Data Augmentation and MCMC for Binary and Multinomial Logit Models

Sylvia Frühwirth-Schnatter () and Rudolf Frühwirth ()
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Sylvia Frühwirth-Schnatter: Johannes-Kepler-Universität Linz, Institut für Angewandte Statistik
Rudolf Frühwirth: Institut für Hochenergiephysik der Österreichischen Akademie der Wissenschaften

A chapter in Statistical Modelling and Regression Structures, 2010, pp 111-132 from Springer

Abstract: Abstract 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 away that only differences of utilities are involved. As a consequence, 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. Alternatively, 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.

Keywords: Binomial dataTrondheim; multinomial data; data augmentation; Markov chain Monte Carlo; logit model; random utility model (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2413-1_7

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DOI: 10.1007/978-3-7908-2413-1_7

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