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

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