A comparison of variational approximations for fast inference in mixed logit models

Nicolas Depraetere and Martina Vandebroek

No 479707, Working Papers of Department of Decision Sciences and Information Management, Leuven from KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven

Abstract: Variational Bayesian methods aim to address some of the weaknesses (computation time, storage costs and convergence monitoring) of mainstream MCMC-based inference at the cost of a biased approximation to the posterior distribution. We investigate the performance of variational approximations in the context of the mixed logit model, which is arguably one of the most used models for discrete choice data. A typical treatment using the variational Bayesian methodology is hindered by the fact that the expectation of the so called log-sum-exponential function has no closed form expression. Therefore, one has to resort to approximating or bounding this term. In this paper we compare seven di_erent possible bounds or approximations. We found that quadratic bounds do not perform particularly well. A recently proposed non-quadratic bound, on the other hand, did perform quite well. We also found that the approximation used in a previous study only performed well for speci_c settings. Our proposed approximation based on quasi Monte Carlo sampling on the other hand performed consistently well across all simulation settings while remaining computationally tractable.

Keywords: Bayesian statistics; Variational Bayes; Discrete choice; Mixed logit models (search for similar items in EconPapers)
Date: 2015-01
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Published in FEB Research Report KBI_1503

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