Improved estimators for the zero-inflated Poisson regression model in the presence of multicollinearity: simulation and application of maternal death data

Abstract In this article, we propose Liu-type shrinkage estimators for the zero-inflated Poisson regression (ZIPR) model in the presence of multicollinearity. Our new approach is a remedy to the problem of inflated variances for the ML estimation technique—which is a standard approach to estimate these types of count data models. When the data are in the form of non-negative integers with a surplus of zeros it induces overdispersion in the dependent variable. Considerable multicollinearity is frequently observed, but usually disregarded, for these types of data sets. Based on a Monte Carlo study we illustrate that our proposed estimators exhibit better MSE and MAE than the usual ML estimator and some other Liu estimators in the presence of multicollinearity. To demonstrate the advantages and the empirical relevance of our improved estimators, maternal death data are analyzed and the results illustrate similar benefits as is demonstrated in our simulation study.