手法を比較

	ベイズ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 (classical); Bayesian extensions established by 1990s	1980
提唱者	Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966)	Peter McCullagh
種類	Bayesian classification model	Ordinal regression / GLM
原典	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	McCullagh, P. (1980). Regression models for ordinal data. Journal of the Royal Statistical Society: Series B (Methodological), 42(2), 109–142.
別名	Bayesian polytomous logistic regression, Bayesian multinomial logit, Bayesian softmax regression, Bayesian nominal logistic regression	proportional-odds model, cumulative link model, ordered logit, OLR
関連	5	6
概要	Bayesian Multinomial Logistic Regression models a nominal outcome with three or more unordered categories by placing prior distributions over the regression coefficients and updating them with data via Bayes' theorem. The result is a full posterior distribution over category probabilities for each observation, enabling principled uncertainty quantification and regularization through the prior.	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.