| Summary: | 碩士 === 國立臺灣大學 === 農藝學系 === 85 === To define a likelihood we have to specify the form of
distribution of the observations. However, to define a quasi-
likelihood function we need only to specify the relationship
between mean and variance of the distribution concerned. Quasi-
likelihood can be used for estimation and it enlarges the scope
of the analysis of data. For the data set which do not satisfy
the assumptions of ordinary analysis, traditional
transformations such as square root, logarithmic and angular
transformation are used to achieve thenormality and stabilize
the variances. This thesis investigates the possibility to use
an alternative, that is, using a generalized linear models with
some given variance functions. Also the similarities and
differences between these two approaches were studied by
numerical examples. We consider six numerical examples for
illustrating the applications of quasi-likelihood functions and
for comparing the two different approaches. First three data
sets are of the form of one-way tables and second three data
sets are of theform of two-way tables. For each data set, we
compute two measures and for comparing the effectiveness in
estimation and model fitting, res of these two approaches. In
the generalized linear model considered, the link functions
which playing the role of achieving the additivity have
different forms from the traditional transformations. However,
the results obtained from this study show that these two
approaches are quite similar in effectiveness in estimation and
model fitting. This kind of similarity suggests that both
approaches might be equivalent and the equivalence might be
proved mathematically.
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