方法对比
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| 稳健分层线性模型× | 稳健多元线性回归× | |
|---|---|---|
| 领域 | 统计学 | 统计学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 2004 | 1964–1980s |
| 提出者≠ | Maas & Hox (2004); Goldstein et al. (2018) | Peter J. Huber (M-estimators, 1964); extended by Rousseeuw, Yohai, and Maronna |
| 类型≠ | Robust multilevel regression | Robust linear regression |
| 开创性文献≠ | Maas, C. J. M., & Hox, J. J. (2004). Robustness issues in multilevel regression analysis. Statistica Neerlandica, 58(2), 127–137. DOI ↗ | Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35(1), 73–101. DOI ↗ |
| 别名 | robust HLM, robust multilevel model, robust mixed-effects linear model, robust nested regression | robust MLR, M-estimator regression, resistant multiple regression, robust OLS |
| 相关≠ | 5 | 6 |
| 摘要≠ | 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. |
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