An Ideal-Point Probabilistic Choice Model for Heterogeneous Preferences

This paper presents a new ideal point probabilistic choice model. Unlike the model suggested by Cooper and Nakanishi (Cooper, L. G., M. Nakanishi. 1983. Two logit models for external analysis of preferences. (4) 607–619.) which attempts to capture choices via a single ideal point, the proposed model, though based on aggregate data, allows for heterogeneity in preferences by estimating a distribution of ideal points. The model accounts for substitutability among choice alternatives and alleviates one of the major sources for the violation of the “Independence from Irrelevant Alternatives” property. It is demonstrated that the final form of the model is a Multinomial Probit, with a covariance matrix that depends on the relative position of the choice alternatives. An empirical application is provided and the resulting parameters are compared to the distributions of ideal points and attribute weights obtained via LINMAP (at the individual level) and via both the Logit and Probit versions of the model proposed by Cooper and Nakanishi (at the aggregate level).