Working Paper Series Categorical Data Categorical Data

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 conditional logit, nested logit, multinomial probit, and random parameters logit. The last two models are estimated using simulation or Bayesian methods. For ordered data, standard multinomial models are ordered logit and probit, or count models are used if ordered discrete data are actually a count. Keywords: Bayesian methods; binary data; bivariate probit; categorical data; choice-based sampling; conditional logit; count data; discrete outcome; extreme value distribution; index model; independence of irrelevant alternatives; latent variable; limited dependent variable; logit; log-odds ratio; logistic distribution; marginal e¤ect; maximum score estimator; multinomial data; multinomial logit; multinomial probit; multivariate outcomes; nested logit; ordered logit; ordered probit; ordinary least squares; panel categorical data; Poisson regression; probit; qualitative response model; random parameters logit; random utility model; simulation-based estimation. JEL Classi…cation: C21, C25 Prepared for New Palgave Dictionary of Economics, 2nd edition.