Bierlaire, M., Bolduc, D., and McFadden, D. (2006)
The estimation of Generalized Extreme Value models from choice-based samples
We consider an estimation procedure for discrete choice models in general and Generalized Extreme Value (GEV) models in particular. It is based on a pseudo-likelihood function, generalizing the Conditional Maximum Likelihood (CML) estimator by Manski and McFadden (1981) and theWeighted Exogenous Sample Maximum Likelihood (WESML) estimator by Manski and Lerman (1977). We show that the property of Multinomial Logit (MNL) models, that consistent estimates of all parameters but the constants can be obtained from an Exogenous Sample Maximum Likelihood (ESML) estimation, does not hold in general for GEV models. We identify a specific class of GEV models with this desired property, and propose a new estimator for the more general case. This new estimator estimates the selection bias directly from the data. We illustrate the new estimator on pseudo-synthetic and real data.