Longitudinal Zero-inflated Count Data Semi-parametric Analysis

In this article, we consider a semiparametric zero-inflated Poisson mixed model that postulates a possible nonlinear relationship between the natural logarithm of the mean of the counts and a particular covariate in the longitudinal studies. A penalized log-likelihood function is proposed and Monte Carlo expectation-maximization algo-rithm is used to derive the estimates. Under some mild conditions, we establish the consistency and asymptotic normality of the resulting estimators. Simulation studies are carried out to investigate the finite sample performance of the proposed method. For illustration purpose, the method is applied to two data sets, which are from the clinical trial of a pharmaceutical company and a social survey about the usage of the stimulant drug, respectively. The aim of our analysis is to study the improvement of the nonparametric method compared with the parametric model when some covariate may have a nonlinear effect on the responses.