Bayesian semiparametric zero-inflated Poisson model for longitudinal count data

This paper presents new methods, using a Bayesian approach, for analyzing longitudinal count data with excess zeros and nonlinear effects of continuously valued covariates. In longitudinal count data there are many problems that can make the use of a zero-inflated Poisson (ZIP) model ineffective. These problems are unobserved heterogeneity and nonlinear effects of continuously valued covariates. Our proposed semiparametric model can simultaneously handle these problems in a unified framework. The framework accounts for heterogeneity by incorporating random effects and has two components. The parametric component of the model which deals with the linear effects of time invariant covariates and the non-parametric component which gives an arbitrary smooth function to model the effect of time or time-varying covariates on the logarithm of mean count. The proposed methods are illustrated by analyzing longitudinal count data on the assessment of an efficacy of pesticides in controlling the reproduction of whitefly.