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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.
IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers in an otherwise normally-distributed data set, for example, by minimizing the least absolute errors rather than the least square errors.
For example, if each observation can belong to any zero or more of k categories then Z, which has one row per observation, can be chosen to have k columns, where a value of 1 for a matrix element of Z indicates that an observation is known to belong to a category and a value of 0 indicates that an observation is known to not belong to a category.
Example: On a 1-5 scale where 1 means disagree completely and 5 means agree completely, how much do you agree with the following statement. "The Federal government should do more to help people facing foreclosure on their homes." A multinomial discrete-choice model can examine the responses to these questions (model G, model H, model I ...
Specifically, in multinomial logistic regression and linear discriminant analysis, the input to the function is the result of K distinct linear functions, and the predicted probability for the j th class given a sample vector x and a weighting vector w is:
Mixed logit is a fully general statistical model for examining discrete choices.It overcomes three important limitations of the standard logit model by allowing for random taste variation across choosers, unrestricted substitution patterns across choices, and correlation in unobserved factors over time. [1]
In statistics, multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. [1] It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables.
However, it would also predict, for example, that a white person might have an average income $7,000 above a black person, and a 65-year-old might have an income $3,000 below a 45-year-old, in both cases regardless of location. A multilevel model, however, would allow for different regression coefficients for each predictor in each location.