قارن الطرق

	نموذج التأثيرات المختلطة البايزي	نموذج التأثيرات المختلطة
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	1990s–2000s (modern Bayesian MCMC era)	1982
صاحب الطريقة	Gelman, Hill, and the broader Bayesian hierarchical modeling tradition	Laird & Ware
النوع	Bayesian regression model	Mixed effects regression
المصدر التأسيسي	Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.
الأسماء البديلة	Bayesian multilevel model, Bayesian random effects model, Bayesian LME, Bayesian hierarchical mixed model	LME, LMM, mixed model, random effects 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.	A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variability. It is the standard tool for repeated-measures, longitudinal, and multilevel data where observations within the same unit are correlated.