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研究生:溥杰瑞
研究生(外文):Jerry Dwi Trijoyo Purnomo
論文名稱:一個修正的廣義估計方程式方法對於共變效果的潛在類別迴歸模型在測量和底層變數
論文名稱(外文):A Modified Generalized Estimating Equation (GEE) Approach for Latent Class Models with Covariate Effects on Measured and Underlying Variables
指導教授:黃冠華黃冠華引用關係陳志榮陳志榮引用關係
指導教授(外文):Huang, Guan-HuaChen, Chih-Rung
口試委員:郭炤裕魏裕中王秀瑛洪慧念黃冠華陳志榮
口試委員(外文):Guo, Chao-YuWei, Yu-ChungWang, HsiuyingHung, Hui-NienHuang, Guan-HuaChen, Chih-Rung
口試日期:2018-04-11
學位類別:博士
校院名稱:國立交通大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:英文
論文頁數:66
中文關鍵詞:潛在類別迴歸廣義季方程式工作共變量高斯-牛頓法
外文關鍵詞:regression extension of latent class analysisgeneralized estimating equationworking covarianceGauss-Newton method
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近期潛在類別迴歸模型在許多研究領域扮演重要的角色。RLCA模型在主要共變數和潛在類別建立起之間的關係,也連結了次共變數對測量之反應變數的效果。這個方法在分析測量多個反應變數和感興趣的共變數之間的關係被證明很有幫助。在這篇論文中,我們提出了一個廣義估計方程式方法來估計RLCA模型的參數。這個方法能夠明確的指出工作共變量,如此一來能夠減輕真實共變量的描述。我們細部描述了許多工作共變量結構,估計參數的高斯-牛頓法迭代演算,和獲得估計共變量參數的程序。使用癌症病患的資料,來分析可能影響脆弱度的變數,作為示範。
Recently, the regression extension of latent class analysis (RLCA) models have played an important role in many fields of research. RLCA models establish the relationship between primary covariates and latent class membership as well as the mediated direct effect of secondary covariates on measured responses. They have proven helpful for analyzing the relationship between measured multiple responses and covariates of interest. In this paper, we propose a generalized estimating equation (GEE) approach for the parameter estimation of RLCA models. This approach allows the specification of a working covariance that can ease the specification of the true covariance structure. We detail several structures of working covariance, iterative algorithms of Gauss-Newton methods for parameter estimation, and procedures for obtaining covariances of parameter estimators. An analysis of variables that probably affect the frailty of patients with cancer is used for illustration.
Contents

摘要 ……………………………………………………………………………………
iii

Abstract ……………………………………………………………………………….. iv
Acknowledgments ……………………………………………………………………. v
Contents ………………………………………………………………………………. vi

List of Tables …………………………………………………………………………. viii

List of Figures ………………………………………………………………………… ix

Abbreviations …………………………………………………………………………. x

Notations ……………………………………………………………………………… xi

1. Introduction ……………………………………………………………………. 1
2. Literature review …………………………………………………………….... 6
2.1 Latent class analysis (LCA) ………………………………………………… 6
2.2 Regression extension of latent class analysis (RLCA) ………………......... 7
2.3 Generalized linear models (GLMs) ……………………………………….. 10
2.4 Generalized estimating equation (GEE) ……………………………………. 12
2.4.1 Selection of working correlation matrices …………………………... 14
2.5 Model selection criteria for different working covariance structures ………. 16
3. Generalized estimating equation for RLCA model ……………………….... 20
3.1 The Proposed GEE approach ……………………………………………... 20
3.2 Working covariance structure …………………………………………….. 21
3.3 Parameter estimation and their covariance matrix …………………….….. 23
3.4 Asymptotic distribution ……………………………………………….…… 26

4. Data example …………………………………………………………….……. 29
4.1 Data ………………………………………………………………………... 29
4.2 Model fitting and data analysis ……………………………………….…… 31
5. Conclusion and discussion ………………………………………………….... 40
Appendix A. First and second partial derivatives of with respect to model parameters …………………………………………………….. 43
Appendix B. Gauss-Newton method ……………...................................................... 45
Appendix C. Sketch of proof of asymptotic normality for GEE model ……………. 47
Appendix D. The summary table for three-class RLCA model ……………………. 48
Bibliography …………………………………………………………………………
50
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