Zero-inflated (ZI) data play a very important role in various sectors of life such as ecology, manufacturing, medical, agriculture, etc. However, when it comes to estimate a zero-inflated Poisson (ZIP) model, it is often taken for a Poisson regression models or other traditional models. ZI models are mixture distributions of a count distribution and the degenerated at zero mass distribution.
In this work, we allow the mean of the ZIP distribution and the mixing probability to be linear predictors of covariates. Some of covariates are assumed to be missing data at random (MAR). Under the MAR, the naïve estimator based on case deletion often is biased. Thus, we propose the semiparametric inverse probability weighting (IPW) estimators and the semiparametric multiple imputation (MI) estimators. We show that our estimators are asymptotic consistent and normally distributed. We compare the performance of our estimators with the parametric and the true weight estimators in the simulation study.
In addition, we explore an example of The 2008 Taiwan motorcycle survey data set. Finally, we discuss some potential future directions.
Keywords: Count data, Zero-excess, Missing covariates, Semiparametric estimator, Selection probability, Multiple imputation, Consistent estimator