%
sex sex * DIAGicd10 DIP ICD-10sex sex DIAGicd10
DIP ICD-10Total
0 male
Population SizeEstimate 4712.507
95% Confidence IntervalLower 4508.928Upper 4916.086
% within DIAGicd10 DIP ICD-10Estimate 59.2%
95% Confidence IntervalLower 56.8%Upper 61.6%
1 female
Population SizeEstimate 3242.493
95% Confidence Interval Lower 3043.639Upper 3441.347
% within DIAGicd10 DIP ICD-10Estimate 40.8%
95% Confidence Interval Lower 38.4%Upper 43.2%
Total
Population SizeEstimate 7955.000
95% Confidence IntervalLower 7826.394Upper 8083.606
% within DIAGicd10 DIP ICD-10Estimate 100.0%
95% Confidence IntervalLower 100.0%Upper 100.0%
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SPSS: Complex Samples Logistic regression
* Complex Samples Logistic Regression.CSLOGISTIC anyIP WITH age_calc /PLAN FILE='D:\SHIPdata_files\DataMain\weighting\SPSS\SHIP_SPSSweighting.csaplan' /MODEL age_calc /INTERCEPT INCLUDE=YES SHOW=YES /STATISTICS PARAMETER EXP CINTERVAL /TEST TYPE=F PADJUST=LSD /ODDSRATIOS COVARIATE=[age_calc(1)] /CRITERIA MXITER=100 MXSTEP=5 PCONVERGE=[1E-006 RELATIVE] LCONVERGE=[0] CHKSEP=20 CILEVEL=95 /PRINT SUMMARY CLASSTABLE VARIABLEINFO SAMPLEINFO.
Complex Samples: Logistic Regression
Sample Design InformationN
Unweighted CasesValid 1825Invalid 0Total 1825
Population Size 7955.000
Stage 1 Strata 1Units 1825
Sampling Design Degrees of Freedom 1824
Categorical Variable InformationWeighted Count Weighted Percent
anyIP Any inpatient admissions - past yeara
0 no/na/dk 4552.607 57.2%1 yesb 3402.393 42.8%
Population Size 7955.000 100.0%
a. Dependent Variableb. Reference Category
Covariate InformationMean
age_calc Age (calculated) in years at time of interview 39.47
Pseudo R SquaresCox and Snell .002Nagelkerke .003McFadden .002
Dependent Variable: anyIP Any inpatient admissions - past year (reference category = 1 yes) Model: (Intercept), age_calc
Tests of Model EffectsSource df1 df2 Wald F Sig.(Corrected Model) 1.000 1824.000 3.883 .049(Intercept) 1.000 1824.000 .101 .751age_calc 1.000 1824.000 3.883 .049
Dependent Variable: anyIP Any inpatient admissions - past year (reference category = 1 yes) Model: (Intercept), age_calc
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Parameter EstimatesanyIP Any inpatient admissions - past year
Parameter B 95% Confidence Interval Exp(B)Lower Upper
0 no/na/dk(Intercept) -.057 -.407 .293 .945age_calc .009 4.109E-005 .018 1.009
Parameter EstimatesanyIP Any inpatient admissions - past year Parameter 95% Confidence Interval for Exp(B)
Lower Upper
0 no/na/dk(Intercept) .666 1.341age_calc 1.000 1.018
Dependent Variable: anyIP Any inpatient admissions - past year (reference category = 1 yes) Model: (Intercept), age_calc
ClassificationObserved Predicted
0 no/na/dk 1 yes Percent Correct0 no/na/dk 4552.607 .000 100.0%1 yes 3402.393 .000 0.0%Overall Percent 100.0% 0.0% 57.2%
Dependent Variable: anyIP Any inpatient admissions - past year (reference category = 1 yes) Model: (Intercept), age_calc
Odds Ratiosa
Units of Change anyIP Any inpatient admissions - past year
Odds Ratio
age_calc Age (calculated) in years at time of interview 1.000 0 no/na/dk 1.009
Odds Ratiosa
Units of Change anyIP Any inpatient admissions - past year 95% Confidence IntervalLower
age_calc Age (calculated) in years at time of interview 1.000 0 no/na/dk 1.000
Odds Ratiosa
Units of Change anyIP Any inpatient admissions - past year 95% Confidence IntervalUpper
age_calc Age (calculated) in years at time of interview 1.000 0 no/na/dk 1.018
Dependent Variable: anyIP Any inpatient admissions - past year (reference category = 1 yes) Model: (Intercept), age_calca
a. Factors and covariates used in the computation are fixed at the following values: age_calc Age (calculated) in years at time of interview=39.47
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SAS example output
SAS: The SURVEYMEANS Procedure
MEAN PROCEDURE FOR AGE
Data SummaryNumber of Observations
1825
Sum of Weights 7955
Statistics
Variable Label N Mean
Std Error of
Mean 95% CL for MeanAGE_CALC Age (calculated) in years at time of
interview182
539.4656
170.27287
738.93043
2240.00080
12
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SAS: The SURVEYFREQ Procedure
Cross tabulation of Sex by Psychotic illness
Data SummaryNumber of Observations
1825
Sum of Weights 7955
Table of SEX by DIAGICD10
SEX DIAGICD10Frequenc
y
Weighted
Frequency
Std Dev of
Wgt FreqPerce
nt
Std Err of
Percentmale schizophrenia 612 2650 94.84571 33.316
91.1668
schizoaffective 157 623.91958
50.64980 7.8431 0.6389
bipolar, mania 141 621.15590
53.24893 7.8084 0.6662
depressive psychosis 33 146.11248
27.03131 1.8367 0.3392
delusional disorders and other non-organic psychosis
65 303.38049
39.57960 3.8137 0.4950
severe depression without psychosis
62 288.22831
38.35848 3.6232 0.4800
screen-positive for psychosis but did not meet full criteria for ICD-10 psychosis
17 79.34982 19.93295 0.9975 0.2504
Total 1087 4713 103.79991
59.2396
1.2216
female
schizophrenia 245 1113 70.60636 13.9895
0.8748
schizoaffective 136 540.86291
47.49690 6.7990 0.5987
bipolar, mania 178 774.09087
58.69530 9.7309 0.7339
depressive psychosis 48 221.88316
33.29560 2.7892 0.4174
delusional disorders and other non-organic psychosis
27 117.84948
24.27508 1.4815 0.3048
severe depression without psychosis
96 427.94215
45.43072 5.3795 0.5684
screen-positive for psychosis but did not meet full criteria for ICD-10 psychosis
8 46.99893 17.08476 0.5908 0.2144
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Table of SEX by DIAGICD10
SEX DIAGICD10Frequenc
y
Weighted
Frequency
Std Dev of
Wgt FreqPerce
nt
Std Err of
Percent
Total 738 3242 101.39056
40.7604
1.2216
Total schizophrenia 857 3763 103.66711
47.3064
1.2396
schizoaffective 293 1165 66.71838 14.6421
0.8442
bipolar, mania 319 1395 75.85090 17.5392
0.9430
depressive psychosis 81 367.99565
42.47047 4.6260 0.5315
delusional disorders and other non-organic psychosis
92 421.22997
46.00675 5.2952 0.5745
severe depression without psychosis
158 716.17047
58.31017 9.0028 0.7259
screen-positive for psychosis but did not meet full criteria for ICD-10 psychosis
25 126.34875
26.17484 1.5883 0.3282
Total 1825 7955 65.57273 100.000
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SAS: The SURVEYLOGISTIC Procedure
Logistic regressionEffect of age on inpatient admission
Model InformationData Set SAHA.SHIPDATAResponse Variable ANYIP Any inpatient admissions -
past yearNumber of Response Levels
2
Weight Variable weightsa weightsaModel Generalized LogitOptimization Technique
Newton-Raphson
Variance Adjustment Degrees of Freedom (DF)
Variance EstimationMethod Taylor SeriesVariance Adjustment
Degrees of Freedom (DF)
Number of Observations Read
1825
Number of Observations Used
1825
Sum of Weights Read 7955
Sum of Weights Used 7955
Response ProfileOrdere
dValue ANYIP
TotalFrequen
cyTotal
Weight1 no/
na/dk1028 4552.60
712 yes 797 3402.39
29
Logits modeled use ANYIP='yes' as the reference category.
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Model Convergence StatusConvergence criterion (GCONV=1E-8)
satisfied.
Model Fit Statistics
Criterion
Intercept
Only
Interceptand
Covariates
AIC 10863.078
10846.426
SC 10868.587
10857.445
-2 Log L 10861.078
10842.426
Testing Global Null Hypothesis: BETA=0
TestChi-
Square DFPr > ChiS
qLikelihood Ratio
18.6517 1 <.0001
Score 18.6230 1 <.0001Wald 3.8805 1 0.0489
Type 3 Analysis of Effects
Effect DF
WaldChi-
SquarePr > ChiS
qAGE_CALC 1 3.8805 0.0489
Analysis of Maximum Likelihood Estimates
Parameter ANYIP DFEstima
te
Standard
Error
WaldChi-
SquarePr > ChiS
qIntercept no/na/
dk1 -0.0568 0.1786 0.1011 0.7506
AGE_CALC no/na/dk
1 0.00884 0.00449 3.8805 0.0489
Odds Ratio Estimates
Effect ANYIP
Point Estima
te
95% WaldConfidence Limit
sAGE_CALC no/na/
dk1.009 1.000 1.018
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Association of Predicted Probabilities and Observed Responses
Percent Concordant
51.8 Somers' D
0.062
Percent Discordant
45.7 Gamma 0.063
Percent Tied 2.5 Tau-a 0.030
Pairs 819316
c 0.531
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