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

Abstract

Count data often contain many zeros. In parametric regression analysis of zero-inflated count data, the effect of a covariate of interest is typically modelled 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 modelling flexibility. Within this modelling 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.

Keywords:

• B-spline
• expectation–maximization (EM) algorithm
• semiparametric zero-inflated Poisson regression model

Acknowledgements

The author thanks a referee 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.