قارن الطرق

	نموذج التأثيرات المختلطة	النمذجة متعددة المستويات
المجال	الإحصاء	إحصاء البحث
العائلة	Regression model	Process / pipeline
سنة النشأة	1982	1992
صاحب الطريقة	Laird & Ware	Anthony Bryk and Stephen Raudenbush
النوع	Mixed effects regression	Method
المصدر التأسيسي	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.	Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE Publications.
الأسماء البديلة	LME, LMM, mixed model, random effects model	HLM, mixed-effects models, random effects models, MLM
ذات صلة	4	3
الملخص	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.	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.