Zero-Inflated Poisson Cluster-Weighted Models: Properties and Applications

In this paper, I propose a new class of Zero-Inflated Poisson models into the family of Cluster Weighted Models (CWMs) called Zero-Inflated Poisson CWMs (ZIPCWM). ZIPCWM extends Poisson cluster weighted models and other mixture models. I propose an Expectation-Maximization (EM) algorithm via an iteratively reweighted least squares for the model. I theoretically and analytically investigate the identifiability of the proposed model through an extensive simulation study. Parameter recovery, classification assessment, and performance of different information criteria are investigated through broad simulation design. ZIPCWM is applied to real data which accounts for excess zeros of over $40\%$. We explore the classification performance of ZIPCWM, Fixed Zero-inflated Poisson mixture model (FZIP), and Poisson cluster weighted model (PCWM) on the data. Based on the confusion matrix, ZIPCWM achieves $97.4\%$ classification power, PCWM achieves $67.30\%$, while FZIP has the worst classification performance. In conclusion, ZIPCWM outperforms both PCWM and FZIP models.