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| 多項ロジスティック回帰× | 順序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≠ | 1966–1974 | 1980 |
| 提唱者≠ | Cox (1966); Theil (1969); formalized by McFadden (1974) | Peter McCullagh |
| 種類≠ | Generalized linear model | Ordinal regression / GLM |
| 原典≠ | Agresti, A. (2002). Categorical Data Analysis (2nd ed.). Wiley-Interscience. ISBN: 978-0471360933 | McCullagh, P. (1980). Regression models for ordinal data. Journal of the Royal Statistical Society: Series B (Methodological), 42(2), 109–142. DOI ↗ |
| 別名 | polytomous logistic regression, softmax regression, multinomial logit, nominal logistic regression | proportional-odds model, cumulative link model, ordered logit, OLR |
| 関連≠ | 4 | 6 |
| 概要≠ | 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. | Ordinal logistic regression — most commonly the proportional-odds model — estimates the relationship between one or more predictors and an ordered categorical outcome (e.g., Likert scales, disease severity grades, educational attainment levels). It models cumulative log-odds across the ordered categories while assuming a single shared effect of each predictor at all thresholds. |
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