قارن الطرق

	نموذج التأثيرات المختلطة	نموذج التأثيرات المختلطة البايزي
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	1982	1990s–2000s (modern Bayesian MCMC era)
صاحب الطريقة	Laird & Ware	Gelman, Hill, and the broader Bayesian hierarchical modeling tradition
النوع	Mixed effects regression	Bayesian regression model
المصدر التأسيسي	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.	Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891
الأسماء البديلة	LME, LMM, mixed model, random effects model	Bayesian multilevel model, Bayesian random effects model, Bayesian LME, Bayesian hierarchical mixed model
ذات صلة	4	5
الملخص	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.	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.