Penalized Conway-Maxwell-Poisson regression for modelling dispersed discrete data: The case study of motor vehicle crash frequency

Statistical modelling of road crashes has been of extreme interest to researchers over the last decades. Such models are necessary for the investigation of the opportunities for road safety improvement. The motor vehicle crash frequency (MVC-F) is probably the most important count of road crashes. In practice, like many of other discrete variables, this count is often diagnosed with over- or underdispersion, i.e. the variance is greater or less than the mean. The traditional regression models, especially those based on the Poisson distribution, are inefficient in modelling dispersed count data. On the contrary, the Conway-Maxwell-Poisson (COM-Poisson) distribution has been proven powerful in modelling count data with a wide range of dispersion. In crash data modelling, many situations may give rise to collinearity between contributory crash factors. Under this situation, the maximum likelihood estimates of the coefficients of the COM-Poisson GLM become increasingly unreliable as the collinearity among the model predictors increases. This paper addresses this issue and proposes a penalized likelihood scheme to be used with the COM-Poisson GLM regression for improving its prediction performance. For better GLM regression output, we suggest implementing the penalized COM-Poisson GLM regression under a K- fold cross-validation framework. A real-world crash example is provided, showing the performance of the penalized COM-Poisson GLM regression compared to the Poisson and the classical COM-Poisson GLM regressions.