قارن الطرق

	النموذج الخطي الهرمي المتين	الانحدار القوي
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	2004	1964
صاحب الطريقة	Maas & Hox (2004); Goldstein et al. (2018)	Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974)
النوع	Robust multilevel regression	Regression with outlier resistance
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. The Annals of Mathematical Statistics, 35(1), 73–101.
الأسماء البديلة	robust HLM, robust multilevel model, robust mixed-effects linear model, robust nested regression	M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation
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 regression estimates the linear relationship between a continuous outcome and predictors while sharply reducing the influence of outliers and leverage points. Unlike OLS, which is highly sensitive to extreme observations, robust methods assign down-weighted influence to atypical data points, producing coefficient estimates that remain stable even when a fraction of the data is contaminated or non-normally distributed.