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Multinomial logistic regression is known by a variety of other names, including polytomous LR, [2] [3] multiclass LR, softmax regression, multinomial logit (mlogit), the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model. [4]
Generalized Extreme Value Model [21] - General class of model, derived from the random utility model [17] to which multinomial logit and nested logit belong; Conditional probit [22] [23] - Allows full covariance among alternatives using a joint normal distribution. Mixed logit [13] [14] [23] - Allows any form of correlation and substitution ...
In statistics, the ordered logit model or proportional odds logistic regression is an ordinal regression model—that is, a regression model for ordinal dependent variables—first considered by Peter McCullagh. [1]
When k = 2, the multinomial distribution is the binomial distribution. Categorical distribution, the distribution of each trial; for k = 2, this is the Bernoulli distribution. The Dirichlet distribution is the conjugate prior of the multinomial in Bayesian statistics. Dirichlet-multinomial distribution. Beta-binomial distribution.
As the logistic distribution, which can be solved analytically, is similar to the normal distribution, it can be used instead. The blue picture illustrates an example of fitting the logistic distribution to ranked October rainfalls—that are almost normally distributed—and it shows the 90% confidence belt based on the binomial distribution.
The Ewens's sampling formula is a probability distribution on the set of all partitions of an integer n, arising in population genetics. The Balding–Nichols model; The multinomial distribution, a generalization of the binomial distribution. The multivariate normal distribution, a generalization of the normal distribution.
Logistic regression is used in various fields, including machine learning, most medical fields, and social sciences. For example, the Trauma and Injury Severity Score (), which is widely used to predict mortality in injured patients, was originally developed by Boyd et al. using logistic regression. [6]
Another approach is given by Rennie and Srebro, who, realizing that "even just evaluating the likelihood of a predictor is not straight-forward" in the ordered logit and ordered probit models, propose fitting ordinal regression models by adapting common loss functions from classification (such as the hinge loss and log loss) to the ordinal case ...