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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
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
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