The Zero-Inflated Poisson - Probit regression model: a new model for count data

Abstract

This paper wishes to propose a new model for count data and it is shortly called a Zero-Inflated Poisson - Probit (ZIP-P) model. The way of setting up for this new model is also based on the traditional model, the Zero-Inflated Poisson (ZIP) model. Note that this new model as well as the ZIP model has a wide range of practical applications and it can be easily applied and analyzed to the real data sets. More specifically, both of these models can be applied very well to count data sets where the frequency of zeros occupies a very high percentage. To achieve the goal of this study, we first recall the construction and general formula of the ZIP model. Then we present the most detailed way for building a new model includes the general formula and related equations necessary for estimating the parameters of the ZIP-P model. In addition, asymptotic results, numerical simulations and analysis of a real data set are also performed in this work. Moreover, we also clarify that this actual data set fits the ZIP-P model better than the other models considered. Finally, several lines of discussions and inferences are made in the study.