A Zero-Inflated Poisson – Complementary Log–Log regression model

This work introduces an approach to modeling count data, it is known as the Zero-Inflated Poisson – Complementary Log–Log (ZIP-CLL) model. This method builds upon the foundation of the traditional Zero-Inflated Poisson (ZIP) model. Both models are particularly well-suited for analyzing and justifying count data sets characterized by a high proportion of zeros. To accomplish the objectives of this research, we begin by revisiting the construction, setup and general recipe of the ZIP model. We then outline a comprehensive approach to developing a regression model, including the derivation of its general recipe, the necessary equations and functions for parameter estimation. Moreover, the study incorporates asymptotic results, simulations, and analyzing a real-world data set. Our findings highlight that this data set aligns more closely with the proposed model compared to other competing models. Lastly, the study concludes with a discussion of key findings and implications.