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| ロバスト多項ロジスティック回帰× | 多項ロジスティック回帰× | |
|---|---|---|
| 分野 | 統計学 | 統計学 |
| 系統 | Regression model | Regression model |
| 提唱年≠ | 2001 (robust GLM); 1970s–1980s (multinomial logistic regression) | 1966–1974 |
| 提唱者≠ | Cantoni & Ronchetti (robust GLM framework); Agresti (multinomial logistic regression) | Cox (1966); Theil (1969); formalized by McFadden (1974) |
| 種類≠ | Robust classification model | Generalized linear model |
| 原典≠ | Cantoni, E., & Ronchetti, E. (2001). Robust inference for generalized linear models. Journal of the American Statistical Association, 96(455), 1022–1030. DOI ↗ | Agresti, A. (2002). Categorical Data Analysis (2nd ed.). Wiley-Interscience. ISBN: 978-0471360933 |
| 別名 | robust polychotomous logistic regression, outlier-resistant multinomial regression, robust nominal logistic regression, M-estimation multinomial logistic regression | polytomous logistic regression, softmax regression, multinomial logit, nominal logistic regression |
| 関連≠ | 5 | 4 |
| 概要≠ | Robust multinomial logistic regression extends the standard multinomial logit model to handle outliers, influential observations, and mild misspecification of the response distribution. It replaces the conventional maximum likelihood score equations with bounded influence functions (M-estimation) or pairs maximum likelihood with sandwich variance estimators, so that a small fraction of anomalous cases cannot distort the estimated log-odds ratios across outcome categories. | Multinomial logistic regression extends binary logistic regression to outcomes with three or more unordered categories. It models the log-odds of each category relative to a chosen reference category as a linear function of the predictors, and estimates all parameters simultaneously via maximum likelihood. It is the standard choice when the dependent variable is nominal with multiple levels. |
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