相關性二分法資料迴歸之樣本數的問題｜國立中央大學博碩士論文系統

簡易檢索 / 詳目顯示

回結果列表

研究生：	王睿愛 Ruei-Ai Wang
論文名稱：	相關性二分法資料迴歸之樣本數的問題 Robust sample size formulae for testing the regression parameter when binary data are correlated
指導教授：	鄒宗山 Tsung-Shan Tsou
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 統計研究所 Graduate Institute of Statistics
畢業學年度：	96
語文別：	中文
論文頁數：	60
中文關鍵詞：	二分類相關性資料、邏輯斯迴歸
外文關鍵詞：	binary data are correlated, logistic regression
相關次數：	點閱：9 下載：0
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

摘要
本論文研究之目的是利用Royall and Tsou (2003)所介紹的強韌概似函數的概念，提出利用二項分配來分析具相關性的二分法資料時，想要達到一定的檢定力所需要的正確樣本數公式。
我們的研究以三種不同的邏輯斯迴歸為例，結果顯示，根據二項分配實作模型所得到的樣本數遠小於正確的樣本數。模擬研究與實例分析也都得到相同的結果。

Abstract
The aim of this research is to make use of the robust likelihood method proposed by Royall and Tsou (2003) to establish sample size formulae for testing parameter in logistic regression when binary data are correlated.
We adopted the binomial distribution as the working model and robustified the naïve likelihood using the robust technique by Royall and Tsou (2003). Robust sample size formulae for testing the regression parameter associated with the cluster-specific covariate is provided. The two versions of the sample size required to achieve a predetermined power, namely, the naïve and the robust formulae, are compared through simulations and analyses of several real data sets.

目錄
第一章 緒論................................................................................................................1
第二章 強韌迴歸........................................................................................................2
2.1 二項實作模型修正項...................................................................................3
2.2 達到目標檢定力所需要的樣本數...............................................................5
第三章 樣本數............................................................................................................7
3.1 簡單邏輯斯迴歸參數經過修正後樣本數和檢定力的關係…...................7
3.1.1 個別群集內的實驗個數不相同的情況............................................8
3.1.2 個別群集內的實驗個數都相同的情況........ ...................................10
3.2 複邏輯斯迴歸參數經過修正後樣本數和檢定力的關係.....................…..12
3.2.1 個別群集內的實驗個數不相同的情況............................................12
3.2.2 個別群集內的實驗個數都相同的情況............................................14
3.3 複邏輯斯迴歸參數經過修正後樣本數和檢定力的關係….......................16
3.3.1 個別群集內的實驗個數不相同的情況............................................16
3.3.2 個別群集內的實驗個數都相同的情況............................................17
第四章 模擬研究........................................................................................................20
4.1. 樣本數之理論數據......................................................................................20
4.2 樣本數之模擬結果.......................................................................................28
4.3 使用模擬方法驗證理論數據.................................................................…..33
第五章 實例分析........................................................................................................38
第六章 結論................................................................................................................53
參考文獻......................................................................................................................54

                                

參考文獻
1. Ahn, H. and Chen, J.J. (1997). Tree structured logistic model for over dispersed
binomial data with application to modeling developmental effects. Biometrics, 53,
435-455.
2. Chen, C.H. and Tsou, T.S. (2007). Parametric robust inference about regression
parameters for the correlation coefficient. Statistics, 41, 1-9.
3. Geert, M. and Louise M.R. (1999). An exponential family model for clustered multivariate binary data. Environmetrics, 10, 279-300.
4. James, F. R. (2000). Eliminating bias in randomized cluster trials with correlated binomial outcomes. Computer Method and Programs in Biomedicine, 61, 119-123.
5. Royall, R.M. and Tsou, T.S. (2003). Interpreting statistical evidence using
mperfect models: robust adjusted likelihood functions. Journal of the Royal
Statistical Society, Series B 65, 391-404.
6. Tsou, T.S. (2005). Inferences of variance functions- a parametric robust way.
Journal of Applied Statistics, 32, 785-796.
7. Tsou, T.S. (2006b). Robust Poisson regression. Journal of Statistical Planning and
Inference, 136, 3173-3186.
8. Tsou, T.S. (2007). A simple and exploratory way to determine the mean-variance
relationship in generalized linear models. Statistics in Medicine, 26, 1623-1631.
9. Weil, C.S. (1970). Selection of the valid number of sampling units and a
consideration of their combination in toxicological studies involving reproduction,
32 teratogenesis or carcinogensis. Food Cosmet Toxicol. 8, 177-182.
10. Williams, D.A. (1975). The analysis of binary responses from toxicological
experiments involving reproduction and teratogenicity. Biometrics, 31, 949-952.
11.鈴木豪志 (2007)，具相關性的二元資料之有母數強韌分析法，國立中央大學統計研究所

簡易檢索 / 詳目顯示

相關論文