مقایسهٔ روش‌ها

	مدل اثرات تصادفی پنل	مدل‌سازی خطی سلسله‌مراتبی (HLM / مدل‌سازی چندسطحی)	مدل اثرات ثابت داده‌های پانل
حوزه	اقتصادسنجی	آمار	اقتصادسنجی
خانواده	Regression model	Hypothesis test	Regression model
سال پیدایش	1978	1986	2014
پدیدآور	Baltagi (textbook treatment); Hausman specification test	Raudenbush & Bryk (popularized); Goldstein (parallel development)	Hsiao (textbook treatment); within transformation of panel data
نوع	Panel data regression	Parametric nested-data regression	Panel data regression
منبع بنیادین	Hausman, J. A. (1978). Specification Tests in Econometrics. Econometrica, 46(6), 1251-1271.	Raudenbush, S.W. & Bryk, A.S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage. ISBN: 978-0761919049	Hsiao, C. (2014). Analysis of Panel Data (3rd ed.). Cambridge University Press.
نام‌های دیگر	random effects panel regression, RE estimator, GLS panel estimator, Panel Rassal Etkiler Modeli	HLM, MLM, multilevel modeling, multilevel analysis	fixed effects model, within estimator, panel fixed-effects regression, Panel Veri — Sabit Etkiler Modeli
مرتبط	5	4	5
خلاصه	The random effects model is a panel data estimator that explains an outcome using both within-unit and between-unit variation, treating the unobserved unit-specific heterogeneity as a random, normally distributed term rather than a fixed parameter. Its validity is judged with the Hausman (1978) specification test, and it is developed in standard treatments such as Baltagi's Econometric Analysis of Panel Data.	Hierarchical Linear Modeling (HLM), also known as Multilevel Modeling (MLM), is a parametric statistical method for analyzing nested or clustered data — for example students within classrooms, patients within hospitals, or employees within organizations. Formalized by Raudenbush and Bryk in their 2002 seminal text (building on work from the mid-1980s), HLM simultaneously estimates individual-level and group-level effects while correctly partitioning variance across levels.	The Panel Data Fixed Effects model estimates relationships from panel data (the same units observed over several time periods) while controlling for unit- and/or time-specific effects, supporting causal inference. It is developed as the within estimator in standard treatments such as Hsiao's Analysis of Panel Data (2014).