  While the hurdle Poisson regression is a popular class of models for count
data with excessive zeros, the link function in the binary component may be
unsuitable for highly imbalanced cases. Ordinary Poisson regression is unable
to handle the presence of dispersion. In this paper, we introduce
Conway-Maxwell-Poisson (CMP) distribution and integrate use of flexible skewed
Weibull link functions as better alternative. We take a fully Bayesian approach
to draw inference from the underlying models to better explain skewness and
quantify dispersion, with Deviance Information Criteria (DIC) used for model
selection. For empirical investigation, we analyze mining injury data for
period 2013-2016 from the U.S. Mine Safety and Health Administration (MSHA).
The risk factors describing proportions of employee hours spent in each type of
mining work are compositional data; the probabilistic principal components
analysis (PPCA) is deployed to deal with such covariates. The hurdle CMP
regression is additionally adjusted for exposure, measured by the total
employee working hours, to make inference on rate of mining injuries; we tested
its competitiveness against other models. This can be used as predictive model
in the mining workplace to identify features that increase the risk of injuries
so that prevention can be implemented.
