A Comparison of Variational Approximations for Fast Inference in Mixed Logit Models

41 Pages Posted: 29 Jan 2015

See all articles by Nicolas Depraetere

Nicolas Depraetere

Katholieke Universiteit Leuven - Faculty of Business and Economics (FBE)

Martina L. Vandebroek

Katholieke Universiteit Leuven - Faculty of Business and Economics

Date Written: January 2015

Abstract

Variational Bayesian methods aim to address some of the weaknesses (computation time, storage costs and convergence monitoring) of mainstream MCMCbased 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 different 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 specific 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

Suggested Citation

Depraetere, Nicolas and Vandebroek, Martina L., A Comparison of Variational Approximations for Fast Inference in Mixed Logit Models (January 2015). Available at SSRN: https://ssrn.com/abstract=2557326 or http://dx.doi.org/10.2139/ssrn.2557326

Nicolas Depraetere (Contact Author)

Katholieke Universiteit Leuven - Faculty of Business and Economics (FBE) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Martina L. Vandebroek

Katholieke Universiteit Leuven - Faculty of Business and Economics ( email )

Naamsestraat 69
B-3000 Leuven
Belgium

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