| 姓名 |
陳垠(Yin Chen)
查詢紙本館藏 |
畢業系所 |
統計研究所 |
| 論文名稱 |
邏輯斯迴 歸架構下比較廣義估計函數與強 韌概似函數
(Comparing the generalized estimation fu nction with the robust likelihood function for inference of logistic regression models)
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| 相關論文 | |
| 檔案 |
 [Endnote RIS 格式]
[Bibtex 格式]
 [相關文章]  [文章引用]  [完整記錄]  [館藏目錄]  至系統瀏覽論文 (2027-6-30以後開放)
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| 摘要(中) |
在醫學應用領域中，常有相關性的二元資料，例如家庭中成員是否患有癌症或是否患有白內障 ，而強韌概似函數方法(robust likelihood function)和廣義估計方程式(Generalized estimating equation, GEE) 可以很好的分析這些有相關性的二元資料。
本文的主要目的是在Tsou and Hsiao(2017)發表的論文基礎上，對強韌概似函數方法與廣義估計方程式進一步做更細緻的比較。本文通過模擬與實例分析比較了強韌概似函數方法和廣義估計方程式的型一誤差率、信賴區間上下界與覆蓋率，發現廣義估計方程在小樣本時會因為虛無假設的不同得出相反的結論。 |
| 摘要(英) |
In the field of medical applications, there are often related binary data, such as whether a family member has cancer or whether there is a cataract, and the robust likelihood function method and the generalized estimating equation can well analyze these correlated binary data.
The main purpose of this paper is to make a more detailed comparison between the robust likelihood function method and the generalized estimating equation(GEE) based on the paper published by Tsou and Hsiao (2017). This paper compares the type I error rate, the upper and lower bounds of the confidence interval and the coverage rate between the robust likelihood function method and the generalized
estimation equation through simulation and case analysis.It is found that the generalized estimating equation will draw the opposite conclusion due to the difference of null hypothesis when the sample is small. |
| 關鍵字(中) |
★ 強韌概似函數
★ 廣義估計方程 |
關鍵字(英) |
★ Robust likelihood function
★ Generalized estimating equation |
| 論文目次 |
摘要-----------------------------------i
Abstract------------------------------ii
致謝詞--------------------------------iii
目录----------------------------------iv
表目錄---------------------------------v
第一章 緒論-----------------------------1
第二章 文獻回顧-------------------------2
第三章 獨立伯努利模型之強韌化-------------3
3.1實作模型可被強韌化--------------------3
3.2修正項A之計算------------------------4
3.3修正項B之計算------------------------6
3.4參數之變異數估計量--------------------8
3.5修正項A與B之估計量-------------------8
3.6參數之華徳檢定統計量------------------9
3.7參數之分數檢定統計量------------------9
3.8參數之概似比檢定統計量---------------10
第四章 模擬研究------------------------11
4.1 資料生成方式-----------------------11
4.2 推算信賴區間之方式-----------------12
4.3 模擬結果--------------------------13
第五章 實例分析------------------------73
5.1實例（一）-------------------------73
5.2實例（二）-------------------------75
第六章 結論---------------------------82
參考文獻------------------------------83 |
| 參考文獻 |
Liang,K.Y. and Zeger,S.L.(1986). Longitudinal data analysis using generalized linear models. Biometrika,73:13-22.
Royall,R.M. and Tsou,T.S.(2003). Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions.Journal of the Royal Statistical Society,Series B,65:391-404.
Tsou,T.S. and Chen,C.H.(2008). Comparing several means of dependent populations of count A parametric robust approach. Statistics in Medicine,27:2576-2585.
Tsou,T.S. and Hsiao,W.C.(2017). Likelihood inference for correlated binary data without any information about the joint distributions. Communications in Statistics-Theory and Methods,46:2151-2160. |
| 指導教授 |
鄒宗山
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審核日期 |
2022-9-23 |
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