قارن الطرق

	النموذج الخطي الهرمي (HLM)	النمذجة متعددة المستويات
المجال	الإحصاء	إحصاء البحث
العائلة	Regression model	Process / pipeline
سنة النشأة	1992	1992
صاحب الطريقة	Bryk & Raudenbush	Anthony Bryk and Stephen Raudenbush
النوع	Multilevel linear regression	Method
المصدر التأسيسي	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049	Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE Publications.
الأسماء البديلة	HLM, multilevel linear model, nested data model, random coefficient model	HLM, mixed-effects models, random effects models, MLM
ذات صلة	4	3
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.	Multilevel modeling (also called hierarchical linear modeling, mixed-effects modeling) is a statistical framework for analyzing data organized in nested or clustered structures—students within schools, patients within hospitals, repeated measures within individuals. Developed by Bryk and Raudenbush (1992), it accounts for dependency among observations and partitions variance into levels (within-cluster and between-cluster), enabling valid inference and revealing context effects. Essential in education, medicine, organizational research, and any field where data have natural hierarchies.