Yongchen Huang

An Introduction of the Generalized Zero-Inflated Poisson Mixture Model and some Comparative Results

To confirm and evaluate the existence of zero-inflation and overdispersion in count data, Lim (2014) proposed the Generalized Zero-Inflated Poisson (GZIP) Mixture Model. Different from the usual Zero-inflated Poisson approach against count data, which separates the source of the observations into a Zero count part and a Poisson count part, this generalized model not only consider multiple components for the nonzero part, but also allows the weight of each component to be dependent on covariate. Expectation Maximization (EM) algorithm was used to obtain the Maximum Likelihood Estimations (MLE) of the parameters interested, which was proved by simulation results to be well-performed. Later in the real data analysis on the dental caries data having excessive zeros, models with more components explaining the nonzero-count part was shown to be better fits for the data in terms of the common AIC, BIC (model selection criteria) value, while the proposed GZIP Model was a relatively better choice than the Fixed-weights Zero-Inflated Poisson Model if the total numbers of components were kept to be the same.