قارن الطرق

	نموذج الانحدار الخطي الهرمي البيزي	النموذج الخطي الهرمي (HLM)
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	2006	1992
صاحب الطريقة	Gelman & Hill (2006); Raudenbush & Bryk (2002) for frequentist HLM; Bayesian treatment consolidated by Gelman et al.	Bryk & Raudenbush
النوع	Bayesian multilevel linear model	Multilevel linear regression
المصدر التأسيسي	Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049
الأسماء البديلة	Bayesian HLM, Bayesian multilevel linear model, Bayesian random-effects linear model, Bayes hierarchical regression	HLM, multilevel linear model, nested data model, random coefficient 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.	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.