U.S. Department of Transportation
1200 New Jersey Avenue, SE
Washington, DC 20590
202-366-4000

Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

 This report is an archived publication and may contain dated technical, contact, and link information
 Federal Highway Administration > Publications > Research Publications > Safety > 98133 > Accident Models for Two-Lane Rural Roads: Segment and Intersections
Publication Number: FHWA-RD-98-133
Date: October 1998

# Accident Models for Two-Lane Rural Roads: Segment and Intersections

## 6. Validation and Further Analysis

Explanatory Value of Final Models

One way to assess the explanatory power of models is to examine the coefficient of determination R2 and see how it changes as one adds variables to the model. In Tables 46 and 47 and Figures 6

Table 46. Accident Variation by Groups of Covariates, Final Segment Model

 Combined Extended Negative Binomial Model (Table 27) Log-Likelihood Coefficient of Determination(%) Randomness 45.20 Exposure 26.81 State 2.63 Lane Width, Shoulder Width 2.33 Roadside Hazard Rating, Driveway Density 1.38 Alignment (DEG{i}, V{i}, GR{i}) 1.95 Unexplained 19.70 TOTAL 100.00

and 7, this is done for three of the models S the combined segment model of Table 27, and the Minnesota three-legged and four-legged models of Table 35. Because all of these models are of

Table 47. Accident Variation by Groups of Covariates, Final Intersection Models

 Minnesota Intersection Models (Table 35) Log-Likelihood Coefficient of Determination (%) three-legged four-legged Randomness 53.96 59.19 Exposure (ADT1, ADT2) 27.12 27.99 Design (All other variables) 1.78 2.06 Unexplained 17.14 10.76 TOTAL 100.00 100.00

negative binomial type, we use the Log-Likelihood R-squared proposed by Fridstrøm et al. (1995). With respect to this measure, negative binomial randomness is represented by 1 - P2 D. The contribution of other factors is represented by R2 D for the first variable when a model with that variable present is used, and then the increment in R2 D for each additional variable as it is added to the model. Finally the unexplained portion of variation is P2 D - R2 D, where R2 D is the R-squared value obtained when all variables are present.

Although the Log-Likelihood R-squared is not the only way to compare explanatory values, it is a reasonable way to do so for negative binomial models (and we presume for their extended negative binomial counterparts). The tables and figures indicate that the portion of mean accident counts explained by variables other than exposure and ADT is small.