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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]
In statistics, the logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent variables. In regression analysis , logistic regression [ 1 ] (or logit regression ) estimates the parameters of a logistic model (the coefficients in the linear or non linear ...
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 ...
If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the odds, i.e.: = = = = (). The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used.
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.
The exploded logit model is the product of standard logit models with the choice set decreasing as each alternative is ranked and leaves the set of available choices in the subsequent choice. Without loss of generality, the alternatives can be relabeled to represent the person's ranking, such that alternative 1 is the first choice, 2 the second ...
As such, it is an alternative to the multinomial logit model as one method of multiclass classification. It is not to be confused with the multivariate probit model , which is used to model correlated binary outcomes for more than one independent variable.
Ordered logit and ordered probit regression for ordinal data. Single index models [clarification needed] allow some degree of nonlinearity in the relationship between x and y, while preserving the central role of the linear predictor β′x as in the classical linear regression model.