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系統識別號 U0002-1107201416402500
中文論文名稱 病例對照研究中多元羅吉斯迴歸模型的適合度檢定
英文論文名稱 A Goodness-of-Fit Test of Multinomial Logistic Regression Model in Case-Control Studies
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 102
學期 2
出版年 103
研究生中文姓名 許育愷
研究生英文姓名 Yu-kai Shiu
學號 601650079
學位類別 碩士
語文別 中文
口試日期 2014-06-05
論文頁數 32頁
口試委員 指導教授-陳麗菁
委員-王俊毅
委員-陳蔓樺
中文關鍵字 拔靴法  病例對照研究  適合度檢定  多元羅吉斯迴歸  半參數最大概似估計量 
英文關鍵字 bootstrap method  case-control studies  goodness-of-fit test  multinomial logistic regression  semiparametric maximum likelihood estimator 
學科別分類
中文摘要 在病例對照研究中,羅吉斯迴歸模型常用來推論疾病與風險因子之間的關係。當研究中的反應變數為多個類別時,需考慮使用多元羅吉斯迴歸模型。本文推廣Qin and Zhang (1997)的想法到多元羅吉斯迴歸模型,推導各個病例組與對照組之間的比例關係,並將此模型重參數化得到多組的半參數化模型,以此推論迴歸參數的半參數最大概似估計量。為了檢測模型的合適性,本文推廣Chen and Wang (2013)的方法,針對多元羅吉斯迴歸模型提出動差形式檢定統計量,並使用拔靴法求算檢定統計量的p值。經由模擬研究發現,即使在有限樣本下該檢定統計量亦表現良好。最後以兩組實際資料分析作為範例。
英文摘要 In case-control studies, the logistic regression model is used popularly for inferring the relationship of disease and risk factors. When a response has multiple categories, the multinomial logistic regression should be considered. By generalizing the concept of Qin and Zhang (1997), this study derives a proportional relationship between the control group and each case group. After reparameterisation, the logistic model is equivalent to several semiparametric models and then the semiparametric maximum likelihood estimator is derived based on this finding. This study generalizes the idea of Chen and Wang (2013) to propose a moment-type test statistic for the multinomial logistic regression. A bootstrap method is used to calculate the p-value of the proposed test. Simulation studies demonstrate that the proposed test performs well even in finite samples. An illustration with two real data sets is provided as well.
論文目次 目錄
第一章 緒論1
第二章 病例對照研究下多元羅吉斯迴歸的統計推論5
第一節 參數估計5
第二節 建構多元羅吉斯迴歸模型的檢定統計量11
第三章 模擬研究14
第四章 實例分析19
第五章 結論21
參考文獻23
附錄一 青少年安置研究資料25
附錄二 城際交通方式選擇資料30

表目錄
1. 動差形式檢定統計量S_0的模擬結果17
2. 動差形式檢定統計量S的模擬結果,J=2 17
3. 動差形式檢定統計量S的模擬結果,J=3 18

參考文獻 Begg, C. B. and Gray, R. (1984). Calculation of polychotomous logistic regression parameters using individualized regressions, Biometrika, vol.71, pp.11-18.
Chen, L. C. and Wang, J. Y. (2013). Testing the fit of the logistic model for matched case-control studies, Computational Statistics and Data Analysis, vol.57, pp.309-319, 2013.
Cheng, K. F. and Chen, L. C. (2004). Testing goodness-of-fit of a logistic regression model with case-control data, Journal of Statistical Planning and Inference, vol.124, pp.409-422.
Cox, D. R. (1970). The Analysis of Binary Data. Methuen, London
Efron, B. and Tibshirani, R. (1993). An introduction to the Bootstrap, Chapman and Hall, London.
Fagerland, M. W. and Hosmer, D. W. and Bofin, A. M. (2008). Multinomial goodness-of-fit test for logistic regression model, Statistics in medicine, vol. 27, pp.4238-4253.
Goeman, J. J. and le Cessie, S. (2006). A goodness-of-fit test for multinomial logistic regression, Biometrics, vol.62, pp.980-985.
Hosmer, D.W. and Lemeshow, S. (1980). Goodness-of-fit tests for the multiple logistic regression model, Communications in Statistics-Theory and Methods, vol.9, pp.1043-1069.
Hosmer, D. W. and Lemeshow, S. (2013). Applied Logistic Regression, 3rd edition, Wiley, New York.
Louviere, J. J. and Hensher, D. A. (2000), Stated Choice Methods Analysis and Applications, Cambridge University Press.
Prentice, R. L. and Pyke, R. (1979). Logistic disease incidence models and case-control studies, Biometrika, vol. 66, pp.403-411.
Qin, J. and Zhang, B. (1997). A goodness-of-fit test for logistic regression models based on case-control data, Biometrika, vol. 84, pp.609-618.
Zhu, K. and Levine, R. S. (2002). Case-control study evaluating the homogeneity and heterogeneity of risk factors between sinonasal and nasopharyngeal cancers, International Journal of Cancer, vol. 99, pp. 119-213.
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