قارن الطرق

	النموذج الخطي الهرمي المتين	الانحدار الخطي المتعدد المتين
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	2004	1964–1980s
صاحب الطريقة	Maas & Hox (2004); Goldstein et al. (2018)	Peter J. Huber (M-estimators, 1964); extended by Rousseeuw, Yohai, and Maronna
النوع	Robust multilevel regression	Robust linear regression
المصدر التأسيسي	Maas, C. J. M., & Hox, J. J. (2004). Robustness issues in multilevel regression analysis. Statistica Neerlandica, 58(2), 127–137.	Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35(1), 73–101.
الأسماء البديلة	robust HLM, robust multilevel model, robust mixed-effects linear model, robust nested regression	robust MLR, M-estimator regression, resistant multiple regression, robust OLS
ذات صلة	5	6
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.	Robust multiple linear regression estimates the linear relationship between a continuous outcome and several predictors while being resistant to outliers and violations of the normality assumption. Instead of minimising the sum of squared residuals, it uses a bounded loss function — most commonly Huber's or Tukey's bisquare — so that extreme observations receive limited influence on the estimated coefficients.