Appendix C
Supplementary Statistical Results

Tables C-1 through C-7 present the outcomes of the LOGISTIC procedure using the Statistical Analysis System (SAS).1 Listed are:

  • The name of each parameter included in the model;

  • The degrees of freedom (DF) associated with each parameter;

  • The estimated coefficient of the parameter, obtained by maximum-likelihood estimation;

  • The standard error of the coefficient (a measure of precision);

  • The Wald Chi-square statistic, computed as the square of the value obtained by dividing the parameter estimate by its standard error; and

  • The p-value (Pr > ChiSq) for the Wald Chi-square statistic with 1 DF, with a value below 0.05 indicating a significant effect of the associated model parameter if a 5 percent significance level is chosen.

The parameters included in the logistic model are the static stability factor (SSF) and the five “dummy” state variables (i.e., 0,1 variables). Note that Missouri, the sixth state in the data, is omitted in the model; it is the baseline state in the model. For example, using the modeling results shown in Table C-1 and the notation of Equation 7 in Chapter 3, the logit model can be written as follows:

where P is the estimated probability of a rollover given a single-vehicle crash, and the adjustments are as follows:

−0.1910

if STORM = 1 (+0 otherwise)

+0.9276

if FAST = 1 (+0 otherwise)

+0.1279

if HILL = 1 (+0 otherwise)

+0.5224

if CURVE = 1 (+0 otherwise)

−0.0913

if MALE = 1 (+0 otherwise)

+0.3187

if YOUNG = 1 (+0 otherwise)

−0.3664

if OLD = 1 (+0 otherwise)

+0.2578

if DRINK = 1 (+0 otherwise)

1

The LOGISTIC Procedure. SAS Institute Inc. SAS/STAT® User’s Guide, Version 6, Fourth Edition, Volume 2, SAS Institute Inc., Cary, N.C., 1989.



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An Assessment of the National Highway Traffic Safety Administration's Rating System for Rollover Resistance: Special Report 265 Appendix C Supplementary Statistical Results Tables C-1 through C-7 present the outcomes of the LOGISTIC procedure using the Statistical Analysis System (SAS).1 Listed are: The name of each parameter included in the model; The degrees of freedom (DF) associated with each parameter; The estimated coefficient of the parameter, obtained by maximum-likelihood estimation; The standard error of the coefficient (a measure of precision); The Wald Chi-square statistic, computed as the square of the value obtained by dividing the parameter estimate by its standard error; and The p-value (Pr > ChiSq) for the Wald Chi-square statistic with 1 DF, with a value below 0.05 indicating a significant effect of the associated model parameter if a 5 percent significance level is chosen. The parameters included in the logistic model are the static stability factor (SSF) and the five “dummy” state variables (i.e., 0,1 variables). Note that Missouri, the sixth state in the data, is omitted in the model; it is the baseline state in the model. For example, using the modeling results shown in Table C-1 and the notation of Equation 7 in Chapter 3, the logit model can be written as follows: where P is the estimated probability of a rollover given a single-vehicle crash, and the adjustments are as follows: −0.1910 if STORM = 1 (+0 otherwise) +0.9276 if FAST = 1 (+0 otherwise) +0.1279 if HILL = 1 (+0 otherwise) +0.5224 if CURVE = 1 (+0 otherwise) −0.0913 if MALE = 1 (+0 otherwise) +0.3187 if YOUNG = 1 (+0 otherwise) −0.3664 if OLD = 1 (+0 otherwise) +0.2578 if DRINK = 1 (+0 otherwise) 1 The LOGISTIC Procedure. SAS Institute Inc. SAS/STAT® User’s Guide, Version 6, Fourth Edition, Volume 2, SAS Institute Inc., Cary, N.C., 1989.

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An Assessment of the National Highway Traffic Safety Administration's Rating System for Rollover Resistance: Special Report 265 +1.1611 if State = Florida (+0 otherwise) +0.7852 if State = Maryland (+0 otherwise) +0.8006 if State = North Carolina (+0 otherwise) +1.2121 if State = Pennsylvania (+0 otherwise) +1.4575 if State = Utah (+0 otherwise) TABLE C-1 Logit Model Results for Data from Six States Combined (See Figure 3-2) Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq Intercept 1 1.5326 0.0555 762.6947 <.0001 SSF 1 -3.6027 0.0416 7510.7110 <.0001 STORM 1 -0.1910 0.0130 214.9444 <.0001 FAST 1 0.9276 0.0123 5642.4241 <.0001 HILL 1 0.1279 0.0124 106.9493 <.0001 CURVE 1 0.5224 0.0122 1844.5867 <.0001 MALE 1 -0.0913 0.0123 55.2705 <.0001 YOUNG 1 0.3187 0.0119 720.3518 <.0001 OLD 1 -0.3664 0.0405 81.6902 <.0001 DRINK 1 0.2578 0.0157 270.7577 <.0001 dummy_fl 1 1.1611 0.0214 2953.9104 <.0001 dummy_md 1 0.7852 0.0257 932.6290 <.0001 dummy_nc 1 0.8006 0.0192 1742.2279 <.0001 dummy_pa 1 1.2121 0.0200 3686.3054 <.0001 dummy_ut 1 1.4575 0.0296 2417.7396 <.0001 TABLE C-2 Logit Model Results for Data from Six States Combined for Risk Scenario Close to the Minimum (See Figure 3-3) Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq Intercept 1 1.0804 2.8127 0.1476 0.7009 SSF 1 -3.7387 2.0212 3.4216 0.0643 dummy_fl 1 0.7377 0.7845 0.8842 0.3470 dummy_md 1 0.5256 1.0138 0.2688 0.6042 dummy_nc 1 0.5774 0.8119 0.5058 0.4770 dummy_pa 1 0.4725 0.8263 0.3270 0.5675 dummy_ut 1 1.9178 1.2993 2.1786 0.1399

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An Assessment of the National Highway Traffic Safety Administration's Rating System for Rollover Resistance: Special Report 265 TABLE C-3 Logit Model Results for Data from Six States Combined for Risk Scenario at the 25th Percentile (See Figure 3-4) Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq Intercept 1 1.9149 0.3158 36.7562 <.0001 SSF 1 -3.7359 0.2384 245.5733 <.0001 dummy_fl 1 1.1069 0.1341 68.1204 <.0001 dummy_md 1 0.7083 0.1964 13.0090 0.0003 dummy_nc 1 0.7284 0.1494 23.7583 <.0001 dummy_pa 1 1.1200 0.1415 62.6115 <.0001 dummy_ut 1 1.0745 0.2143 25.1399 <.0001 TABLE C-4 Logit Model Results for Data from Six States Combined for Risk Scenario at the Mean (See Figure 3-5) Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq Intercept 1 3.1380 0.3896 64.8641 <.0001 SSF 1 -4.1671 0.3083 182.6660 <.0001 dummy_fl 1 1.0949 0.1610 46.2240 <.0001 dummy_md 1 0.7980 0.1861 18.3786 <.0001 dummy_nc 1 0.4573 0.1555 8.6466 0.0033 dummy_pa 1 1.0435 0.1521 47.0791 <.0001 dummy_ut 1 1.3395 0.1965 46.4858 <.0001 TABLE C-5 Logit Model Results for Data from Six States Combined for Risk Scenario at the Median (See Figure 3-6) Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq Intercept 1 2.8052 0.2493 126.5779 <.0001 SSF 1 -3.9525 0.1990 394.5406 <.0001 dummy_fl 1 1.4559 0.0895 264.3365 <.0001 dummy_md 1 0.6796 0.1198 32.1621 <.0001 dummy_nc 1 0.4733 0.0885 28.6180 <.0001 dummy_pa 1 0.9663 0.0978 97.6930 <.0001 dummy_ut 1 1.8160 0.1236 215.9163 <.0001

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An Assessment of the National Highway Traffic Safety Administration's Rating System for Rollover Resistance: Special Report 265 TABLE C-6 Logit Model Results for Data from Six States Combined for Risk Scenario at the 75th Percentile (See Figure 3-7) Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq Intercept 1 4.1884 0.4747 77.8564 <.0001 SSF 1 -4.9957 0.3954 159.5922 <.0001 dummy_fl 1 0.7393 0.1901 15.1233 0.0001 dummy_md 1 0.8961 0.2166 17.1126 <.0001 dummy_nc 1 0.3376 0.1571 4.6142 0.0317 dummy_pa 1 1.2998 0.1448 80.5297 <.0001 dummy_ut 1 1.6824 0.2122 62.8738 <.0001 TABLE C-7 Logit Model Results for Data from Six States Combined for Risk Scenario Close to Maximum (See Figure 3-8) Parameter DF Estimate Standard Error Wald Chi-Square Pr > ChiSq Intercept 1 0.7049 0.5683 1.5388 0.2148 SSF 1 -1.7458 0.4509 14.9929 0.0001 dummy_fl 1 1.5017 0.1989 56.9796 <.0001 dummy_md 1 0.3726 0.5993 0.3865 0.5342 dummy_nc 1 1.6822 0.1713 96.4075 <.0001 dummy_pa 1 0.7427 0.2205 11.3456 0.0008 dummy_ut 1 2.2298 0.4830 21.3100 <.0001