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系統識別號 U0002-1906200811312500
中文論文名稱 分層病例對照資料下羅吉斯迴歸模型的適合度檢定
英文論文名稱 Goodness-of-fit of logistic regression model for stratified case-control data
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 96
學期 2
出版年 97
研究生中文姓名 梁正憲
研究生英文姓名 Chung-Hsian Liang
學號 695650233
學位類別 碩士
語文別 中文
口試日期 2008-05-30
論文頁數 46頁
口試委員 指導教授-陳麗菁
委員-王俊毅
委員-林哲揚
委員-吳碩傑
中文關鍵字 分層病例對照研究  羅吉斯迴歸模型  雙樣本半參數化模型  半參數最大概似估計量  適合度檢定 
英文關鍵字 stratified case-control study  logistic regression model  two-sample semiparametric model  goodness-of-fit  semiparametric maximum likelihood estimate 
學科別分類 學科別自然科學統計
中文摘要 在分層病例對照研究下,針對羅吉斯迴歸模型我們推論迴歸參數的半參數最大概似估計量(SMLE),並提出動差型式檢定統計量以診斷模型的適合度。我們的方法主要是推廣Qin & Zhang (1997) 的概念,將模型重參數化後得到多組的雙樣本半參數化模型,以此推論SMLE,並利用描述反應變數在非參數和半參數化模型下二階動差的差距來建立檢定統計量。我們推論得到SMLE的大樣本性質,及檢定統計量將分配收斂至卡方分配。模擬研究中我們發現即使在有限樣本的情況下,該檢定統計量亦執行良好。最後呈述一個關於痲瘋病研究的範例。
英文摘要 We inference the semiparametric maximum likelihood estimate (SMLE) and present the moment specification test of the logistic regression model for stratified case-control data. By generalizing the concept of Qin & Zhang (1997), we get the two-sample semiparametric model in each stratum and then inference the SMLE base on this finding.
The test statistic is constructed via a discrepancy between two second moments under nonparmetric and semiparametric model. The large sample properties of SMLE are described. The proposed test statistic converges in
distribution to the Chi-squared distribution. Simulation studies demonstrate that the test statistic perform well
even in finite sample. Illustration with a leprosy disease study is provided
論文目次 目錄

第 一 章 緒論………………………………………………………1

第 二 章 羅吉斯迴歸模型的統計推論……………………………6
第 一 節 迴歸參數的估計……………………………………..8
第 二 節 參數估計量的近似分配…………………………….11
第 三 節 迴歸模型的適合度檢定…………………………….15

第 三 章 模擬研究………………………………………………...18
第 一 節 適合度檢定的模擬研究…………………………….18
第 二 節 實例分析…………………………………………….21

第 四 章 結論……………………………………………………...23

參考文獻……………………………………………………………....24

附錄……………………………………………………….…...27

表目錄
1.假設f_{0j}(x)為常態分配N(mu,1) 之密度函數,f_{1j}(x)為常
態分配N(mu+0.5,sigma^2)之密度函數時,檢定統計量W的顯著水
準與檢定力………………………………………………………20
2.以年齡分群,有無接受BCG預防接種與有無患痲瘋病人.....21

參考文獻 1. Arbogast, P.G. and Lin, D.Y. (2005) Model-checking
techniques for strati‾ed case-control studies.
Statistics in Medicine 24, 229-247.
2. Breslow, N. E. and Cain, K. C. (1988) Logistic
regression for two-stage case-control data.
Biometrika 75, 11-20.
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in cancer research, 1, The analysis of case-control
studies. Lyon:IARC.
4. Clayton D, and Hills, M. (1993) Statistical models in
5. Cox, D. R. (1970) The analysis of binary data. London:
Methuen.
6. Farewell, V. (1979) Some results on the estimation of
logistic models based on retrospective data.
Biometrika 66, 27-32.
7. Fears, T.R. and Brown, C.C. (1986) Logistic regression
methods for retrospective case-control studies using
complex sampling procedures.
Biometrics 42, 955-960.
8. Fokianos, K., Peng, A. and Qin, J. (1999) A generalized-
moments specification test for the logistic link.
The Canadian Journal of Statistics 27,735-750.
9. Hosmer, D. W., Hosmer, T., Le Cessie S. and Lemeshow,
S. (1997) A comparison of goodness-of-fit tests for the
logistic regression model.
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fit test for the multiple logistic regression model.
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11. Hosmer, D. W. and Lemeshow, S. (2000) Applied logistic
regression. 2nd edn. Wiley: New York.
12. Osius, G. and Rojeck, D. (1992) Normal goodness-of-fit
tests for multionomial models with large dregress-of-
freedom. Journal of the American
Statistical Association 87, 1145-1152.
13. Pregibon, D. (1981) Logistic regression diagnostics.
The Annals of Statistics 9, 705-724.
14. Prentice, R. L. and Pyke, R. (1979) Logistic disease
incidence models and case-control sutides.
Biometrika 66, 403-11.
15. Qin, J. and Zhang, B. (1997) A goodness-of-fit for
logistic regression models based on case-control data.
Biometrika 84, 609-618.
16. Scott, A.J. and Wild, C.J. (1997) Fitting regression
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Biometrika 84, 1, 57-71.
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Biometrika 78, 705-17.
18. Zhang, B. (1999) A chi-squared goodness-of-fit test
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