قارن الطرق

	نموذج التأثيرات العشوائية للبيانات المقطعية	النمذجة الخطية الهرمية (HLM / نمذجة المستويات المتعددة)	انحدار المربعات الصغرى العادية (OLS)	نموذج التأثيرات الثابتة لبيانات السلاسل الزمنية المقطعية
المجال	الاقتصاد القياسي	الإحصاء	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Hypothesis test	Regression model	Regression model
سنة النشأة	1978	1986	2019	2014
صاحب الطريقة	Baltagi (textbook treatment); Hausman specification test	Raudenbush & Bryk (popularized); Goldstein (parallel development)	Wooldridge (textbook treatment); classical least squares	Hsiao (textbook treatment); within transformation of panel data
النوع	Panel data regression	Parametric nested-data regression	Linear regression	Panel data regression
المصدر التأسيسي	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	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Hsiao, C. (2014). Analysis of Panel Data (3rd ed.). Cambridge University Press.
الأسماء البديلة	random effects panel regression, RE estimator, GLS panel estimator, Panel Rassal Etkiler Modeli	HLM, MLM, multilevel modeling, multilevel analysis	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	fixed effects model, within estimator, panel fixed-effects regression, Panel Veri — Sabit Etkiler Modeli
ذات صلة	5	4	5	5
الملخص	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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	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).