臺灣博碩士論文加值系統

本文主要探討反應變數為類別型下, 伴隨變數有部分隨機缺失(MAR)之情形，引用Wang and Chen(2009)使用條件經驗分配(Conditional Empirical Distribution)生成插補值之概念，提出兩種不同的多重插補法(Multiple Imputation)應用在多元邏輯斯迴歸模型(Multiple Logistic Regression)參數估計上，並與完整資料估計法(Complete-Case Estimator)、加權估計法(Weighted Estimator)、迴歸校正法(Regression Calibration)和鏈式方程多重插補法(Multiple Imputation by Chained Equations)，藉由統計模擬比較不同樣本數及不同缺失率之估計結果。從模擬結果呈現，本文所提出之兩種多重插補法的表現，優於其他四種估計方法。最後，以彰化縣的高血壓調查問卷實例，說明各種估計結果的表現。

This article considers the categorical response variable with missing covariate that is missing at random (MAR).We propose two kinds of Multiple Imputations(MI) estimate parameter in multiple logistic regression are based on the conditional empirical distribution from Wang and Chen(2009),and compare with four different estimate methods:Complete-Case Estimator (CC),Weighted Estimator (WE),Regression Calibration (RC) and Mutiple Imputation by Chained Equations (MICE).We compare their results through simulations using various values of the sample size and missing rate.The methods are illustrated using data from the high blood pressure studay in Changhua.

1 緒論. . . . . . . . . . . . . . . . . . . . . . . . . .1
2 文獻探討. . . . . . . . . . . . . . . . . . . . . . . 4
2.1 缺失型態的定義. . . . . . . . . . . . . . . . . . . 5
2.2 完整資料分析法(Complete-case estimator) . . . . . . 6
2.3 迴歸校正法(Regression Calibration) . . . . . . . . . 6
2.4 多重插補法(Mutiple imputation) . . . . . . . . . . . 7
2.5 鏈式方程多重插補法(MICE) . . . . . . . . . . . . . . 8
2.6 NORM法. . . . . . . . . . . . . . . . . . . . . . . 9
2.7 確認概似估計法(Validation likelihood estimator) . . 10
2.8 聯合條件概似估計法(Joint conditional likelihood estimator) 11
2.9 加權估計法(Weighted estimator) . . . . . . . . . . 13
3 研究方法. . . . . . . . . . . . . . . . . . . . . . . 14
3.1 多元邏輯斯迴歸模型. . . . . . . . . . . . . . . . . 14
3.2 加權估計法(Weighted estimator) . . . . . . . . . . .15
3.3 多重插補法一之條件機率(Multiple imputation I) . . . 17
3.4 多重插補法二之平均估計函數(Multiple imputation II) . 19
3.5 其它估計方法. . . . . . . . . . . . . . . . . . . . 20
3.5.1 完整資料分析法(Complete-case estimator) . . . . 20
3.5.2 迴歸校正法(Regression Calibration) . . . . . . . . 20
3.5.3 鏈式方程多重插補法(MICE) . . . . . . . . . . . . 21
4 統計模擬. . . . . . . . . . . . . . . . . . . . . . . 23
4.1 參數平均數之估計. . . . . . . . . . . . . . . . . . 23
4.2 標準差之估計. . . . . . . . . . . . . . . . . . . . 23
4.3 信賴區間(CI)與涵 � 率(CP)之估計. . . . . . . . .24
4.4 模擬結果分析. . . . . . . . . . . . . . . . . . . .24
5 實證分析. . . . . . . . . . . . . . . . . . . . . . 30
6 結論. . . . . . . .. . . . . . . . . . . . . . . . . 34
參考文獻. . . . . . . . . . . . . . . . . . . . . . . 35

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