Categorical outcome (or discrete outcome or qualitative response) regression models are models for a discrete dependent variable recording in which of two or more categories an outcome of interest lies. For binary data (two categories) probit and logit models or semiparametric methods are used. For multinomial data (more than two categories) that are unordered, common models are multinomial and...

Inspired by the interactive discrete choice logit models [Aggarwal, 2019], this paper presents the advanced families of discrete choice models, such as nested logit, mixed logit, and probit models to consider the interaction among the attributes. Besides the DM's attitudinal character is also taken into consideration in the computation of choice probabilities. The proposed choice models make us...

3 Model Specification 5 3.1 Binary choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.1 The binary probit model . . . . . . . . . . . . . . . . . . 6 3.1.2 The binary logit model . . . . . . . . . . . . . . . . . . . 7 3.2 More than two choices . . . . . . . . . . . . . . . . . . . . . . . 8 3.2.1 The multinomial probit model . . . . . . . . . . . . . . . 8 3.2.2 The multinomi...

Bayesian classification commonly relies on probit models, with data augmentation algorithms used for posterior computation. By imputing latent Gaussian variables, one can often trivially adapt computational approaches used in Gaussian models. However, MCMC for multinomial probit (MNP) models can be inefficient in practice due to high posterior dependence between latent variables and parameters,...

Standard Bayesian multinomial probit (MNP) models that are fit using different base categories can give different predictions. Therefore, we propose the symmetric MNP model, which does not make reference to a base category. To achieve this, we employ novel sum-to-zero identifying restrictions on the latent utilities and regression coefficients that define the model. This results in a model whos...

The Multinomial Logit, discrete choice model of transport demand, has several restrictions when compared with the more general Multinomial Probit model. The most famous of these are that unobservable components of utilities should be mutually independent and homoskedastic. Correlation can be accommodated to a certain extent by the Hierarchical Logit model, but the problem of heteroskedasticity ...