A note on modeling road accident frequency: a flexible elasticity model

Count data models and their variants have been widely applied in accident modeling. The traditional log-linear function is used to represent the relationship between explanatory variables and the dependent variable (accident frequency). However, this function assumes constant elasticity for the estimation parameters, which is a limitation in the analysis of the effects of explanatory variables on accident risk. Although interaction effects between explanatory variables have been studied in the road safety context (where they are normally assessed by logistic regression), no one has yet examined the possibility of using a flexible function form allowing non-constant elasticity values. This paper seeks to explore the use of the translog function usually used in the economics context to allow the elasticity to vary with the values of other explanatory variables. Therefore, the objective of this study was to evaluate the application of the translog function to accident modeling and to compare the results with those of the traditional log-linear function negative binomial (NB) model. The results show that, in terms of goodness-of-fit statistics and residual analysis, the NB model with the translog function performs better than the traditional NB model. Additional evaluations in terms of predictive performance, hotspot identification and uncertainty associated with the estimated values were taken into account. Although this study is exploratory in nature, it suggests that the translog function has considerable potential for modeling accident observations. It is hoped that this novel accident modeling methodology will open the door to the reliable interpretation and evaluation of the influence of explanatory variables on accident frequency.