قارن الطرق

	آليات البيانات المفقودة: MCAR، MAR، و MNAR	خوارزمية التوقع-تعظيم (EM)	MICE
المجال	الإحصاء	الإحصاء	الإحصاء
العائلة	Process / pipeline	Machine learning	Process / pipeline
سنة النشأة	1976	1977	2011
صاحب الطريقة	Donald Rubin	Dempster, Laird & Rubin	Stef van Buuren & Karin Groothuis-Oudshoorn
النوع	Diagnostic / classification framework	Iterative optimization algorithm	Iterative multiple imputation algorithm
المصدر التأسيسي	Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3), 581–592.	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.
الأسماء البديلة	Missing Data Typology, Rubin's Missing Data Framework, Missingness Mechanisms, Kayıp Veri Mekanizmaları	EM, Expectation-Maximization, Maximum Likelihood via Incomplete Data, BM Algoritması	Fully Conditional Specification, Sequential Regression Multivariate Imputation, Chained Equations Imputation, Zincirleme Denklemlerle Çoklu Atama
ذات صلة	3	2	3
الملخص	Missing data mechanisms, introduced by Donald Rubin in 1976, provide a formal taxonomy for classifying why observations are absent from a dataset. The three categories — Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR) — describe the relationship between the probability of missingness and the observed or unobserved values. Identifying the correct mechanism is essential because it determines which analytical strategies preserve valid and unbiased inference.	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.