Flexible Modeling of Hurdle Conway–Maxwell–Poisson Distributions with Application to Mining Injuries

The Poisson regression is the most popular class of models for count data, but with excessive zeros and unequal dispersion, the ordinary Poisson may be unsuitable to handle the significant presence of zero inflation and dispersion. In this paper, we apply the Hurdle structure with Conway–Maxwell–Poisson (CMP) distribution and integrate use of binary link function as better alternative to Poisson and Negative Binomial. We take a fully Bayesian approach to draw inference from the underlying models to better investigate our inferential methodology, with the Deviance Information Criteria (DIC), Watanabe-Akaike Information Criterion (WAIC) and Logarithm of the Pseudo Marginal Likelihood (LPML) used for model selection. Those criteria incorporate the effective number of parameters to adjust for overfitting, and can be calculated efficiently via likelihood function decomposition. For empirical investigation, we analyze mining injury data from the U.S. Mine Safety and Health Administration (MSHA). The Hurdle regressions are additionally adjusted for exposure, measured by the total employee working time in month; the proposed methodology is of specialty for studying occurrence and severity of the injuries. We tested its competitiveness from a business perspective against other models by estimating the expected injury cost due to adverse predictions.