Joint Analysis of Crash Frequency by Severity Based on a Random Parameters Approach

Abstract

Unobserved heterogeneity is a major challenge in estimating reliable road safety models. The random parameters approach has been proven to be an effective way to account for unobserved heterogeneity but has rarely been used for crash frequency by severity level. In this paper, a fixed parameters model, a basic random parameters model, and an improved random parameters model, allowing for heterogeneity in the means and correlation of random parameters, are estimated and comparatively evaluated. To quantitatively analyze the impact of explanatory variables on the crash frequency of various severity levels, the calculating method of marginal effects for estimated models is proposed. The results indicate that (1) the basic random parameters model statistically outperforms the fixed parameters model, and the statistical fit can be further improved by introducing heterogeneous means and correlation of random parameters; (2) for the predictive performance, the basic random parameters model is more accurate than the fixed parameters model, and the improved random parameters model can further reduce the mean error, mean absolute error, and root mean square error by 40–100%, 3.7–8.3%, and 7.6–8.9%, respectively; (3) ignoring the unobserved heterogeneity or neglecting the heterogeneity in the means and correlation of random parameters may result in biased safety inferences, and the maximum bias of marginal effects can easily exceed 100 percent; and (4) the safety effects of explanatory variables are thoroughly discussed and the potential safety countermeasures are provided. The random parameters approach and the method for calculating marginal effects proposed in this study are expected to provide a new methodological alternative for the joint analysis of crash frequency by severity and should be helpful in uncovering the mechanism of crash occurrence and the resulting injury severity accurately.