قارن الطرق

	نموذج التأثيرات المختلطة البايزي	النمذجة متعددة المستويات
المجال	الإحصاء	إحصاء البحث
العائلة	Regression model	Process / pipeline
سنة النشأة	1990s–2000s (modern Bayesian MCMC era)	1992
صاحب الطريقة	Gelman, Hill, and the broader Bayesian hierarchical modeling tradition	Anthony Bryk and Stephen Raudenbush
النوع	Bayesian regression model	Method
المصدر التأسيسي	Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE Publications.
الأسماء البديلة	Bayesian multilevel model, Bayesian random effects model, Bayesian LME, Bayesian hierarchical mixed model	HLM, mixed-effects models, random effects models, MLM
ذات صلة	5	3
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.	Multilevel modeling (also called hierarchical linear modeling, mixed-effects modeling) is a statistical framework for analyzing data organized in nested or clustered structures—students within schools, patients within hospitals, repeated measures within individuals. Developed by Bryk and Raudenbush (1992), it accounts for dependency among observations and partitions variance into levels (within-cluster and between-cluster), enabling valid inference and revealing context effects. Essential in education, medicine, organizational research, and any field where data have natural hierarchies.