مقایسهٔ روش‌ها

	مدل اثرات تصادفی بیزی	مدل خطی سلسله مراتبی (HLM)
حوزه	اقتصادسنجی	آمار
خانواده	Regression model	Regression model
سال پیدایش	1972–1995	1992
پدیدآور	Lindley & Smith (1972); extended by Gelman, Rubin and colleagues	Bryk & Raudenbush
نوع	Bayesian hierarchical panel model	Multilevel linear regression
منبع بنیادین	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049
نام‌های دیگر	Bayesian hierarchical model, Bayesian mixed effects model, Bayesian multilevel model, BREM	HLM, multilevel linear model, nested data model, random coefficient model
مرتبط	5	4
خلاصه	The Bayesian random effects model combines panel-data random effects with a Bayesian prior framework, allowing unit-specific effects to be treated as draws from a population distribution whose hyperparameters are estimated from the data. This produces regularised, uncertainty-quantified estimates that borrow strength across units — particularly valuable for short panels, sparse groups, or settings where frequentist variance-component estimation is unstable.	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.