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.
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Acknowledgments
The first author’s research is supported by the Austrian Science Foundation (FWF) under the grant S 10309-G14 (NRN “The Austrian Center for Labor Economics and the Analysis of the Welfare State”, Subproject “Bayesian Econometrics”).
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Frühwirth-Schnatter, S., Frühwirth, R. (2010). Data Augmentation and MCMC for Binary and Multinomial Logit Models. In: Kneib, T., Tutz, G. (eds) Statistical Modelling and Regression Structures. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2413-1_7
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DOI: https://doi.org/10.1007/978-3-7908-2413-1_7
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