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

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.