A score-type test for heterogeneity in zero-inflated models in a stratified population

We propose a score-type statistic to evaluate heterogeneity in zero-inflated models for count data in a stratified population, where heterogeneity is defined as instances in which the zero counts are generated from two sources. Evaluating heterogeneity in this class of models has attracted considerable attention in the literature, but existing testing procedures have primarily relied on the constancy assumption under the alternative hypothesis. In this paper, we extend the literature by describing a score-type test to evaluate homogeneity against general alternatives that do not neglect the stratification information under the alternative hypothesis. The limiting null distribution of the proposed test statistic is a mixture of chi-squared distributions that can be well approximated by a simple parametric bootstrap procedure. Our numerical simulation studies show that the proposed test can greatly improve efficiency over tests of heterogeneity that ignore the stratification information. An empirical application to dental caries data in early childhood further shows the importance and practical utility of the methodology in using the stratification profile to detect heterogeneity in the population.