Michel Bierlaire, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, Denis Bolduc, Université Laval, Québec, Canada, Daniel McFadden, University of California, Berkeley, , USA
Sampling issues with GEV models (assigned to theme
The issue of sampling strategies in the context of the Multinomial Logit model is well known since the late 70’s (see, for instance, Manski and Lerman, 1977, and Manski and McFadden, 1981). It is also discussed at length in the textbook by Ben-Akiva and Lerman (1985). In short, random sampling can be safely assumed when exogenous sampling is performed, and maximum likelihood estimation can be used. The same is true if choice-based samples are used, leading to consistent estimates of all parameters except the constants. In this case, the Alternative Specific Constants must be corrected in order to reproduce market shares. In this paper, we use a property of GEV model to show that maximum likelihood methods for GEV choice probabilities in simple random samples can also be applied to non-random samples, both exogenous and choice-based. The same property is also used to show that, under some conditions, a GEV model can be estimated with samples of the alternatives (see Bierlaire et al., 2003). We illustrate these theoretical results by numerical evidences based on simulation.
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