Data Augmentation and MCMC for Binary and Multinomial Logit Models

The paper introduces two new data augmentation algorithms for sampling the parameters of a binary or multinomial logit model from their posterior distribution within a Bayesian framework. The new samplers are based on rewriting the underlying random utility model in such a way that only differences of utilities are involved. As a conseqence, the error term in the logit model has a logistic distribution. If the logistic distribution is approximated by a finite scale mixture of normal distributions, auxiliary mixture sampling can be implemented to sample from the posterior of the regression parameters. ternatively, a data augmented Metropolis–Hastings algorithm can be formulated by approximating the logistic distribution by a single normal distribution. A comparative study on five binomial and multinomial data sets shows that the new samplers are superior to other data augmentation samplers and to Metropolis–Hastings sampling without data augmentation.