On random-parameter count models for out-of-sample crash prediction: Accounting for the variances of random-parameter distributions

One challenge faced by the random-parameter count models for crash prediction is the unavailability of unique coefficients for out-of-sample observations. The means of the random-parameter distributions are typically used without explicit consideration of the variances. In this study, by virtue of the Taylor series expansion, we proposed a straightforward yet analytic solution to include both the means and variances of random parameters for unbiased prediction. We then theoretically quantified the systematic bias arising from the omission of the variances of random parameters. Our numerical experiment further demonstrated that simply using the means of random parameters to predict the number of crashes for out-of-sample observations is fundamentally incorrect, which necessarily results in the underprediction of crash counts. Given the widespread use and ongoing prevalence of the random-parameter approach in crash analysis, special caution should be taken to avoid this silent pitfall when applying it for predictive purposes.