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

Abstract

Most of the existing methodologies for evaluating heterogeneity in zero-inflated Poisson (ZIP) models are often assuming that the Poisson mean is a function of nuisance parameters. However, these nuisance parameters can be misspecified when performing these methodologies, the validity and the power of the test may be affected. In this article, we primarily focus 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 ${\chi }^2$ 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.

KEYWORDS:

• Zero-inflated Poisson model
• Score test
• Misspecification
• Nuisance parameter

Acknowledgments

I would like to express my sincere appreciation to Dr. Wei-Wen Hsu for his great help. Also, I would like to show my gratitude to China Life Insurance Company Limited for providing the Inpatient Care Insurance data. Finally, I am willing to thank everyone in the Department of Statistics at Kansas State University for their kindness and help.