Assessing the explanatory and predictive performance of a random parameters count model with heterogeneity in means and variances

•A random parameters model with heterogeneity in means/variances was estimated.•The negative binomial model was more reliable in general for safety analysis.•Allowing heterogeneous means/variances of random parameters offered more insights.•Interactive effects of safety factors on crash frequency were concluded.•A k-fold cross-validation method was used to assess the predictability. Random parameters model has been demonstrated to be an effective method to account for unobserved heterogeneity that commonly exists in highway crash data. However, the predefined single distribution for each random parameter may limit how the unobserved heterogeneity is captured. A more flexible approach is to develop a random parameters model with heterogeneity in means and variances by allowing the mean and variance of potential each random parameter to be an estimable function of explanatory variables. This burgeoning technique for modelling unobserved heterogeneity has been increasingly applied to various safety evaluation scenarios recently. However, the predictive performance of this emerging method, which determines the practicability of the model for a specific circumstance, has never been investigated as far as our knowledge. In addition, the explanatory power by including heterogeneous means and variances of random parameters need to be further investigated to confirm the potential merits of this method in crash data analysis. In this paper, a random parameters negative binomial with heterogeneity in means and variances (RPNBHMV) model, a standard random parameters negative binomial (RPNB) model and a traditional fixed parameters negative binomial (NB) model were estimated using the same dataset. The explanatory and predictive performance of the three models were thoroughly evaluated and compared. Results showed that: 1) the RPNB model fitted the data significantly better than the NB model, and the RPNBHMV model further improved the statistical fit of the RPNB model but the improvement was slight; 2) more insights into interactions of safety factors were inferred from the RPNBHMV model, which demonstrates the explanatory benefit of this model; 3) the RPNBHMV and RPNB models had both advantages (e.g., produced overall better prediction accuracy) and disadvantages (e.g., provided reduced prediction accuracy across the range of explanatory variables) when applied to in-sample observations (i.e., observations used to estimate the model); 4) the RPNBHMV and RPNB models mi