Non-parametric estimation of mixed discrete choice models
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In this paper, different strands of literature are combined in order to obtain algorithms for semi-parametric estimation of discrete choice models that include the modelling of unobserved heterogeneity by using mixing distributions for the parameters defining the preferences. The models use the theory on non-parametric maximum likelihood estimation (NP-MLE) that has been developed for general mixing models. The expectation-maximization (EM) techniques used in the NP-MLE literature are combined with strategies for choosing appropriate approximating models using adaptive grid techniques. Jointly this leads to techniques for specification and estimation that can be used to obtain a consistent specification of the mixing distribution. Additionally, also algorithms for the estimation are developed that help to decrease problems due to the curse of dimensionality. The proposed algorithms are demonstrated in a small scale simulation study to be useful for the specification and estimation of mixture models in the discrete choice context providing some information on the specification of the mixing distribution. The simulations document that some aspects of the mixing distribution such as the expectation can be estimated reliably. They also demonstrate, however, that typically different approximations to the mixing distribution lead to similar values of the likelihood and hence are hard to discriminate. Therefore it does not appear to be possible to reliably infer the most appropriate parametric form for the estimated mixing distribution.
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