## Discrete Choice

Discrete Choice is a package for the fitting of a variety of models with categorical dependent variables. It provides an adaptable environment for estimating and evaluating discrete choice models. Model specificity is accommodated with tools for incorporating parameter bounds, linear or nonlinear constraints, default or user specified starting values, and user specified Gradient and Hessian procedures. These models are particularly useful for researchers in the social, behavioral, and biomedical sciences, as well as economics, public choice, education, and marketing.

Output for these models includes full information maximum likelihood estimates with either standard and quasi-maximum likelihood inference. In addition, estimates of marginal effects are computed either as partials of the probabilities with respect to the means of the exogenous variables or optionally as the average partials of the probabilities with respect to the exogenous variables.

### Supported models include:

**Adjacent Categories Multinomial Logit Model:**The log-odds of one category versus the next higher category is linear in the cutpoints and explanatory variables.**Logit and Probit Regression Models:**Estimates dichotomous dependent variable with either Normal or extreme value distributions.**Conditional Logit Models:**Includes both variables that are attributes of the responses as well as, optionally, exogenous variables that are properties of cases.**Mutltinomial Logit Model:**Qualitative responses are each modeled with a separate set of regression coefficients.**Negative Binomial Regression Model (left or right truncated, left or right censored, or zero-inflated):**Estimates model with negative binomial distributed dependent variable. This includes censored models – the dependent variable is not observed but independent variables are available – and truncated models where not even the independent variables are observed. Also, a zero-inflated negative binomial model can be estimated where the probability of the zero category is a mixture of a negative binomial consistent probability and an excess probability. The mixture coefficient can be a function of independent variables.**Nested Logit Regression Model:**Derived from the assumption that residuals have a generalized extreme value distribution and allows for a general pattern of dependence among the responses thus avoiding the IIA problem, i.e., the “independence of irrelevant alternatives.”**Ordered Logit and Probit Regression Models:**Estimates model with an ordered qualitative dependent variable with Normal or extreme value distributions.**Possion Regression Model (left or right truncated, left or right censored, or zero-inflated):**Estimates model with Poisson distributed dependent variable. This includes censored models – the dependent variable is not observed but independent variables are available – and truncated models where not even the independent variables are observed. Also, a zero-inflated Poisson model can be estimated where the probability of the zero category is a mixture of a Poisson consistent probability and an excess probability. The mixture coefficient can be a function of independent variables.**Stereotype Multinomial Logit Model:**The coefficients of the regression in each category are linear functions of a reference regression

### GAUSS provided output includes:

- all parameter estimates
- variance-covariance matrix for coefficient estimates
- the percentages of dependent variables by category (where applicable)
- complete data description of all independent variables
- marginal effects of independent variables (by category of dependent variable, when applicable)
- variance-covariance matrices of marginal effects
- matrix of predicted counts
- matrix of residuals

### GAUSS performs and reports a number of goodness of fit tests including:

- Full model and restricted model log-likelihoods
- Chi-square statistic
- Agresti’s G-squared statistic
- Likelihood ratio statistics and accompanying probability values
- McFadden’s Psuedo R-squared
- McKelvey and Zovcina’s Psuedo R-Squared
- Cragg and Uhler’s normed likelihood ratios
- Count R-Squared
- Adjusted count R-Squared
- Akaike and Bayesian information criterions

**Platform:** Windows, Mac, and Linux.

**Requirements:** GAUSS/GAUSS Light version 8.0 or higher.