The impact of misspecification of nuisance parameters on test for homogeneity in zero-inflated Poisson model: a simulation study

Abstract

The zero-inflated Poisson (ZIP) model consists of a Poisson model and a degenerate distribution at zero. Under this model, zero counts are generated from two sources, representing a heterogeneity in the population. In practice, it is often interested to evaluate this heterogeneity is consistent with the observed data or not. Most of the existing methodologies to examine this heterogeneity are often assuming that the Poisson mean is a function of nuisance parameters which are simply the coefficients associated with covariates. However, these nuisance parameters can be misspecified when performing these methodologies. As a result, the validity and the power of the test may be affected. Such impact of misspecification has not been discussed in the literature. This report primarily focuses on investigating the impact of misspecification on the performance of score test for homogeneity in ZIP models. Through an intensive simulation study, we find that: 1) under misspecification, the limiting distribution of the score test statistic under the null no longer follows a chi-squared distribution. A parametric bootstrap methodology is suggested to use to find the true null limiting distribution of the score test statistic; 2) the power of the test decreases as the number of covariates in the Poisson mean increases. The test with a constant Poisson mean has the highest power, even compared to the test with a well-specified mean. At last, simulation results are applied to the Wuhan Inpatient Care Insurance data which contain excess zeros.