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 pseudo-simultaneously 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) zero-inflated data, b) non-linear 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. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy
| Identifer | oai:union.ndltd.org:HKU/oai:hub.hku.hk:10722/167213 |
| Date | January 2012 |
| Creators | Wu, Ka-yui, Karl., 胡家銳. |
| Contributors | Li, WK |
| Publisher | The University of Hong Kong (Pokfulam, Hong Kong) |
| Source Sets | Hong Kong University Theses |
| Language | English |
| Detected Language | English |
| Type | PG_Thesis |
| Source | http://hub.hku.hk/bib/B48199370 |
| Rights | The author retains all proprietary rights, (such as patent rights) and the right to use in future works., Creative Commons: Attribution 3.0 Hong Kong License |
| Relation | HKU Theses Online (HKUTO) |
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