Briefly saying, in this thesis, I endeavor to deliver both the parametric and non-parametric modelling and selection tools for longitudinal data analysis.The first part of my work, is to extend the GEEs with random effects into thejoint modelling of longitudinal data. This is a parametric approach in which theheterogeneity and heteroscedasticity for different individuals are taken into account.With the only assumption about the existence of the first four order moments of theresponses, random effects are treated as a kind of penalty in the extended GEEs. Thisapproach includes both the virtues of GEEs and joint modelling with random effects.The modified Cholesky decomposition is used here for joint modelling because it hasa explicit statistical interpretation. This work could be applied to the longitudinaldata analysis in which the individual performance is of our main interest.The second part of this thesis, dedicates to the selection of random effects in theGeneralized Linear Mixed Model (GLMM). In this work, the penalized functions areimplemented into the selection of random effects covariance components. And the Pe-nalized Quasi-Likelihood (PQL) is recruited to deal with the integration of likelihood.When nonzero random effects covariance components are selected, their correspond-ing random effects are selected and other zero ones are eliminated. A backfittingalgorithm is proposed here for variable estimation and the leave-one-subject-out CV(SCV) method is used to select the optimal value of tuning parameter in penaltyfunction. This work is valuable in the aspect that random effects could also be par-simoniously selected with penalty functions. Besides, extension of this work to theselection of both fixed-effects and random effects are quite straight forward and therefore applicable to a more general area.The last part of this thesis aims to utilize a nonparametric data-driven approach,i.e., polynomial techniques to analyze the longitudinal data. Also based on the mod-ified Cholesky decomposition, the within subject covariance matrix is decomposedinto a unit lower triangle matrix involving generalized autoregressive coefficients anda diagonal matrix involving innovation variances. Local polynomial smoothing esti-mation is proposed to model the nonparametric smoothing functions of mean, gen-eralized autoregressive parameters and log-innovation variance, simultaneously. Theleave-one-subject-out CV (SCV) method is also implemented for the bandwidth se-lection. This work is creative in joint-modelling mean and covariance parameters bylocal polynomial method with the modified Choleskey decomposition. Besides, theproposed approach shows the robustness in computation in application.
|Date of Award||1 Aug 2011|
- The University of Manchester
|Supervisor||Jianxin Pan (Supervisor)|