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

TL;DR

This paper introduces a flexible Bayesian hurdle CMP model with skewed link functions for count data with excess zeros and dispersion, applied to mining injury data to improve risk factor analysis and injury rate prediction.

Contribution

It develops a novel Bayesian hurdle CMP regression model with flexible link functions and applies it to mining injury data, addressing zero inflation and dispersion issues.

Findings

The hurdle CMP model outperforms traditional models in fit and prediction.

The approach effectively captures skewness and dispersion in injury count data.

Identifies key risk factors influencing mining injuries.

Abstract

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.