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Data augmentation, frequentist estimation, and the Bayesian analysis of multinomial logit models

Content Provider	Springer Nature Link
Author	Scott, Steven L.
Copyright Year	2009
Abstract	This article describes a convenient method of selecting Metropolis– Hastings proposal distributions for multinomial logit models. There are two key ideas involved. The first is that multinomial logit models have a latent variable representation similar to that exploited by Albert and Chib (J Am Stat Assoc 88:669–679, 1993) for probit regression. Augmenting the latent variables replaces the multinomial logit likelihood function with the complete data likelihood for a linear model with extreme value errors. While no conjugate prior is available for this model, a least squares estimate of the parameters is easily obtained. The asymptotic sampling distribution of the least squares estimate is Gaussian with known variance. The second key idea in this paper is to generate a Metropolis–Hastings proposal distribution by conditioning on the estimator instead of the full data set. The resulting sampler has many of the benefits of so-called tailored or approximation Metropolis–Hastings samplers. However, because the proposal distributions are available in closed form they can be implemented without numerical methods for exploring the posterior distribution. The algorithm converges geometrically ergodically, its computational burden is minor, and it requires minimal user input. Improvements to the sampler’s mixing rate are investigated. The algorithm is also applied to partial credit models describing ordinal item response data from the 1998 National Assessment of Educational Progress. Its application to hierarchical models and Poisson regression are briefly discussed.
Starting Page	87
Ending Page	109
Page Count	23
File Format	PDF
ISSN	09325026
Journal	Statistical Papers
Volume Number	52
Issue Number	1
e-ISSN	16139798
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-02-11
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multinomial Poisson transformation Discrete choice model Partial credit model Markov chain Monte Carlo Gibbs sampler Metropolis–Hastings Logistic regression Polytomous Polychotomous Economic Theory Probability Theory and Stochastic Processes Operations Research/Decision Theory Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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