A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

Abstract

Count datasets are traditionally analyzed using the ordinary Poisson distribution. However, said model has its applicability limited, as it can be somewhat restrictive to handling specific data structures. In this case, the need arises for obtaining alternative models that accommodate, for example, overdispersion and zero modification (inflation/deflation at the frequency of zeros). In practical terms, these are the most prevalent structures ruling the nature of discrete phenomena nowadays. Hence, this paper’s primary goal was to jointly address these issues by deriving a fixed-effects regression model based on the hurdle version of the Poisson–Sujatha distribution. In this framework, the zero modification is incorporated by considering that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the g-prior method. Intensive Monte Carlo simulation studies were performed to assess the Bayesian estimators’ empirical properties, and the obtained results have been discussed. The proposed model was considered for analyzing a real dataset, and its competitiveness regarding some well-established fixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p-value and the randomized quantile residuals were considered for the task of model validation.