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Linear mixed effects models in functional data analysis Wang, Wei
Abstract
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.
Item Metadata
Title |
Linear mixed effects models in functional data analysis
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2008
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Description |
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.
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Extent |
680020 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2008-01-03
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0066202
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2008-05
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International