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An orthodox blup approach to generalized linear mixed models Ma, Renjun
Abstract
We introduce a new class of generalized linear mixed models assuming Tweedie exponential dispersion model distributions for both the response and the random effects. This class of models accommodates a wide range of discrete, continuous and mixed data. By letting the random effects enter as weights as well as means in the conditional distributions, the variance matrix may be expressed as a sum of variance components. We consider an orthodox BLUP approach to parameter estimation and random effects prediction for this new class of models based on a predictor of the random effects that is truly best linear and unbiased, in contrast to the conventional BLUP which is the conditional mode. We obtain an optimal estimating equation based on the orthodox BLUP, which is solved by a modified Newton algorithm. This approach facilitates analysis of residuals and allows justification of asymptotic results under realistic conditions through standard estimating equation theory. An important feature of this approach is that the principal results depend only on the first and second moment assumptions of unobserved random effects. The common fitting algorithm based on orthodox BLUP enables us to study this new class of models as a single class, rather than as a collection of unrelated different models. This approach is illustrated with the analyses of seed germination data, epilepsy data and cake baking data. By means of asymptotic justifications, simulations and worked examples, we conclude that the orthodox BLUP approach is of practical value for analysis of clustered non-normal data.
Item Metadata
Title |
An orthodox blup approach to generalized linear mixed models
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1999
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Description |
We introduce a new class of generalized linear mixed models assuming Tweedie
exponential dispersion model distributions for both the response and the random effects.
This class of models accommodates a wide range of discrete, continuous and
mixed data. By letting the random effects enter as weights as well as means in the
conditional distributions, the variance matrix may be expressed as a sum of variance
components. We consider an orthodox BLUP approach to parameter estimation and
random effects prediction for this new class of models based on a predictor of the
random effects that is truly best linear and unbiased, in contrast to the conventional
BLUP which is the conditional mode. We obtain an optimal estimating equation
based on the orthodox BLUP, which is solved by a modified Newton algorithm. This
approach facilitates analysis of residuals and allows justification of asymptotic results
under realistic conditions through standard estimating equation theory. An important
feature of this approach is that the principal results depend only on the first
and second moment assumptions of unobserved random effects. The common fitting
algorithm based on orthodox BLUP enables us to study this new class of models as a
single class, rather than as a collection of unrelated different models. This approach
is illustrated with the analyses of seed germination data, epilepsy data and cake baking
data. By means of asymptotic justifications, simulations and worked examples,
we conclude that the orthodox BLUP approach is of practical value for analysis of
clustered non-normal data.
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Extent |
5190557 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-07-03
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0089321
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1999-05
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.