臺灣博碩士論文加值系統

一般線性模型中，共變數分析(ANCOVA)大都假設兩迴歸線具相同斜率，因此線上各點差距相等，容易理解與解釋，但這種分析方式採循序檢定的過程，第一階段，先檢定斜率是否相等，在無法拒絕時，作進一步的比較，過程中將因接受斜率相等產生無法控制的型二誤差，且當迴歸線在觀察值均值附近交叉時，可能作出錯誤推論。
Johnson-Neyman (1936)、Potthoff(1964)及Rogosa,D.(1980)先後針對不同斜率之迴歸線作過探討與比較，該方法(J-N)首先求出兩條迴歸線相減產生之直線L，針對L上任一點X求出信賴區間，若該信賴區間與X軸相交，代表兩模型在X點之Y 值無顯著差距，接著引進Working-Hotelling band (Miller,1966,p.111) 的觀點，求出L之信賴帶，同時以代數及圖式法求取並觀察L之信賴帶與X軸的關係，進而作出一同時(simultaneous)檢定。
以上為一般線性模型的探討，架構在殘差獨立且相等之常態分配，但實務上，如二元、多元或計數等類別資料，一般線性模型方法並不適用，Nelder 與 Wedderburn(1972)針對一般線性模型的不足，發展出廣義線性模型(Generalized Linear Model)，模型中包含隨機單元(Random Component)、連結函數(Link Function)及系統單元(Systematic Component)三部份，主要運用在類別(Categorical )、非常態資料或Y值受限情形之分析，而一般線性模型為具常態分配與單位連結函數(Identity Link Function　) 之特例，近來運用在二元資料之Logistic 或計數資料之Poisson 迴歸均屬其範疇。
如同一般線性模型之共變數分析需先檢定斜率是否相等，廣義線性模型中也存在類似情形，為解決此問題，但更複雜的，即使兩廣義線性模型中系統變項之斜率相等，轉換到條件期望值的比較時，兩模型中各點的差異仍將不同，此時已無法比照一般線性模式中以特殊點解釋模型的差異，本文運用了J-N 技巧，引進Hauck,W.W(1983)計算Logistic 迴歸中信賴帶的觀念，採Bonferroni與Scheffé等同時檢定法，並以術後麻醉藥劑對疼痛降低指數之實例，將J-N 技巧運用在Logistic 迴歸模型，分析探討其結果，期能針對模型比較應用上，提供另一面向的思維探討與研究。

Statistical comparisons of experimental groups frequently are discussed based upon General Linear Models. If the outcome depends on concomitant variable, it is usually called ANCOVA (analysis of covariates). Under the assumptions of ANCOVA, the existence of parallel is important because the measure of model difference is the same. The test stage of parallel, sometimes, will make a serious problem because the type II error of accepting parallel isn’t controlled well.
Johnson-Neyman(1936),Potthoff,R.F.(1964),and Rogosa,D.(1980) developed Johnson-Neyman technical (J-N),which is a comprehensive strategy for the statistical comparison of within-group regressions regardless of whether the population regressions are parallel. However, the J-N has a wrong error structure in prediction and overfitting because of the exclusion of the test of each parameter.
Recently, the prevalent use of categorical data analysis (CDA) interested us to consider the comparison of generalized linear models. Agresti (2002) made a model comparison in horseshoe crab example, in order to understand whether the nonparallel exists, he used dummy variables and found the evidence of interaction is weak. His approach, nonsimultaneous comparison, built on large sample theorem and Delta method is simple when the covariates are categorical. However, we can’t pick a appropriate point like as ANCOVA to estimate an overall treatment effect even though the systematic components are parallel between the models if the predictors are quantile because the difference, except some special link, between the inverse link function of systematic components are heterogeneity. Like as J-N used in ANCOVA determines a region of significance, we extended it to CDA to specify the significant range base on the asymptotic normal distribution of the coefficient in simultaneous studies. In J-N extended to CDA in the article, the raw data converted to binary doesn’t blur the sharp distinction because of the non-significance of slope and lose of information in the converting stage. It is still an alternative approach to make model comparison.
Clearly, the power analysis and variance stability in the expose are worth studying. Until more work has been done, we could get more information and evaluation about the approach. Hoping the technique can offer another methodology on model comparison.

第一章 緒論 1
第一節 背景說明 1
第二節 研究動機 1
第三節 研究目的 2
第二章 文獻探討 4
第一節 共變數分析 4
第二節 Johnson-Neyman 技巧 9
第三節 信賴帶的估計 10
第一項 Bonferroni法 11
第二項 Scheffé法 12
第三項 方法比較 14
第四節 廣義線性模型 14
第一項 模型架構 14
第二項 信賴帶估計與檢定 15
第三章 研究方法 17
第一節 廣義線性模型 17
第一項 模型架構（指數族） 17
第二項 J-N法運用在一般線性模型的特點 19
第三項 大樣本理論 20
第四項 廣義線性模型的參數解 21
第二節 兩模型間非同時與同時檢定 22
第一項 非同時檢定 22
第二項 同時檢定 23
第三項 不對等不平衡模型 26
第三節 J-N 法在Logistic模型的運用 28
第一項 Logistic 模型之參數估計 28
第二項 傳統與J-N 法Logistic模型的比較 29
第四節 信賴帶的估計 30
第一項 整體誤差的控制 31
第二項 信賴帶的計算 31
第五節 範圍的限制 31
第四章 實例分析 33
第一節 變數定義 33
第二節 J-N法的運用 34
第一項 模型參數估計及檢定 34
第二項 模型比較 36
第三項 分析結果 38
第五章 結論 41
第一節 研究結論 41
第二節 研究建議 41
參考文獻 43

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