قارن الطرق

	النموذج الهرمي البيزي	النموذج الخطي الهرمي (HLM)
المجال	بايزي	الإحصاء
العائلة	Bayesian methods	Regression model
سنة النشأة	2006	1992
صاحب الطريقة	Gelman & Hill (2006); Bayesian multilevel tradition	Bryk & Raudenbush
النوع	hierarchical probabilistic model	Multilevel linear regression
المصدر التأسيسي	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049
الأسماء البديلة	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	HLM, multilevel linear model, nested data model, random coefficient 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.	The Hierarchical Linear Model (HLM) is a multilevel regression method designed for data in which lower-level units (e.g., students, patients) are nested within higher-level groups (e.g., schools, hospitals). It simultaneously models within-group relationships and between-group variation, producing unbiased estimates and correct standard errors that ordinary regression cannot provide for nested data.