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.