International Choice Modelling Conference, International Choice Modelling Conference 2015

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A Bayesian approach to sampling of alternatives
Thijs Dekker

Last modified: 18 May 2015


Recent works in the fields of transport, environmental economics and marketing (Daly et al. 2014; Guevara and Ben-Akiva 2013a, 2013b; von Haefen and Domanski 2013; Keane and Wasi 2012) have renewed the attention towards the issue of sampling of alternatives in large-scale discrete choice models. The referred studies build on McFadden's (1978) result that consistent parameter estimates can be obtained by estimating a basic multinomial logit models over a subset of randomly sampled alternatives after applying a sampling correction to the utility function. The major benefit of such sampling procedures is that significant reductions in computing time can be attained at relatively low costs. It recently turned out that the McFadden (1978) correction factor is also sufficient to derive consistent parameter estimates for Generalized Extreme Value type of models, such as nested and cross-nested logit (Guevara and Ben-Akiva, 2013a). These advances form a first step towards the closing of the gap between the complex discrete choice models typically applied in small-scale stated preference research and the relatively simple choice models adopted by most large-scale transport demand models.


In this paper, Bayesian estimation techniques are combined with sampling of alternatives investigating the extent to which the computational benefits of both approaches can reinforce each other. Bayesian estimation of discrete choice models is typically fruitful when latent constructs are included in the likelihood function. Specifically, the principle of data augmentation (Tanner and Wong, 1987) enables analysts to circumvent the approximation of integrals, as required in the simulated maximum likelihood approach, such that significant time savings can be attained possibly in combination with sampling of alternatives.

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