A model for broad choice data

This paper analyzes a discrete choice model where the observed outcome is not the exact alternative chosen by a decision maker but rather the broad group of alternatives which contain the chosen alternative. The model is designed for situations where the choice behavior at a particular level is of interest but only broader level data are available. For example, consider analyzing a household's choice for a vehicle at the make-model-trim level but only choice data at the make-model level are observed. The proposed model is a generalization of the multinomial logit model and collapses to it when there is full observability of the exact choices. We show that the parameters in the model are at least locally identified, but for certain configurations of the data, they are only weakly identified. Methods to address weak identification are proposed when there are data available on the overall market shares of all alternatives, and both maximum likelihood and Bayesian estimation methods are explored.