قارن الطرق

	النموذج الخطي الهرمي المتين	النمذجة متعددة المستويات
المجال	الإحصاء	إحصاء البحث
العائلة	Regression model	Process / pipeline
سنة النشأة	2004	1992
صاحب الطريقة	Maas & Hox (2004); Goldstein et al. (2018)	Anthony Bryk and Stephen Raudenbush
النوع	Robust multilevel regression	Method
المصدر التأسيسي	Maas, C. J. M., & Hox, J. J. (2004). Robustness issues in multilevel regression analysis. Statistica Neerlandica, 58(2), 127–137.	Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE Publications.
الأسماء البديلة	robust HLM, robust multilevel model, robust mixed-effects linear model, robust nested regression	HLM, mixed-effects models, random effects models, MLM
ذات صلة	5	3
الملخص	Robust Hierarchical Linear Model (Robust HLM) extends standard HLM by replacing or protecting its standard errors against violations of distributional assumptions — chiefly non-normal residuals, heteroscedasticity, and influential clusters. It retains the nested, two-level (or higher) structure while producing more trustworthy inference under real-world data conditions.	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.