قارن الطرق

	نموذج الانحدار الخطي الهرمي البيزي	نموذج التأثيرات المختلطة البايزي
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	2006	1990s–2000s (modern Bayesian MCMC era)
صاحب الطريقة	Gelman & Hill (2006); Raudenbush & Bryk (2002) for frequentist HLM; Bayesian treatment consolidated by Gelman et al.	Gelman, Hill, and the broader Bayesian hierarchical modeling tradition
النوع	Bayesian multilevel linear model	Bayesian regression model
المصدر التأسيسي	Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891
الأسماء البديلة	Bayesian HLM, Bayesian multilevel linear model, Bayesian random-effects linear model, Bayes hierarchical regression	Bayesian multilevel model, Bayesian random effects model, Bayesian LME, Bayesian hierarchical mixed model
ذات صلة	5	5
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 Bayesian mixed effects model extends the classical mixed effects framework by placing prior distributions on all parameters — fixed effects, random effect variances, and residual variance — and updating them with data to produce full posterior distributions. This provides coherent uncertainty quantification for both population-level and group-level effects simultaneously.