Auxiliary mixture sampling with applications to logistic models

A new method of data augmentation for binary and multinomial logit models is described. First, the latent utilities are introduced as auxiliary latent variables, leading to a latent model which is linear in the unknown parameters, but involves errors from the type I extreme value distribution. Second, for each error term the density of this distribution is approximated by a mixture of normal distributions, and the component indicators in these mixtures are introduced as further latent variables. This leads to Markov chain Monte Carlo estimation based on a convenient auxiliary mixture sampler that draws from standard distributions like normal or exponential distributions and, in contrast to more common Metropolis–Hastings approaches, does not require any tuning. It is shown how the auxiliary mixture sampler is implemented for binary or multinomial logit models, and it is demonstrated how to extend the sampler to mixed effect models and time-varying parameter models for binary and categorical data. Finally, an application to Austrian labor market data is discussed.