臺灣博碩士論文加值系統

數量性狀在遺傳分析上受到廣泛地討論，但數量性狀的外在表現型常受到遺傳及環境等因素的影響，在收集資料中，難免會出現離群值。若此離群值對模型的參數估計造成較大影響，進而導致影響模型之解釋力與分析結果，此即為「影響點」。當離群值為影響點，在資料分析上反而比其他值有較大的貢獻。所以，必須儘可能找出影響點並加以分析，以期得到更清楚的資訊及正確的分析結果。有鑑於此，如何在以家庭結構為基礎的數量性狀中找出離群值成為當務之急。本論文分析的主要對象是以「三元體家庭」為單位的數量性狀資料。研究中，將採用羅吉斯迴歸來建構三元體家庭數量性狀資料傳遞/不傳遞遺傳機制，進一步利用診斷測度來偵測離群值及影響點。研究結果顯示，資料中存有單一離群值時，可利用標準化偏離性殘差、概似殘差及交叉驗證機率等作為判斷標準；當資料中存有多個離群值或聯合影響點時，必須注意是否有遮蔽及誤判效應，而需使用不同判斷標準，才能獲得足夠的資訊及正確結果。

Quantitative trait is aggressively discussed in the area of genetic analysis. The external phenotype of quantitative trait is influenced by genetic and environmental factors. The data may contain particular observations, termed outliers, that are not well fitted by the model, or observations, termed influential observations, that have an undue impact on the conclusions to be drawn from the analysis. In fact, an influential observation contribute more than other general one. Thus, it is necessary to find out influential observations as many as possible to obtain explainable information and correct analysis results. The first thing to do in family-based quantitative trait is to find out outliers. This research takes logistic regression to constitute triad families quantitative trait transmission/non-transmission mechanism. For further analysis, diagnostic measures is used to discover outliers and influential observations. The results show that：(1) When an outlier exists in a data set, using the ‘standardized deviance residuals’ or ‘likelihood residuals’ or ‘cross-validation probability’ could detect out the influential observation. (2) The detection of multiple outliers or influential subsets is more difficult, owing to masking and swamping problems. Thus, in order to obtain affluent information and correct result, it is necessary to take different judge standards.

第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 3
第三節 論文架構 3
第二章 文獻探討 4
第一節 線性迴歸模型之離群值偵測 4
第二節 羅吉斯迴歸模型之離群值偵測 11
第三節 研究步驟 21
第三章 研究方法 22
第一節 數量性狀 22
第二節 TDT型資料 24
第三節 資料分析方法 27
第四章 資料分析與結果 32
第一節 資料模擬 32
第二節 資料分析 34
第五章 結論與建議 47
參考文獻 49
附錄 一 52
附錄 二 55
附錄 三 59

陳順宇（2000）迴歸分析，華泰書局
黃登源（1998）應用迴歸分析，華泰書局
楊民鉉（2001）應用類神經網路於數量性狀之遺傳連鎖分析，台灣大學流行病學研究所碩士論文
廖佩珊（2003）迴歸分析，輔仁大學管理學院管理技術中心
戴 政 （2002） 遺傳流行病學，藝軒圖書出版社
Andrade, M.D., Fridley, B., Boerwinkle, E. and Turner, S.（2003） “Diagnostic Tools in Linkage Analysis for Quantitative Traits.” Genetic Epidemiology, 24, 302-308.
Barrett, B. E. and Gray, J. B. （1992）”Diagnosing Joint Influence in Regression Analysis.” in Preceeding of the Statistical and Computational Section, American Statistical Association, 40-45.
Beckman, R. J. and Cook, R. D.（1983）”Outlier……s.” Technometrics, 25, 119-146.
Belsley, D. A., Kuh, E. and Welsch, R. E. （1980）Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Wiley, New York.
Collett,D.（1991）Modelling Binary Data. Chapman and Hall, London.
Cook, R. D.（1977）Detection of Influential Observation in Linear Regression. Technometrics, 19, 15-18.
Davison, A. C.（1988）Contribution to the Discussion of a Paper by J. B. Copas. Journal of Royal Statistical Society B, 50, 258-259.
Gray, J. B. （1986） “A Simple Graphic for Assessing Influence in Regression.” Journal of Statistical Computation and Simulation, 24, 121-134.
Gray, J. B. （1989）”On the Use of Regression Diagnostics.” The Statistician, 38, 97-105.
Gupta, S. S. and Huang, D. Y.（1996）”On Detection Influential Data and Selecting Regression Variables.” Journal of Statistical Planning and Inference, 53, 421-435.
Hosmer, D. W. and Lemeshow, S.（1989）Applied Logistic Regression. John wiley ＆ Sons, Inc
Hosmer, D. W. and Lemeshow, S.（1991） ”The Importance of Assessing the Fit of Logistic Regression Models: A Case Study.” American Journal of Public Health, 81, 1630-1635.
Landwehr, J. M., Pregibon, D. and Shoemaker, A. C. （1984）”Graphical Methods for Assessing Logistic Regression Models.” Journal of the American Statistical Association, 79, 61-71.
Lawrance, A. J., （1995）”Deletion Influence and Masking in Rrgression.” Journal of Royal Statistical Society B, 57, 181-189.
Pena, D. and Yohai, V. J.（1995）”The Detection of Influential Subsets in Linear Regression by using an Influence Matrix” Journal of Royal Statistical Society B, 57, 145-156.
Pregibon,D.（1981）”Logistic Regression Diagnostic.” Annals of Statistics, 9, 705-724.
Rancel, M.M.S. and Sierra, M.A.G.（2000）”Weighting and Deletion Approaches to Regression Diagnostics：A Comparison and an Extension.” Journal of Economic and Social Research 2(1). 85-97.
Scott, M. （1995）Applied Logistic Regression analysis. Series: Quantitative Applications in the Social Sciences.
Welsch, R.E. （1982） Influence Functions and Regression Diagnostics. In: R.L. Launer and A.F. Siegel, (ed.) Modern Data Analysis, New York: Academic Press.
Welsch, R.E. and Kuh, E.（1977）”Linear Regression Diagnostics.” Technical Report 923-977, Sloan School of Management, Massachusetts Institute of Technology.
Wang, P.C.（1985）”Adding a variable in generalized linear models.” Technometrics, 27, 273-276.
Wang, P.C.（1987）”Residual plots for detecting nonlinearity in generalized models.” Technometrics, 29, 435-438.
Williams, D.A.（1984）”Residuals in generalized linear models.” XIIth International Biometrics Conference, Tokyo, 59-68.
Williams, D.A.（1987）”Generalized Linear Model Diagnostic Using the Deviance and single case deletions. ” Journal of Royal Statistical Society C, 36, 181-191.