مقایسهٔ روش‌ها

	مدل‌سازی خطی سلسله‌مراتبی (HLM / مدل‌سازی چندسطحی)	مدل اثرات مختلط (یا مدل خطی مختلط) رگرسیون معمولی را با گنجاندن هر دو اثرات ثابت	مدل‌سازی معادلات ساختاری (SEM)
حوزه	آمار	آمار	آمار
خانواده	Hypothesis test	Regression model	Latent structure
سال پیدایش	1986	1982	1970
پدیدآور	Raudenbush & Bryk (popularized); Goldstein (parallel development)	Laird & Ware	Karl Jöreskog (LISREL framework, 1970s)
نوع	Parametric nested-data regression	Mixed effects regression	Latent variable / causal modeling
منبع بنیادین	Raudenbush, S.W. & Bryk, A.S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage. ISBN: 978-0761919049	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.	Hair, J. F., Black, W. C., Babin, B. J. & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage Learning. ISBN: 978-1473756540
نام‌های دیگر	HLM, MLM, multilevel modeling, multilevel analysis	LME, LMM, mixed model, random effects model	Yapısal Eşitlik Modellemesi (SEM), structural equation modelling, covariance structure analysis, latent variable modeling
مرتبط	4	4	5
خلاصه	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.	A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variability. It is the standard tool for repeated-measures, longitudinal, and multilevel data where observations within the same unit are correlated.	Structural equation modeling is a multivariate statistical framework that simultaneously estimates a measurement model — relating observed indicators to latent constructs — and a structural model specifying directional or reciprocal relationships among those constructs. Rooted in the LISREL tradition developed by Karl Jöreskog in the 1970s, SEM is the standard tool for testing complex theoretical models in the social, behavioural, and management sciences.