Testing the Lack-of-Fit of Zero-Inflated Poisson Regression Models

Abstract

A zero-inflated Poisson regression model has been widely used for the effect of a covariate in count data containing many zeros with a linear predictor. To assess the adequacy of the linear relationship, we approximate the covariate effect with cubic B-splines. The semiparametric model parameters are estimated by maximizing the likelihood function through an expectation-maximization algorithm. A log-likelihood ratio test is then used to evaluate the adequacy of the linear relation. A simulation study is conducted to study the power performance of the test. A real example is provided to demonstrate the practical use of the methodology.

Keywords:

• B-splines
• Expectation-maximization (EM) algorithm
• Lack-of-fit test
• Log-likelihood ratio test

Mathematics Subject Classification:

• 62G05
• 62G08
• 62G10
• 62G20

Acknowledgments

The author expresses his thanks to an Associate Editor whose helpful comments improved the presentation. This publication was made possible by Grant Number UL1 RR024146 from the National Center for Research Resources (NCRR), a component of the National Institutes of Health (NIH), and NIH Roadmap for Medical Research.