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72 Table 15. Criteria for assessing goodness-of-fit Poisson regression model. Criteria DF Value Value/DF Deviance Scaled Deviance Pearson Chi-Square Scaled Pearson X2 Log Likelihood 1990 1990 1990 1990 881.5022 881.5022 3432.5818 3432.5818 −568.4558 0.4430 0.4430 1.7249 1.7249 −2 (LL (Poisson) - LL (negative binomial)) = −2* (−568.4558 − (−548.7469)) = 2* (568.4558 − 548.7469) = 39.4178 Thus, the null hypothesis is rejected for α = 0.01, and we conclude that the Poisson distribution is inadequate for this model.(40) RESIDUALS Because generalized estimating equations (GEE) were used, the interpretation of residuals is problematic and no residual analysis was undertaken. MULTICOLLINEARITY Certainly multicollinearity is an issue, because the marked crosswalk and the unmarked crosswalk were matched on geographic terms, thus the number of lanes, median type, and traffic ADT are distributed very similarly in the marked and the unmarked crosswalks. Multicollinearity was explored using the regression diagnostics suggested by Belsley, Kuh, and Welsch. They suggest two different measures: variance inflation factor (VIF) and the proportion of variation. VIF gauges the influence potential near dependencies may have on the estimation of the standard error of the estimate of the regression parameters. The proportion of variation is a diagnostic which permits the detection of morel complex dependencies. For the final model with predictor variables, the values were: an indicator for marked versus unmarked, pedestrian ADT, and traffic ADT; two indicators for number of lanes; two indicators for type of median; an interaction between the indicator for marked versus unmarked and pedestrian ADT; and an interaction between indicator for marked versus unmarked and traffic ADT. The largest VIF was 4.0; this is not high (VIF < 10), however, it is more than the suggested criterion of VIF > 1.55. Thus, the VIF for indicator for marked versus unmarked VIF = 3.5, traffic ADT, VIF = 2.5, and the interaction of these two predictor variables VIF = 4.0. There is some variance inflation in this model. Since none of the VIF are greater than 10, we can conclude that the model has not been degraded by collinearity. We should interpret the results with some care, because three predictors have VIFs greater than 1.55. (41) The proportion of variation suggested by Belsley, Kuh, and Welsch with a condition index of 9.4 suggests a weak dependency between the three predictors: indicator for marked versus unmarked, traffic ADT, and the interaction of these two predictor variables. It is not surprising that an interaction is correlated with the main factors. In conclusion, the model does have a weak dependency among the predictor variables. This does not inflate the variance too much; thus, reasonable tests may be conducted. The mild nature of the collinearity does not present a threat to the interpretability of the model.(41)