Estimation Techniques for MEV Models with Sampling of Alternatives
R Hurtubia, G Flötteröd, M Bierlaire, Ecole Polytechnique Federale de Lausanne, CH
This article proposes a method that estimates a reduced choice problem for a subset of the population with known choice set constraints and then infers the coefficients of a related large scale choice model from this limited estimation effort.
Estimation of MEV models with large choice sets requires sampling of alternatives, which might be a difficult task due to the correlated-structure of the error terms. Standard sampling techniques like the ones traditionally used for Multinomial Logit models cannot be directly applied in the estimation of more complex MEV models. State of the art estimators for MEV models with sampling of alternatives either require knowledge of the full choice set or produce biased estimates for small sample sizes.
This paper proposes two estimation techniques for MEV models with sampling of alternatives. The first technique is based on bootstrapping and allows to reduce the bias for existing estimators. A Monte Carlo simulation experiment is performed to show how this technique reduce the bias of a state-of the-art estimator for a Nested Logit model considering sampling of alternatives. The second technique introduces a new estimator, based on importance sampling of alternatives . A second Monte Carlo experiment is performed to compare this estimator with the current state of the art. The proposed estimator generates unbiased parameter estimates for a Nested Logit model considering small sample sizes. The techniques can be easily applied to other members of the MEV family of models, like the Cross-Nested Logit.
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