قارن الطرق

	النموذج الخطي الهرمي المتين	نموذج التأثيرات المختلطة
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	2004	1982
صاحب الطريقة	Maas & Hox (2004); Goldstein et al. (2018)	Laird & Ware
النوع	Robust multilevel regression	Mixed effects regression
المصدر التأسيسي	Maas, C. J. M., & Hox, J. J. (2004). Robustness issues in multilevel regression analysis. Statistica Neerlandica, 58(2), 127–137.	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.
الأسماء البديلة	robust HLM, robust multilevel model, robust mixed-effects linear model, robust nested regression	LME, LMM, mixed model, random effects model
ذات صلة	5	4
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.	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.