Estimation for zero-inflated over-dispersed count data model with missing response

In this paper, we develop estimation procedure for the parameters of a zero-inflated over-dispersed/under-dispersed count model in the presence of missing responses. In particular, we deal with a zero-inflated extended negative binomial model in the presence of missing responses. A weighted expectation maximization algorithm is used for the maximum likelihood estimation of the parameters involved. Some simulations are conducted to study the properties of the estimators. Robustness of the procedure is shown when count data follow other over-dispersed models, such as the log-normal mixture of the Poisson distribution or even from a zero-inflated Poisson model. An illustrative example and a discussion leading to some conclusions are given. Copyright © 2016 John Wiley & Sons, Ltd.