Examples of "logit"
Discrete choice models take many forms, including: Binary Logit, Binary Probit, Multinomial Logit, Conditional Logit, Multinomial Probit, Nested Logit, Generalized Extreme Value Models, Mixed Logit, and Exploded Logit. All of these models have the features described below in common.
NLOGIT is a full information maximum likelihood estimator for a variety of multinomial choice models. NLOGIT includes the discrete estimators in LIMDEP plus model extensions for multinomial logit (many specifications), random parameters mixed logit, random regret logit, WTP space specifications in mixed logit, scaled multinomial logit, nested logit, multinomial probit, heteroscedastic extreme value, error components, heteroscedastic logit and latent class models.
As with standard logit, the exploded logit model assumes no correlation in unobserved factors over alternatives. The exploded logit can be generalized, in the same way as the standard logit is generalized, to accommodate correlations among alternatives and random taste variation. The "mixed exploded logit" model is obtained by probability of the ranking, given above, for "L" in the mixed logit model (model I).
The following sections describe Nested Logit, GEV, Probit, and Mixed Logit models in detail.
In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution. If "Y" is a random variable with a normal distribution, and "P" is the logistic function, then "X" = "P"("Y") has a logit-normal distribution; likewise, if "X" is logit-normally distributed, then "Y" = logit("X")= log ("X"/(1-"X")) is normally distributed. It is also known as the logistic normal distribution, which often refers to a multinomial logit version (e.g.).
Under the same assumptions as for a standard logit (model F), the probability for a ranking of the alternatives is a product of standard logits. The model is called "exploded logit" because the choice situation that is usually represented as one logit formula for the chosen alternative is expanded ("exploded") to have a separate logit formula for each ranked alternative. 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.
By far the most common specification for QRE is logit equilibrium (LQRE). In a logit equilibrium, player's strategies are chosen according to the probability distribution:
where "μ" and "σ" are the mean and standard deviation of the variable’s logit (by definition, the variable’s logit is normally distributed).
Closely related to the probit function (and probit model) are the logit function and logit model. The inverse of the logistic function is given by
Econometric Software, Inc. was founded in the early 1980s by William H. Greene. NLOGIT was released in 1996 with the development of the FIML nested logit estimator, originally an extension of the multinomial logit model in LIMDEP. The program derives its name from the Nested LOGIT model. With the additions of the multinomial probit model and the mixed logit model among several others, NLOGIT became a self standing superset of LIMDEP.
The probit model has been around longer than the logit model. They behave similarly, except that the logistic distribution tends to be slightly flatter tailed. One of the reasons the logit model was formulated was that the probit model was computationally difficult due to the requirement of numerically calculating integrals. Modern computing however has made this computation fairly simple. The coefficients obtained from the logit and probit model are fairly close. However, the odds ratio is easier to interpret in the logit model.
"cumulative logit model" for ordinal categorical regression.
which is the negative logit function multiplied by 0.5.
fit a multinomial logit model to, e.g., transport choices.
and the model is called the multinomial logit model.
As shown in the graph, the logit and probit functions are extremely similar, particularly when the probit function is scaled so that its slope at y=0 matches the slope of the logit. As a result, probit models are sometimes used in place of logit models because for certain applications (e.g., in Bayesian statistics) the implementation is easier.
The logit ( ) function is the inverse of the sigmoidal "logistic" function or logistic transform used in mathematics, especially in statistics. When the function's parameter represents a probability , the logit function gives the log-odds, or the logarithm of the odds .
Thus the logit transformation is referred to as the "link function" in logistic regression—although the dependent variable in logistic regression is binomial, the logit is the continuous criterion upon which linear regression is conducted.
Logit transformations are interesting, as they usually transform various shapes (including J-shapes) into (usually skewed) bell-shaped densities over the logit variable, and they may remove the end singularities over the original variable:
The standard logit model's "taste" coefficients, or formula_1's, are fixed, which means the formula_1's are the same for everyone. Mixed logit has different formula_1's for each person (i.e., each decision maker.)