قارن الطرق

	نموذج الانحدار الخطي الهرمي البيزي	نموذج التأثيرات المختلطة
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	2006	1982
صاحب الطريقة	Gelman & Hill (2006); Raudenbush & Bryk (2002) for frequentist HLM; Bayesian treatment consolidated by Gelman et al.	Laird & Ware
النوع	Bayesian multilevel linear model	Mixed effects regression
المصدر التأسيسي	Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.
الأسماء البديلة	Bayesian HLM, Bayesian multilevel linear model, Bayesian random-effects linear model, Bayes hierarchical regression	LME, LMM, mixed model, random effects model
ذات صلة	5	4
الملخص	The Bayesian Hierarchical Linear Model (Bayesian HLM) estimates linear relationships in nested or clustered data by placing prior distributions on all model parameters and updating them with observed data. It simultaneously models variation within groups and between groups, propagating uncertainty fully through posterior distributions rather than relying on asymptotic approximations.	A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variability. It is the standard tool for repeated-measures, longitudinal, and multilevel data where observations within the same unit are correlated.