Comparative analysis of alternative random parameters count data models in highway safety

Unobserved heterogeneity has been a major challenge in developing reliable road safety models. A number of statistical techniques have been developed to account for unobserved heterogeneity and of which, the random parameters approach is one of the most effective method and has been frequently used recently. In this study, to ascertain the performance of various methods that can account for unobserved heterogeneity, the following six models in the negative binomial framework were estimated and thoroughly evaluated: 1) a fixed parameters model; 2) a random parameters model; 3) a random parameters model with heterogeneity in means; 4) a random parameters model with heterogeneity in means and variances; 5) a correlated random parameters model; 6) a correlated random parameters model with heterogeneity in means. These models were thoroughly evaluated from several angles including statistical fit, predictability, causality, marginal effects, explanatory power and practicality. Results indicate that: 1) the simple fixed parameters model resulted in reduced statistical fit, relatively inaccurate predictions, restrictive inferences and added risk of biased marginal effects, though the model is simple for application and interpretive analysis; 2) introducing random parameters could improve the goodness-of-fit, prediction accuracy and the ability to uncover causality; 3) compared with a basic random parameters model, considering the heterogeneity in means/variances or correlation of random parameters brought further improvement in statistical fit, predictive performance and causal inferences; 4) estimating complex models with heterogeneity in means/variances or correlated random parameters provided more insights, but at the expense of significant increase in computational cost and less intuitive outputs; 5) using global means of random parameters rather than the simulated observation-specific parameters was more likely to result in biased marginal effects and erroneous safety measures; 6) new insights into safety factors and their interactions were derived. Results from this study are expected to provide safety analysts with additional guidance for choosing appropriate models when unobserved heterogeneity exists. Additionally, the concluded interactions of safety factors can potentially help develop more effective safety measures.