Multilevel zero-inflated Generalized Poisson regression modeling for dispersed correlated count data

Poisson or zero-inflated Poisson models often fail to fit count data either because of over- or underdispersion relative to the Poisson distribution. Moreover, data may be correlated due to the hierarchical study design or the data collection methods. In this study, we propose a multilevel zero-inflated generalized Poisson regression model that can address both over- and underdispersed count data. Random effects are assumed to be independent and normally distributed. The method of parameter estimation is EM algorithm base on expectation and maximization which falls into the general framework of maximum-likelihood estimations. The performance of the approach was illustrated by data regarding an index of tooth caries on 9-year-old children. Using various dispersion parameters, through Monte Carlo simulations, the multilevel ZIGP yielded more accurate parameter estimates, especially for underdispersed data.