The estimation of Generalized Extreme Value models from choice-based samples
In the presence of choice-based sampling strategies for data collection, the property of Multinomial Logit (MNL) models, that consistent estimâtes of all parameters but the constants can be obtained from an Exogenous Sample Maximum Likelihood (ESML) estimation, does not hold in general for Generalized Extreme Value (GEV) models. We propose a consistent ESML estimator for GEV models in this context. We first identify a specific class of GEV models with the desired property that, similarly to MNL, the constants absorb the potential bias. We then propose a new and simpleWeighted Conditional Maximum Likelihood (WCML) estimator for the more general case. Contrarily to the Weighted Exogenous Sample Maximum Likelihood (WESML) estimator by Manski and Lerman (1977), the new WCML estimator does not require an external knowledge of the market shares. We illustrate the use of the estimator on synthetic and real data.