Zero-inflated regression models for count data : an application to under-5 deaths

摘要

Zero-inflated (ZI) count data models overcome the restriction of equality relationship betweenmean and variance, but functional relationship still exists. For ZI models it is important toknow whether the proportion of zeros and the rate of counts have any influence on the fit ofthe model. In this study we have considered three zero-inflated models, namely, ZIP, ZINB,and Hurdle model. We also considered Poisson and negative binomial model as classicalcount data models. Our simulation experiment suggests that the proportion of zeros forgiven rate parameter does not a↵ect the fit of the models as long as model is correctlyspecified. In case of misspecification of the model, it does not perform well for large rateparameter. These three zero-inflated models performed better than the classical models asthe rate parameter and the proportion of zeros become larger. We applied five models tothe BDHS 2011 survey data to understand the social determinants associated with a motherto experience under-5 deaths of her children. The classical models failed to di↵erentiatebetween mothers who have experienced under-5 deaths of their children and who have neverexperienced under-5 deaths. While zero-inflated models were able to di↵erentiate betweenthose two groups of mothers in terms of zero counts and positive counts of number of under-5deaths of their children with associated covariates in opposite slope of coefficients. Amongthe three zero-inflated models, Hurdle model performed best in fitting the data compared tothe ZIP and ZINB models.