Score tests for zero-inflated generalized Poisson mixed regression models

Authors:
Feng-Chang Xie;Bo-Cheng Wei;Jin-Guan Lin
Affiliations:
Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, China and Department of Mathematics, Southeast University, Nanjing 210096, China;Department of Mathematics, Southeast University, Nanjing 210096, China;Department of Mathematics, Southeast University, Nanjing 210096, China
Venue:
Computational Statistics & Data Analysis
Year:
2009

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Abstract

Zero-inflated Poisson (ZIP) regression model is a popular approach to the analysis of count data with excess zeros. For correlated count data where the observations are either repeated or clustered outcomes from individual subjects, ZIP mixed regression model may be appropriate. However, ZIP model may often fail to fit such data either because of over-dispersion or because of under-dispersion in relation to the Poisson distribution. In this paper, we extend the ZIP mixed regression model to zero-inflated generalized Poisson (ZIGP) mixed regression model, where the base-line discrete distribution is generalized Poisson (GP) distribution, which is a natural extension of standard Poisson distribution. Furthermore, the random effects are considered in both zero-inflated and GP components throughout the paper. An EM algorithm for estimating parameters is proposed based on the best linear unbiased prediction-type (BLUP) log-likelihood and the residual maximum likelihood (REML). Meanwhile, several score tests are presented for testing the ZIP mixed regression model against the ZIGP mixed regression model, and for testing the significance of regression coefficients in zero-inflation and generalized Poisson portion. A numerical example is given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations.