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|Title: ||Conditional inference in generalized linear mixed models : model identification and robust estimation|
|Other Titles: ||Ji yu tiao jian fen bu de guang yi xian xing hun he mo xing de tong ji tui duan : mo xing shi bie he wen jian gu ji|
基於條件分佈的廣義線性混合模型的統計推斷 : 模型識別和穩健估計
|Authors: ||Yu, Dalei ( 喻達磊)|
|Department: ||Department of Management Sciences|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2011|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Linear models (Statistics)|
|Notes: ||CityU Call Number: QA276 .Y8 2011|
x, 135 leaves : ill. 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2011.
Includes bibliographical references (leaves 101-110)
|Abstract: ||In this thesis, statistical inference problems in generalized linear mixed
models (GLMMs) are considered. In particular, model identification and
robust residual maximum likelihood (REML) estimation for the GLMMs
are studied in detail.
The formulation and estimation for the GLMMs are first reviewed, and the
differences between conditional likelihood based and marginal likelihood
based methods are then discussed. Simulation results indicate that both
methods are promising when the sample size is relatively large. The REML
estimation method is effective in reducing the negative bias in the estimation
of the variance component parameters when the sample size is small.
To address the problem of model selection in the GLMMs, a model identification
instrument based on the conditional Akaike information (cAI) is
developed. In particular, an asymptotically unbiased estimator of the cAI
(denoted as cAICC) is derived as the model selection criterion, which takes
the estimation uncertainty in the variance component parameter into consideration.
The relationship between bias correction and generalized degree
of freedom for GLMMs is also explored. Simulation results show that
the estimator performs well. An adjusted model selection criterion (denoted
as cAICA), which is based on heuristic arguments, is also proposed
as an alternative tool for model identification. Both criteria demonstrate high proportion of correct model identification for GLMMs. Three sets of
real data (i.e. epilepsy seizure count data, polio incidence data and US
strike data) are used to illustrate the proposed model identification methods.
To limit the effect of outliers, a robust version of the REML estimation
for Poisson log-linear mixed model is developed. The method not only
provides robust estimation for the fixed effect and variance component
parameters, but also gives robust prediction of the random effects. Theoretical
and numerical aspects of the estimators are examined. Simulation
results show that the proposed method is effective in limiting the effect
of outliers under different contamination schemes. The epilepsy seizure
count data are used to illustrate the method.
The robust REML estimation method is then extended to the k-component
Poisson mixture model with random effects. The behavior of the estimator
is studied, and the formulae for obtaining the asymptotic covariance matrix
are derived. Simulation study shows that the performance of the proposed
robust REML estimator is comparable with the conventional REML estimator
for regular data, and it outperforms in the presence of outliers. The
urinary tract infections data are taken to demonstrate the proposed robust
Following similar lines of derivations, extensions of the developed methodologies
are possible for a general class of hierarchical generalized linear
models and generalized additive models. These topics are considered as
future research directions.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b4086011|
|Appears in Collections:||MS - Doctor of Philosophy |
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