Score Tests for Zero-Inflation and Overdispersion in Two-Level Count Data
Hwa-Kyung Lim1, Juwon Song2, Byoung Cheol Jung3, Kee-Hoon Kang4
1Institute of Statistics, Korea University, Seoul, Korea; 2Department of Statistics, Korea University, Seoul, Korea; 3Department of Statistics, University of Seoul, Seoul, Korea; 4Department of Statistics, Hankuk University of Foreign Studies, Mohyun, Cheoin-Koo, Yongin, Korea

Poisson regression models have been widely used for analyzing count data. Sometimes, the number of observed zero counts is greater than the expected frequency by the Poisson distribution. The zero-inflated Poisson (ZIP) regression model is chosen for analyzing count data with excess zeros. When observations are either clustered or represented by repeated measurements of counts, the ZIP mixed regression model is appropriate. Although the ZIP model can handle zero-inflation for Poisson data, the non-zero part of count data may also be overdispersed. The zero-inflated negative binomial (ZINB) regression model is suggested to analyze such data and the ZINB mixed regression model is proposed as an extension of the ZINB regression model for addressing clustered count data. Previous studies have used score tests for zero-inflation and overdispersion separately in correlated count data. Here, we also deal with simultaneous score tests for zero-inflation and overdispersion in two-level count data by using the ZINB mixed regression model. Score tests are suggested for 1) zero-inflation in the presence of overdispersion, 2) overdispersion in the presence of zero-inflation, and 3) zero-inflation and overdispersion simultaneously. The level and power of score test statistics are evaluated by a simulation study. The simulation results indicate that score test statistics may occasionally underestimate or overestimate the nominal significance level due to variations in random effects. This study proposes a parametric bootstrap method to overcome this problem. The simulation results of the bootstrap test indicate that score tests hold the nominal level and provide good power.

Keywords: Zero-Inflation; Overdispersion; Zero-Inflated Negative Binomial; Score Test

Biography: Dr. Hwa-Kyung Lim is a research professor in institute of Statistics at Korea University.