Linear mixed effects models in functional data analysis

Regression models with a scalar response and a functional predictor have been extensively studied. One approach is to approximate the functional predictor using basis function or eigenfunction expansions. In the expansion, the coefficient vector can either be fixed or random. The random coefficient vector is also known as random effects and thus the regression models are in a mixed effects framework. The random effects provide a model for the within individual covariance of the observations. But it also introduces an additional parameter into the model, the covariance matrix of the random effects. This additional parameter complicates the covariance matrix of the observations. Possibly, the covariance parameters of the model are not identifiable. We study identifiability in normal linear mixed effects models. We derive necessary and sufficient conditions of identifiability, particularly, conditions of identifiability for the regression models with a scalar response and a functional predictor using random effects. We study the regression model using the eigenfunction expansion approach with random effects. We assume the random effects have a general covariance matrix and the observed values of the predictor are contaminated with measurement error. We propose methods of inference for the regression model's functional coefficient. As an application of the model, we analyze a biological data set to investigate the dependence of a mouse's wheel running distance on its body mass trajectory.

Name thesis:degree_name

Doctor of Philosophy - PhD

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

University of British Columbia

Year dc:date

2008

Author dc:creator

• Wang, Wei

Statement dc:rights

• Attribution-NonCommercial-NoDerivatives 4.0 International

Licence

• http://creativecommons.org/licenses/by-nc-nd/4.0/

Language dc:language

eng

Handle dc:identifier

http://hdl.handle.net/2429/253

OAI identifier oai:identifier

oai:circle.library.ubc.ca:2429/253