方法对比
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| Plackett-Luce 模型× | Bradley-Terry 模型× | 多项逻辑回归× | |
|---|---|---|---|
| 领域≠ | 决策 | 决策 | 计量经济学 |
| 方法族 | Regression model | Regression model | Regression model |
| 起源年份≠ | 1975 | 1952 | 1974 |
| 提出者≠ | Robin Plackett; R. Duncan Luce | Ralph Bradley & Milton Terry | McFadden |
| 类型≠ | Probabilistic ranking model | Probabilistic paired comparison model | Multinomial logistic regression |
| 开创性文献≠ | Plackett, R. L. (1975). The analysis of permutations. Journal of the Royal Statistical Society: Series C, 24(2), 193–202. DOI ↗ | Bradley, R. A., & Terry, M. E. (1952). Rank analysis of incomplete block designs: I. The method of paired comparisons. Biometrika, 39(3/4), 324–345. DOI ↗ | McFadden, D. (1974). Conditional Logit Analysis of Qualitative Choice Behavior. In P. Zarembka (Ed.), Frontiers in Econometrics (pp. 105-142). Academic Press. ISBN: 978-0127761503 |
| 别名 | Luce's Choice Axiom Model, Rank-Ordered Logit Model, Exploded Logit Model, Sıralama Tercih Modeli | BT Model, Bradley-Terry-Luce Model, Paired Comparison Model, İkili Karşılaştırma Modeli | multinomial logistic regression, polytomous logistic regression, softmax regression, Çok Kategorili Lojistik Regresyon |
| 相关≠ | 3 | 3 | 5 |
| 摘要≠ | The Plackett-Luce model is a probabilistic framework for analysing and predicting rank-ordered data. Introduced by Robin Plackett (1975) — building on R. Duncan Luce's earlier axiom of choice (1959) — it models the probability of any complete ranking of items as a sequential selection process, where each item's chance of being chosen at each position is proportional to its latent worth parameter. It is widely used in preference learning, recommender systems, and choice modelling. | The Bradley-Terry model is a probabilistic model for paired comparisons that assigns a latent strength parameter to each item and predicts the probability that one item beats another in a head-to-head contest. Introduced by Ralph A. Bradley and Milton E. Terry in 1952, it provides a principled statistical framework for ranking items from pairwise preference data, including incomplete comparison designs where not every pair is directly observed. | Multinomial logistic regression is a maximum-likelihood method for a nominal (unordered) dependent variable with more than two categories. Building on McFadden's 1974 treatment of qualitative choice, it gives each category its own set of coefficients relative to a reference category. |
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