Untangle Structural and Random Zeros in Statistical Modelling

Count responses with structural zeros are common in social behavior studies. There are much research activities focusing on zero-inflated models such as zero-inflated Poisson (ZIP) and zero-inflated Negative Binomial (ZINB) models to model such zero-inflated count responses. However, when such variables are used as covariates or predictors, the differences between structural and random zeros are often ignored. Such an approach may produce biased estimate and hence yield false conclusions. One remedy is to include an indicator for the structural zeros in the model as predictor. However, the structural zeros are not observed in most cases,  and no statistical methods are available to address this issue. This paper is then aimed to fill this methodological gap to develop parametric models to incorporate zero-inflated count models from the covariate and make statistical inference based on the theory of maximum likelihood estimation methods. The response variable can be any type of data including continuous, binary, and count or zero-inflated count responses. Simulation studies are performed to assess the numerical performance of this novel approach when sample size is small and moderate.  
    Key words: generalized linear models; maximum likelihood method; structural zeros; zero-inflated Poisson;