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Models for Univariate and Multivariate Analysis of Longitudinal and Clustered Data Open Access


Other title
Longitudinal Data Analysis
Zero-inflated Data
Clustered Data Analysis
Type of item
Degree grantor
University of Alberta
Author or creator
Luo, Dandan
Supervisor and department
Peng, Zhang (Mathematical and Statistical Sciences)
Examining committee member and department
Byron, Schmuland (Mathematical and Statistical Sciences)
Grace, Y. Yi (Statistical & Actuarial Sciences)
Peng, Zhang (Mathematical and Statistical Sciences)
Narasimha, Prasad (Mathematical and Statistical Sciences)
Yan, Yuan (Public Health Sciences)
Department of Mathematical and Statistical Sciences
Date accepted
Graduation date
Doctor of Philosophy
Degree level
Longitudinal studies of repeated observations on subjects are commonly undertaken in medical and biological sciences. The responses on a given occasion may be either univariate or multivariate. We concentrate on three topics related to longitudinal and clustered data analysis. The first topic is the development of a class of generalized linear latent variable models. The second involves the modelling of count data with excess zeros. The third is the development of a non-Gaussian linear mixed effects model for multiple outcomes. In addressing the first problem, we propose random mean models to account for correlation among repeated measures. We extend random mean models to include mixed outcomes, renaming them random mean joint models. The difficulty in joint modelling of continuous and discrete outcomes is the lack of a natural multivariate distribution. We overcome the difficulty by introducing two cross-correlated latent processes. We apply the Monte Carlo EM (MCEM) algorithm to find the MLEs of regression coefficients and variance components, by treating the latent variables as missing data. This thesis also proposes regression models for count data with excess zeros. We solve the problem from a perspective different from that of mixture model framework. By employing the zero truncated distribution and the zero modified distribution, we establish a broad class of distributions to model data with excess zeros. We consider the zero modified Poisson regression model and zero modified binomial regression model for cross-sectional data. We extend the zero modified regression models to models with random effects. We further extend random mean models to model zero-inflated data, and formulate the corresponding zero modified random mean models. A non-Gaussian linear mixed effects model for multiple outcomes is proposed to the third question. The methodology is motivated by a glaucoma study. The normality assumption for random effects may be unrealistic, raising concerns about the validity of inferences on fixed effects and random effects if it is violated. To accommodate the skewness of the responses and the associations among multiple characteristics, we propose a mixed effects model, in which non-normal random effects are assumed by the log-gamma distribution.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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