手法を比較

	EMアルゴリズム	MICE	Multiple Imputation
分野	統計学	統計学	統計学
系統	Machine learning	Process / pipeline	Process / pipeline
提唱年	1977	2011	1987
提唱者	Dempster, Laird & Rubin	Stef van Buuren & Karin Groothuis-Oudshoorn	Donald B. Rubin
種類	Iterative optimization algorithm	Iterative multiple imputation algorithm	Missing-data handling procedure
原典	Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B, 39(1), 1–38.	van Buuren, S., & Groothuis-Oudshoorn, K. (2011). mice: Multivariate imputation by chained equations in R. Journal of Statistical Software, 45(3), 1–67.	Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. Wiley.
別名	EM, Expectation-Maximization, Maximum Likelihood via Incomplete Data, BM Algoritması	Fully Conditional Specification, Sequential Regression Multivariate Imputation, Chained Equations Imputation, Zincirleme Denklemlerle Çoklu Atama	MICE, Multivariate Imputation by Chained Equations, Çoklu Atama (Multiple Imputation — MICE)
関連	2	3	1
概要	The Expectation-Maximization (EM) algorithm is an iterative optimization procedure for finding maximum likelihood or maximum a posteriori estimates of parameters in statistical models with latent variables or missing data. Introduced by Dempster, Laird, and Rubin in their landmark 1977 paper, EM alternates between computing the expected complete-data log-likelihood (E-step) and maximizing it with respect to the parameters (M-step), guaranteeing monotone non-decreasing likelihood at each iteration.	Multivariate Imputation by Chained Equations (MICE) is an iterative procedure for handling missing data in multivariate datasets. Introduced by Stef van Buuren and Karin Groothuis-Oudshoorn through the R package mice (2011), the algorithm fills each missing variable using a separate regression model conditioned on all other variables, cycling through variables repeatedly until the imputed values converge. The result is m completed datasets that are analysed separately and combined using Rubin's rules.	Multiple Imputation (MI), formally introduced by Donald B. Rubin in 1987, is a principled statistical procedure for handling missing data. Rather than replacing each missing value once, MI fills the gaps m times — each time drawing plausible values from the posterior predictive distribution of the missing data — producing m complete datasets. Each dataset is analysed independently, and the results are combined into a single set of estimates using Rubin's pooling rules. The MICE variant (Multivariate Imputation by Chained Equations), popularised by van Buuren and Groothuis-Oudshoorn (2011), extends the approach to mixed variable types by imputing each variable in turn through a sequence of conditional regression models.