Modeling road traffic accidents in Mauritius using clustered longitudinal COM-Poisson with gamma random effects

This article proposes a nonstationary clustered longitudinal model to analyze road traffic accident time series data from 2016 to 2017 in Mauritius. The Conway–Maxwell–Poisson model (COM-Poisson) is used as the baseline model with gamma-distributed random effects (CMP-G). Several time-variant explanatory variables are incorporated into the model specification link predictor to identify the likely causes of road crashes in the Mauritius. The proposed model competes with the popular Poisson gamma and log-normal mixtures when modeling over-dispersion. The model parameters namely the regression, serial, and dispersion effects, are estimated suitably by a generalized quasi-likelihood (GQL) estimation method while the serial parameter is treated as nuisance and estimated by method of moments. The asymptotic properties of the GQL estimators are discussed. A simulation study based on an integer-valued auto-regressive of order 1 structure (INAR(1)) with CMP-G distributed innovation terms, is also proposed to assess the performance of GQL based on the CMP-G. Data application is of road traffic accidents in Mauritius where some model criteria have been computed to assess the goodness of fits of the proposed model against the Poisson-gamma and Poisson-log normal mixtures.