مقایسهٔ روش‌ها

	Bayesian Hierarchical Linear Model	مدل‌سازی چندسطحی
حوزه	آمار	آمار پژوهش
خانواده	Regression model	Process / pipeline
سال پیدایش	2006	1992
پدیدآور	Gelman & Hill (2006); Raudenbush & Bryk (2002) for frequentist HLM; Bayesian treatment consolidated by Gelman et al.	Anthony Bryk and Stephen Raudenbush
نوع	Bayesian multilevel linear model	Method
منبع بنیادین	Gelman, A., & Hill, J. (2006). 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.
نام‌های دیگر	Bayesian HLM, Bayesian multilevel linear model, Bayesian random-effects linear model, Bayes hierarchical regression	HLM, mixed-effects models, random effects models, MLM
مرتبط	5	3
خلاصه	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.	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.