قارن الطرق

	النموذج الخطي الهرمي المتين	النموذج الخطي الهرمي (HLM)
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	2004	1992
صاحب الطريقة	Maas & Hox (2004); Goldstein et al. (2018)	Bryk & Raudenbush
النوع	Robust multilevel regression	Multilevel linear regression
المصدر التأسيسي	Maas, C. J. M., & Hox, J. J. (2004). Robustness issues in multilevel regression analysis. Statistica Neerlandica, 58(2), 127–137.	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049
الأسماء البديلة	robust HLM, robust multilevel model, robust mixed-effects linear model, robust nested regression	HLM, multilevel linear model, nested data model, random coefficient 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.	The Hierarchical Linear Model (HLM) is a multilevel regression method designed for data in which lower-level units (e.g., students, patients) are nested within higher-level groups (e.g., schools, hospitals). It simultaneously models within-group relationships and between-group variation, producing unbiased estimates and correct standard errors that ordinary regression cannot provide for nested data.