Logitüübid

Logitüübid are a family of statistical models that use the logit link function to model the probability of a categorical outcome. They are widely used in binary and multiclass classification, discrete choice analysis, and ordinal response modeling. In many formulations they can be viewed as generalized linear models with a binomial or multinomial distribution and a logit link, or as discrete-choice models where the probability of each alternative is proportional to exponentiated utilities.

Binary logit, or logistic regression, models the probability of a binary outcome Y = 1 as P(Y=1|X) = exp(Xβ)/(1+exp(Xβ)). The logit of the probability is logit(P) = Xβ.

Multinomial logit extends to more than two categories: P(Y=j|X) = exp(Xβ_j)/Sum_k exp(Xβ_k). One category is typically treated as a baseline with a corresponding parameter vector set to zero.

Conditional logit, used for discrete choice with attributes of alternatives, specifies P(i selects j) = exp(V_ij)/Sum_k exp(V_ik), where V_ij = X_ijβ. The predictors vary by alternative.

Nested logit and mixed (random-parameters) logit relax some assumptions of the simple multinomial logit. Nested logit allows correlation of utilities within nests of alternatives, while mixed logit incorporates random coefficients to capture taste variation across individuals.

Ordered logit models ordinal outcomes by modeling the cumulative probability P(Y ≤ k) with a logistic link and a set of thresholds.

Estimation is typically done by maximum likelihood. Limitations include the independence of irrelevant alternatives (IIA) property in some models and the need for careful specification and data structure. Logitüübid are applied in economics, marketing, transportation, political science, and risk modeling to analyze choice and probability patterns.