قارن الطرق

	النموذج الهرمي البيزي	نموذج التأثيرات المختلطة
المجال	بايزي	الإحصاء
العائلة	Bayesian methods	Regression model
سنة النشأة	2006	1982
صاحب الطريقة	Gelman & Hill (2006); Bayesian multilevel tradition	Laird & Ware
النوع	hierarchical probabilistic model	Mixed effects regression
المصدر التأسيسي	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.
الأسماء البديلة	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	LME, LMM, mixed model, random effects model
ذات صلة	4	4
الملخص	Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations.	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.