قارن الطرق

	نموذج التأثيرات المختلطة البايزي	النموذج الخطي الهرمي (HLM)
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	1990s–2000s (modern Bayesian MCMC era)	1992
صاحب الطريقة	Gelman, Hill, and the broader Bayesian hierarchical modeling tradition	Bryk & Raudenbush
النوع	Bayesian regression model	Multilevel linear regression
المصدر التأسيسي	Gelman, A., & Hill, J. (2007). 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 multilevel model, Bayesian random effects model, Bayesian LME, Bayesian hierarchical mixed model	HLM, multilevel linear model, nested data model, random coefficient model
ذات صلة	5	4
الملخص	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.	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.