قارن الطرق

	النموذج الخطي الهرمي (HLM)	نموذج التأثيرات المختلطة
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	1992	1982
صاحب الطريقة	Bryk & Raudenbush	Laird & Ware
النوع	Multilevel linear regression	Mixed effects regression
المصدر التأسيسي	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.
الأسماء البديلة	HLM, multilevel linear model, nested data model, random coefficient model	LME, LMM, mixed model, random effects model
ذات صلة	4	4
الملخص	The Hierarchical Linear Model (HLM) is a multilevel regression method designed for data in which lower-level units (e.g., students, patients) are nested within higher-level groups (e.g., schools, hospitals). It simultaneously models within-group relationships and between-group variation, producing unbiased estimates and correct standard errors that ordinary regression cannot provide for nested data.	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.