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

• Published in: Journal of statistical computation and simulation Vol. 81; no. 9; pp. 1081 - 1098
• Main Author: Li, Chin-Shang
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01-09-2011; Taylor & Francis Ltd
• Subjects: Algorithms; B-spline; Computer simulation; Counting; Dependent variables; expectation-maximization (EM) algorithm; Flexibility; Mathematical analysis; Mathematical models; Modelling; Poisson distribution; Regression analysis; semiparametric zero-inflated Poisson regression model; Simulation
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949651003677410

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.