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일시: 2010년 9월 29일 수요일 오후 5시
장소: 정경관 202호
연사: Hwa-Kyung Lim
(Institute of Statistics, Korea University)
주제 : " Score tests for Zero-Inflation and Overdispersion
in Multilevel Count Data using a Random Effects Model "
The Poisson regression model has been extensively used to analyze the count data. There are often the case that the number of observed zero counts may be larger than the expected frequency by the Poisson distribution. The Zero-Inflated Poisson (ZIP) regression is often chosen for analyzing count data with excess zeros.
When the observations are either clustered or represent 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 the count data may be overdispersed. The Zero-Inflation Negative Binomial (ZINB) regression is suggested to analyze such data. Previous published works deal with the score test for zero-inflation and overdispersion separately in correlated count data. In this thesis, we deal with simultaneous score tests for zero-inflation and overdispersion in two-level count data and three-level autoregressive count data 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) simultaneously for zero-inflation and overdispersion. The levels and powers of score test statistics are evaluated by a simulation study. Our simulation shows that the score test statistics sometimes underestimate or overestimate the nominal significance level due to variation of random effects. A parametric bootstrap method is proposed to overcome this problem in a score test. The simulation result of the bootstrap test indicates that the score tests hold nominal levels and provide good power.
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