A lack-of-fit test for parametric zero-inflated poisson models

Count data often contain many zeros. In parametric regression analysis of zero-inflated count data, the effect of a covariate of interest is typically modeled via a linear predictor. This approach imposes a restrictive, and potentially questionable, functional form on the relation between the independent and dependent variables. To address the noted restrictions, a flexible parametric procedure is employed to model the covariate effect as a linear combination of fixed-knot cubic basis splines or B-splines. The semiparametric zero-inflated Poisson regression model is fitted by maximizing the likelihood function through an expectation-maximization algorithm. The smooth estimate of the functional form of the covariate effect can enhance modeling flexibility. Within this modeling framework, a log-likelihood ratio test is used to assess the adequacy of the covariate function. Simulation results show that the proposed test has excellent power in detecting the lack of fit of a linear predictor. A real-life data set is used to illustrate the practicality of the methodology.