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postgraduate thesis: On some extensions of generalized linear models with varying dispersion
Title  On some extensions of generalized linear models with varying dispersion 

Authors  
Advisors  Advisor(s):Li, WK 
Issue Date  2012 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Wu, K. K. [胡家銳]. (2012). On some extensions of generalized linear models with varying dispersion. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4819937 
Abstract  When dealing with exponential family distributions, a constant dispersion
is often assumed since it simplifies both model formulation and estimation.
In contrast, heteroscedasticity is a common feature of almost every empirical
data set. In this dissertation, the dispersion parameter is no longer considered
as constant throughout the entire sample, but defined as the expected
deviance of the individual response yi and its expected value _i such that it
will be expressed as a linear combination of some covariates and their coefficients.
At the same time, the dispersion regression is an essential part of a
double Generalized Linear Model in which mean and dispersion are modelled in two interlinked and pseudosimultaneously estimated submodels.
In other words, the deviance is a function of the response mean which on the
other hand depends on the dispersion. Due to the mutual dependency, the
estimation algorithm will be iterated as long as the improvement of the one
parameter leads to significant changes of the other until it is not the case.
If appropriate covariates are chosen, the model’s goodness of fit should
be improved by the property that the dispersion is estimated by external
information instead of being a constant. In the following, the advantage
of dispersion modelling will be shown by its application on three different
types of data: a) zeroinflated data, b) nonlinear time series data, and
c) clinical trials data. All these data follow distributions of the exponential
family for which the application of the Generalized Linear Model is justified,
but require certain extensions of modelling methodologies.
In this dissertation, The enhanced goodness of fit given that the constant
dispersion assumption is dropped will be shown in the above listed
examples. In fact, by formulating and carrying out score and Wald tests
on testing for the possible occurrence of varying dispersion, evidence of
heterogeneous dispersion could be found to be present in the data sets considered.
Furthermore, although model formulation, asymptotic properties
and computational effort are more extensive when dealing with the double
models, the benefits and advantages in terms of improved fitting results and
more efficient parameter estimates appear to justify the additional effort not
only for the types of data introduced, but also generally for empirical data
analysis, on different types of data as well. 
Degree  Doctor of Philosophy 
Subject  Linear models (Statistics) 
Dept/Program  Statistics and Actuarial Science 
Persistent Identifier  http://hdl.handle.net/10722/167213 
HKU Library Item ID  b4819937 
DC Field  Value  Language 

dc.contributor.advisor  Li, WK   
dc.contributor.author  Wu, Kayui, Karl.   
dc.contributor.author  胡家銳.   
dc.date.issued  2012   
dc.identifier.citation  Wu, K. K. [胡家銳]. (2012). On some extensions of generalized linear models with varying dispersion. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4819937   
dc.identifier.uri  http://hdl.handle.net/10722/167213   
dc.description.abstract  When dealing with exponential family distributions, a constant dispersion is often assumed since it simplifies both model formulation and estimation. In contrast, heteroscedasticity is a common feature of almost every empirical data set. In this dissertation, the dispersion parameter is no longer considered as constant throughout the entire sample, but defined as the expected deviance of the individual response yi and its expected value _i such that it will be expressed as a linear combination of some covariates and their coefficients. At the same time, the dispersion regression is an essential part of a double Generalized Linear Model in which mean and dispersion are modelled in two interlinked and pseudosimultaneously estimated submodels. In other words, the deviance is a function of the response mean which on the other hand depends on the dispersion. Due to the mutual dependency, the estimation algorithm will be iterated as long as the improvement of the one parameter leads to significant changes of the other until it is not the case. If appropriate covariates are chosen, the model’s goodness of fit should be improved by the property that the dispersion is estimated by external information instead of being a constant. In the following, the advantage of dispersion modelling will be shown by its application on three different types of data: a) zeroinflated data, b) nonlinear time series data, and c) clinical trials data. All these data follow distributions of the exponential family for which the application of the Generalized Linear Model is justified, but require certain extensions of modelling methodologies. In this dissertation, The enhanced goodness of fit given that the constant dispersion assumption is dropped will be shown in the above listed examples. In fact, by formulating and carrying out score and Wald tests on testing for the possible occurrence of varying dispersion, evidence of heterogeneous dispersion could be found to be present in the data sets considered. Furthermore, although model formulation, asymptotic properties and computational effort are more extensive when dealing with the double models, the benefits and advantages in terms of improved fitting results and more efficient parameter estimates appear to justify the additional effort not only for the types of data introduced, but also generally for empirical data analysis, on different types of data as well.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.source.uri  http://hub.hku.hk/bib/B48199370   
dc.subject.lcsh  Linear models (Statistics)   
dc.title  On some extensions of generalized linear models with varying dispersion   
dc.type  PG_Thesis   
dc.identifier.hkul  b4819937   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Statistics and Actuarial Science   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.5353/th_b4819937   
dc.date.hkucongregation  2012   