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In binary logistic regression there is a single binary dependent variable, coded by an indicator variable, where the two values are labeled "0" and "1", while the independent variables can each be a binary variable (two classes, coded by an indicator variable) or a continuous variable (any real value).
The simplest direct probabilistic model is the logit model, which models the log-odds as a linear function of the explanatory variable or variables. The logit model is "simplest" in the sense of generalized linear models (GLIM): the log-odds are the natural parameter for the exponential family of the Bernoulli distribution, and thus it is the simplest to use for computations.
The formulation of binary logistic regression as a log-linear model can be directly extended to multi-way regression. That is, we model the logarithm of the probability of seeing a given output using the linear predictor as well as an additional normalization factor , the logarithm of the partition function :
In practice, Somers' D is most often used when the dependent variable Y is a binary variable, [2] i.e. for binary classification or prediction of binary outcomes including binary choice models in econometrics. Methods for fitting such models include logistic and probit regression.
The resulting model is known as logistic regression (or multinomial logistic regression in the case that K-way rather than binary values are being predicted). For the Bernoulli and binomial distributions, the parameter is a single probability, indicating the likelihood of occurrence of a single event.
Binomial regression is closely connected with binary regression. If the response is a binary variable (two possible outcomes), then these alternatives can be coded as 0 or 1 by considering one of the outcomes as "success" and the other as "failure" and considering these as count data : "success" is 1 success out of 1 trial, while "failure" is 0 ...
Commonly used models in the GLM family include binary logistic regression [5] for binary or dichotomous outcomes, Poisson regression [6] for count outcomes, and linear regression for continuous, normally distributed outcomes. This means that GLM may be spoken of as a general family of statistical models or as specific models for specific ...
[14] [15] Yet, in the context of binary choice models (Logit or Probit), heteroscedasticity will only result in a positive scaling effect on the asymptotic mean of the misspecified MLE (i.e. the model that ignores heteroscedasticity). [16] As a result, the predictions which are based on the misspecified MLE will remain correct.