The Estimation of Generalized Extreme Value Models from Choice-based Samples



The Estimation of Generalized Extreme Value Models from Choice-based Samples

Authors

M Bierlaire, Ecole Polytechnique Fédérale de Lausanne, CH; D Bolduc, Université Laval, Québec, CA; D McFadden, University of California, Berkeley, US

Description

We propose a simple estimator providing consistent estimates of all parameters, including the constants, for non-MNL GEV models, which does not require an a priori knowledge of the sampling
probabilities.

Abstract

Sampling issues are of greater importance in the estimation of statistical models in general, and of discrete choice models in particular.
Although simple random sampling strategies are theoretically convenient, they are practically never feasible in a transportation context.
However, it is well known that maximum likelihood estimation of the multinomial logit (MNL) model on stratified samples yields to consistent estimates for all parameters except the constants, which must be
corrected afterward.
This property does not generalize to non-MNL generalized extreme value (GEV) models, so that classical estimation procedures do not yield to maximum likelihood estimators from choice-based samples.
In this paper, we propose a simple estimator providing consistent estimates of all parameters, including the constants, for non-MNL GEV models, which does not require an a priori knowledge of the sampling
probabilities. The new estimator require minor modifications of existing estimation codes.
We illustrate the concept on synthetic and real data for nested and cross-nested logit models. The results show that the classical "exogenous sample maximum likelihood" estimator produces biased
estimates, even for parameters other than the constants. The new estimator is able to identify all the parameters, including the constants if the GEV model is non-trivial.
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Publisher

Association for European Transport