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Statistics Colloquium/PhD Proposal
November 18 (Fri) 11 a.m.
Alavi Commons Room, 6625 Everett Tower
Xiaomeng Niu
Department of Statistics
Western Michigan University
Abstract:Longitudinal count data is comprised of repeated response variables and a set of independent variables. When the response variable is subject to overdispersion, the overdispersion parameter influences a marginal variance. In such cases, the overdispersion parameter plays a significant role in efficient estimation of the regression parameter. This raises the need for joint estimation of the regression parameter and the overdispersion parameter. On the other hand, inclusion of the overdispersion parameter can hinder efficient estimation and inference for the regression parameter when overdispersion is not present. In this proposal, we provide new modeling for longitudinal count data and propose a test detecting the presence of overdispersion.
Specifically, Poisson regression model is commonly used for longitudinal count data. However, the variance of responses is often larger than the mean of responses in many cases, which is contradictory with the Poisson model assumption. When the overdispersion is present, negative binomial regression model can be a viable alternative by accommodating an overdispersion parameter. Since the negative binomial model involves two sets of parameters, regression parameter and overdispersion parameter, this motivates us to improve efficient estimation with a joint estimating equation. We develop a correlation structure for longitudinal count data in negative binomial regression model, which is incorporated into joint estimating equation to estimate both regression parameter and overdispersion parameter simultaneously. This yields more efficient estimators in the regression model. More importantly, the proposed procedure enables us to detect overdispersion, and thereby recommend a more proper model for longitudinal count data.
Bio:Xiaomeng Niu is a doctoral candidate in the Department of Statistics.
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All statistics students are expected to attend.