قارن الطرق

	النمذجة الخطية الهرمية (HLM / نمذجة المستويات المتعددة)	نموذج التأثيرات المختلطة	تحليل التباين أحادي الاتجاه	نمذجة المعادلات البنيوية (SEM)
المجال	الإحصاء	الإحصاء	الإحصاء	الإحصاء
العائلة	Hypothesis test	Regression model	Hypothesis test	Latent structure
سنة النشأة	1986	1982	1925	1970
صاحب الطريقة	Raudenbush & Bryk (popularized); Goldstein (parallel development)	Laird & Ware	Ronald A. Fisher	Karl Jöreskog (LISREL framework, 1970s)
النوع	Parametric nested-data regression	Mixed effects regression	Parametric mean comparison	Latent variable / causal modeling
المصدر التأسيسي	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.	Fisher, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.	Hair, J. F., Black, W. C., Babin, B. J. & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage Learning. ISBN: 978-1473756540
الأسماء البديلة	HLM, MLM, multilevel modeling, multilevel analysis	LME, LMM, mixed model, random effects model	one-factor ANOVA, single-factor ANOVA, analysis of variance, tek yönlü ANOVA	Yapısal Eşitlik Modellemesi (SEM), structural equation modelling, covariance structure analysis, latent variable modeling
ذات صلة	4	4	4	5
الملخص	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.	One-way ANOVA is a parametric hypothesis test that compares the means of three or more independent groups on a single continuous outcome to decide whether at least one group mean differs. It rests on the variance-partitioning framework introduced by Ronald A. Fisher in 1925.	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.