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) |
+1.1611 |
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 |
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 |
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 |