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Publication Number: FHWA-RD-98-133
Date: October 1998
Accident Models for Two-Lane Rural Roads: Segment and Intersections
6. Validation and Further Analysis
Validation based on a chi-square statistic c2, mean absolute deviation MAD, and mean absolute scaled deviation MASD suggests that the models have some predictive power. The Minnesota models behave well on the later Minnesota data (Table 41): the segment model is even underdispersed. This does not constitute a real test, though, since the data sets are dependent so that accidents in the later time period might be expected to correlate well with accidents on the same segment in the earlier time period (and the latter are the basis for the model). A better test is to validate models from one State with data from the other. On Washington data (Table 42) the Minnesota models give small values for MAD and MASD, although the Washington four-legged sample gives somewhat large values. The Washington segment model also gives small values of MAD and MASD on Minnesota data (Table 44). To get a small value of c2, one adjusts the intercept term of the model to account for a difference in accident experience between the States. Inspection of Tables 43 and 44 shows that the multiplier that makes c2 smallest for the Minnesota segment model applied to Washington data is approximately 1.35, while the best multiplier for the Washington segment model applied to the Minnesota data is on the order of 0.85. The product of these numbers is approximately 1.0, as is reasonable.
As assessed by the Log-Likelihood R-squared, the explanatory power of the highway variables is rather limited. Exposure and ADT account for about 27% of the variation. For the segments a total of 5.7% of the variation is accounted for by other highway variables (while STATE accounts for 2.6%). For the three-legged intersections, all highway variables other than ADT account for only 1.8% (perhaps in part because of the large overdispersion parameter in the three-legged model), while for the four-leggeds the other variables account for 2.1%. See Tables 46 and 47, and Figures 6 and 7.
Although the cumulative scaled residual graphs for the segments suggest some differences in regimes, the graphs in Figures 8 through 15 are generally consistent with the model forms in Tables 27 and 35. Different models applied when some of the highway variables are confined to subsets of their full range (first quartile, second quartile, etc.) might yield better fits, but if a single overarching model is wanted for each of the three classes of data, the final models in Tables 27 and 35 are plausible candidates (with adjustments for different States and times).