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題名：非隨機遺漏之結構方程模型估計─潛在變項選擇模型與組型混合模型
作者：鄭中平 引用關係
作者(外文)：Chung-Ping Cheng
校院名稱：國立臺灣大學
系所名稱：心理學研究所
指導教授：翁儷禎
學位類別：博士
出版日期：2003
主題關鍵詞：結構方程模型；不可忽略遺漏；選擇模型；組型混合模型；EM算則；structural equation modeling；nonignorable missingness；selection model；pattern mixture model；EM algorithm
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結構方程模型為心理學常用分析方法之一，研究者需收集實徵資料檢驗模型的適當性，在資料收集過程中難免得到不完整資料。結構方程模型現行之遺漏值處理法大多假設資料遺漏機制為完全隨機遺漏或隨機遺漏，均侷限於外顯變項對資料遺漏的影響，而文獻中討論之遺漏機制，包括選擇模型與組型混合模型，亦僅著眼於外顯變項與資料遺漏間的關係，對於心理學研究而言乃嫌不足。是故，本研究即將潛在變項引入選擇模型與組型混合模型，稱為潛在變項選擇模型與潛在變項組型混合模型。
針對潛在變項選擇模型，本研究採Muthén等人（1987）之遺漏機制模型，假設變項遺漏機率受潛在連續變項影響，為選擇模型之延伸。研究中以隨機EM算則配合捨選抽樣法，估計潛在變項選擇模型時結構方程模型之參數，稱之為潛在變項選擇模型最大概似估計。
潛在變項組型混合模型將潛在類別變項加入組型混合模型中，假設觀察變項的遺漏組型並非受訪者的分類，而是潛在類別的指標變項，此模型為Little組型混合模型擴充至潛在變項層次之延伸。本研究以EM算則估計結構方程模型參數，稱之為潛在變項組型混合模型最大概似估計。
本研究並以三個模擬研究，探討當資料遺漏符合潛在變項遺漏機制時，本研究建議之遺漏值處理法的表現。結果發現，在遺漏機制符合潛在變項選擇模型時，資料遺漏比率較高，且越偏離完全隨機遺漏，潛在變項選擇模型最大概似估計法的表現越好。若資料遺漏為潛在變項組型混合模型，潛在變項組型混合模型最大概似估計法的表現良好，對於遺漏機制參數估計表現亦良好。本研究並討論兩類遺漏值處理法之假設與未來研究方向。
Structural equation modeling (SEM) is a popular statistical method for social science research. Incomplete data are often encountered when researchers make an effort to collect empirical data for test of their hypothesized models. Most missing data treatment methods in SEM assume that data are missing completely at random or missing at random. These two missing patterns consider the impact of manifest variables on data missingness. Missing data mechanisms of selection model and pattern mixture model also focus on the relationship between missingness and manifest variables. For psychologists interested in latent variables, the missing data mechanisms that ignore the influences of latent variables tend to be insufficient. The research therefore introduced latent variables into selection model and pattern mixture model, referred to as latent variable selection model and latent variable pattern mixture model, respectively.
Latent variable selection models assume that missingness is affected by continuous latent variables, as suggested by Muthén et al. (1987). Stochastic EM algorithm with rejection/acceptance sampler was developed to estimate the parameters. The method was called “latent variable selection model maximum likelihood estimation (LVSM-ML)”.
Latent variable pattern mixture model assume that missing data patterns reflect latent classes. Categorical latent variables were added to the pattern mixture model. Maximum likelihood estimation using the EM algorithm was developed and referred to as “latent variable pattern mixture model maximum likelihood estimation (LVPM-ML)”.
Three Monte Carlo studies were employed to explore the performance of LVSM-ML and LVPM-ML when latent variables affected data missingness. Results of the present study showed that with missing data mechanism of latent variable selection model, LVSM-ML performed better than other missing data treatment methods at high degrees of data missingness and severe departure from missing completely at random. If the missing data mechanism is latent variable pattern mixture model, LVPM-ML also performed better than other methods. The assumptions of the two missing data treatment methods proposed and directions for future research were also discussed.
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