Laserfiche WebLink
<br />71 <br />APPENDIX B. STATISTICAL TESTING OF THE <br />FINAL CRASH PREDICTION MODEL <br /> <br />To test the final crash prediction model in the terms of validity for the available database, several types of <br />tests were conducted. These tests included: <br /> <br />• Goodness-of-fit. <br />• Test for functional form. <br />• Residuals. <br /> <br />GOODNESS-OF-FIT <br /> <br />Below is as excerpt from the PROC GENMOD output (table 14). In assessing the goodness-of-fit of the <br />negative binomial regression model for crosswalks, we can see that the scaled deviance and the Pearson chi- <br />square are small indicating that the model fits the data well. <br /> <br />Table 14. Criteria for assessing goodness-of-fit negative binomial regression model. <br />Criteria DF Value Value/DF <br />Deviance <br />Scaled Deviance <br />Pearson chi-square <br />Scaled Pearson P2 <br />Log Likelihood <br />1990 <br />1990 <br />1990 <br />1990 <br />609.5499 <br />609.5499 <br />2769.9029 <br />2769.9029 <br />−548.7469 <br />0.3063 <br />0.3063 <br />1.3919 <br />1.3919 <br /> <br />TEST FOR FUNCTIONAL FORM <br /> <br />We can test for overdispersion with a likelihood ratio test based on Poisson and negative binomial <br />distributions. This test tests equality of the mean and the variance imposed by the Poisson distribution <br />against the alternative that the variance exceeds the mean. For the negative binomial distribution, the <br />variance = mean + k mean2 (k> = 0, the negative binomial distribution reduces to Poisson when k = 0). The <br />null hypothesis is: H0: k = 0 and the alternative hypothesis is: Ha: k>0. <br /> <br />To test the functional form, we used the likelihood ratio test, that is, compute LR statistic, -2 (LL (Poisson) – <br />LL (negative binomial)). The asymptotic distribution of the LR statistic has probability mass of one half at <br />zero and one half – chi-square distribution with 1 df.(40) To test the null hypothesis at the significance level <br />α, use the critical value of chi-square distribution corresponding to significance level 2α, that is reject H0 if <br />LR statistic > χ2 (1-2α, 1 df). <br /> <br />Table 15 is an excerpt from the PROC GENMOD output for a Poisson regression model with the same <br />independent variables are is the final negative binomial model.