臺灣博碩士論文加值系統

定義概度函數必須知道其觀測值的分布型態,但是定義類似概度函數
卻只需要一個特定的均值與變方的關係式,即找出其變方函數,便可用來對
參數做估計,這使得可以被用來分析的資料其範圍更加擴大.對於未能符合
變方分析假設前題的資料,傳統上是利用變數變換,如:開方根轉換,對數轉
換及角度轉換來達到常態性及變方的同質性.本文利用給定變方函數的廣
義線型模式提供此類資料另一種分析方法,並舉實際的數例來比較兩種方
法的相似性及差異性.其中前三個數例為單向變方分析的資料,後三個數例
為雙向變方分析的資料,並分別計算其D平方及R平方值作為比較傳統便數
變換分析法與類似概度函數分析法兩者所得預測值及模式配適的比較量.
在廣義線型模式中,使資料達到加成性的連結函數,其型式不同於傳統的變
數變換,但從本文的結果卻顯示此兩種分析方法在預測值及模式配適上有
相當的相似性.此種相似性提示了這兩種方法可能是相同的,並且應該可以
利用更嚴謹的數學方法加以證明.

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.