مقایسهٔ روش‌ها

	آزمون مشخصه هاوسمن (اثرات ثابت در مقابل اثرات تصادفی)	مدل‌سازی خطی سلسله‌مراتبی (HLM / مدل‌سازی چندسطحی)	رگرسیون حداقل مربعات معمولی (OLS)	مدل اثرات ثابت داده‌های پانل
حوزه	اقتصادسنجی	آمار	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Hypothesis test	Regression model	Regression model
سال پیدایش	1978	1986	2019	2014
پدیدآور	Jerry A. Hausman	Raudenbush & Bryk (popularized); Goldstein (parallel development)	Wooldridge (textbook treatment); classical least squares	Hsiao (textbook treatment); within transformation of panel data
نوع	Specification test for panel data models	Parametric nested-data regression	Linear 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	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.
نام‌های دیگر	Hausman specification test, FE vs RE test, Durbin-Wu-Hausman test, Hausman Spesifikasyon Testi (FE vs RE)	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
مرتبط	5	4	5	5
خلاصه	The Hausman test is a specification test, introduced by Jerry A. Hausman in 1978, that decides between the fixed-effects (FE) and random-effects (RE) estimators in panel data models. The null hypothesis is that the random-effects estimator is consistent and efficient and should be preferred; the alternative is that random effects is inconsistent and fixed effects is required because the unit-specific effects are correlated with the explanatory variables.	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).