臺灣博碩士論文加值系統

潛在類別分析(latent class analysis，LCA)在社會科學及醫學上已漸漸地被廣泛的運用，在潛在類別分析中加入共變數(covariates)的影響，就形成潛在類別迴歸分析(latent class regression，LCR)，和潛在類別分析一樣，潛在類別迴歸分析主要是在處理類別型的資料。潛在類別迴歸分析因為多考慮了共變數(covariates)的影響，所以用潛在類別迴歸分析得到的參數估計，比起用潛在類別分析所得到的參數估計，有更精準的估計效果(Karen Bandeen，Miglioretti，Zeger，Rachouz；1997)，所以本研究採用潛在類別迴歸分析作為主要的研究模型。
在潛在類別分析下處理缺失值的問題已有許多相關的研究，然而在潛在類別迴歸分析下處理缺失值的問題相關的文獻卻不多；本研究主要是討論資料為單調缺失時，使用鑑別函數(discriminant function)和羅吉斯迴歸(logistic regression)兩種插補(imputation)方法來插補缺失值，觀察插補之後的資料進行潛在類別迴歸分析所得的參數(潛在類別比例和潛在類別條件機率)，和用原始資料參數的假設理論值的差異情形，來評斷各個因子對參數估計的精準度影響為何。
本研究將模擬潛在類別迴歸模型的資料，觀察變數設定為4個：y1,y2,y3,y4 ，共變數設定為一個，潛在類別的個數控制為2個，而控制實驗的影響因子有：潛在類別比例、潛在類別條件機率比例、樣本大小、y3,y4 缺失比例及插補方法，觀察不同影響因子的組合對參數估計的精準度有何影響。
研究結果顯示，樣本數增加、y4 缺失比例降低、潛在類別比例為0.5：0.5時，估計參數會有較精準的效果，y3 缺失比例對估計影響不顯著，潛在類別條件機率比例和插補方法對參數估計則沒有一致的作用。

In social science and medicine, latent class analysis (LCA) is already of make use of gradually and extensively. Consider the influence of covariates in latent class analysis, we can get latent class regression analysis (LCR). As the same as latent class analysis, latent class regression analysis deal with categorical data mainly. Estimating parameter in latent class regression model is more accurate because of covariates (Karen Bandeen, Miglioretti, Zeger, Rachouz; 1997), so we use latent class regression model as the main model in this study.
In many related study, process missing data in latent class analysis has already be developed. However the related literatures which handle missing data in latent class regression analysis are not so much. What we are interested in is monotone missing data, and we use discriminant function imputation method and logistic regression imputation method to impute missing values. According to the imputed data, we get the estimation of parameter (latent class proportions and latent class conditional probability) by using latent class regression analysis, and observe the difference between the estimation of parameter and the theorical values of parameter.
We simulate data in latent class regression model, and control the data that has four observed variables:y1,y2,y3,y4 ,one covariates and two latent classes. The exploring factors are latent class proportions, latent class conditional probability, sample size, missing proportions of y3,y4, and imputation methods. We want to discuss the influence of the accuracy of parameter estimation under different combination of exploring factors.
The result showed that when increasing sample size, decreasing the missing proportions of y4 , and the latent class proportion is 0.5:0.5, the estimation of parameter is more accurate. The influence of the missing proportions of y3 is not significant, and latent class conditional probability and imputation methods do not have consistent effect on parameter estimation.

目錄
第一章 緒論
第一節 研究背景與動機
第二節 研究目的
第三節 研究的範圍和重要性
第二章 文獻回顧
第一節 潛在類別分析(Latent Class Analysis)
第二節 潛在類別迴歸模型(Latent Class Regression Model)
第三節 缺失值的結構(Missing Mechanism)
第四節 多重插補方法(Multiple imputation)
第五節 潛在類別迴歸分析處理缺失值的探討
第三章 研究方法
第一節 研究設計
第二節 分析計畫
第四章 研究結果
第一節 實驗組合
第二節 影響因子對參數估計精準度之討論
第五章 結論與建議
第一節 研究結論
第二節 研究建議與方向
文獻參考

Agresti, A. (1984). Analysis of Categorical Data. New York: Wiley.

Allison, P.D. (2005). Imputation of Categorical Variables with PROC MI. Philadelphia, PA, University of Pennsylvania.

Bandeen-Roche, K., Miglioretti, D.L., Zeger, S.Z., & Rathouz P.J. (1997). Latent Variable Regression for Multiple Discrete Outcomes. Journal of the American Statistical Association, Volume 92, 440, 1375-1386.

Brand, J.P.C. (1999). Development, Implementation and Evaluation of Multiple Imputation Strategies for the Statistical Analysis of Incomplete Data Sets. Thesis, University of Erasmas, Rotterdam/TNO, Prevention and Health, Leiden.

Clogg, C.C. (1995). Latent Class Models. New York: Plenum Press, 311-360.

Dayton, C.M. (1999). Latent Class Scaling Analysis, Sage Publications.

Dayton, C.M., & Macready, G.B. (1988) Concomitant-variable latent class models.
Journal of the American Statistical Association, 83, 173-178.

Goodman, L.A. (1974). Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models. Biometrika, 61, 215-231.

Harel, O., & Miglioretti. D. (2005). Missing information as a diagnostic tool for Latent Class Analysis. University of Connecticut.

Lazarsfeld, P.F., & Henry, N.W. (1968). Latent Structure Analysis. New York: Houghton-Mifflin.

Little, R.J.A. (1988). A Test of Missing Completely at Random for Multivariate Data with Missing Values. Journal of the American Statistical Association, Volume 83, 404, 1198-1202.

Magidson, J., & Vermunt, J.K. (2003). Latent Class Models. University of Tilburg, mimeo.


Magidson, J., & Vermunt, J.K. (2004). Latent Class Models. Newbury Park, CA: Sage Publications.

McCutcheon, A.L. (1987). Latent Class Analysis. Newbury Park, CA: Sage Publications.

McCullagh, P., & Nelder, J.A. (1989). Generalized Lineal Models. London: Chapman & Hall.

Rubin, D.B. (1976). Inference and Missing Data. Biometrika, 63, 581-592.

Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. New York: J.Wiley & Sons.

Schafel, J.L. (1997). Analysis of Incomplete Multivariate Data. London: Chapman & Hall.

Schafer, J.L., & Graham J.W. (2002). Missing Data：Our View of the State of the Art. American Psychological Association, Volume 7, 2, 147-177.

Schafer, J.L., & Olsen, M.K. (1998). Multiple Imputation for multivariate missing-data problems：a data analyst's perspective. University of Pennsylvania.

Sinharay, S., Stern, H.S., & Russell, D. (2001). The Use of Multiple Imputation for the Analysis of Missing Data. American Psychological Association, Volume 6, 4, 317-329.

Yang C. Yuan. (2002). Multiple Imputation for Missing Data：Concepts and New Development. SAS Institute Inc. Rockeville, MD.