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https://hdl.handle.net/2142/87404
Description
Title
Linear Mixed Models With Non-Normal Distributions
Author(s)
Zhou, Tianyue
Issue Date
2005
Doctoral Committee Chair(s)
He, Xuming
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
Linear mixed models based on the normality assumption are widely used in health related studies. Although the normality assumption leads to simple, mathematically tractable, and powerful tests, violation of the assumption may easily invalidate the statistical inference. In this dissertation, we propose two approaches to make robust inferences for linear mixed models. The first approach is the weighted likelihood method. We extend the weighting method proposed by Markatou, Basu and Lindsay (1996 and 1997) to linear mixed models where weights are determined at both the subject level and the observation level. The second approach is to substitute the normal distributions in linear mixed models by flexible skew t distributions (Azzalini and Capitanio, 2003), which account for skewness and heavy tails for both the random effects and the errors. This approach has been applied to the real data obtained from deglutition and respiration studies and showed significant improvement over normal model fits. The estimators are shown to be asymptotically normal with good efficiency and robustness.
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