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Inflated data and over-dispersion are two common problems when modeling count data with traditional Poisson regression models. In this study, we propose a latent class inflated Poisson (LCIP) regression model to solve the unobserved heterogeneity that leads to inflations and over-dispersion. The performance of the model estimation is evaluated through simulation studies. We illustrate the usefulness of introducing a latent class variable by analyzing the Behavioral Risk Factor Surveillance System (BRFSS) data, which contain several excessive values and characterized by over-dispersion. As a result, the new model we proposed displays a better fit than the standard Poisson regression and zero-inflated Poisson regression models for the inflated counts.

Solving unobserved heterogeneity with latent class inflated Poisson regression model