Empirical Likelihood and Mean-Variance Models for Longitudinal Data

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Abstract

Improving the estimation efficiency has always been one of important aspects instatistical modelling. Our goal is to develop new statistical methodologies yieldingmore efficient estimators in the analysis of longitudinal data. In this thesis, weconsider two different approaches, empirical likelihood and jointly modelling the meanand variance, to improve the estimation efficiency.In part I of this thesis, empirical likelihood-based inference for longitudinal datawithin the framework of generalized linear model is investigated. The proposed proceduretakes into account the within-subject correlation without involving direct estimationof nuisance parameters in the correlation matrix and retains optimality even ifthe working correlation structure is misspecified. The proposed approach yields moreefficient estimators than conventional generalized estimating equations and achievesthe same asymptotic variance as quadratic inference functions based methods.The second part of this thesis focus on the joint mean-variance models. Weproposed a data-driven approach to modelling the mean and variance simultaneously,yielding more efficient estimates of the mean regression parameters than theconventional generalized estimating equations approach even if the within-subjectcorrelation structure is misspecified in our joint mean-variance models. The jointmean-variances in parametric form as well as semiparametric form has been investigated.Extensive simulation studies are conducted to assess the performance of our proposedapproaches. Three longitudinal data sets, Ohio Children’s wheeze statusData (Ware et al., 1984), Cattle data (Kenward, 1987) and CD4+ data (Kaslowet al., 1987), are used to demonstrate our models and approaches.

Keyword(s)

Correlation structures ; Empirical likelihood; Generalized estimating equations; Generalized linear models ; Longitudinal data; Mean-varaince models; Quadratic inference functions ; Quasi-likelihood; Variance function

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