Copula-based direct utility models for correlated choice alternatives

Abstract

We propose a general framework of copula-based direct utility models and suggest two approaches (Gaussian and FGM approaches) that can accommodate correlations among unobserved utilities. We investigate how and in which directions the biases in parameter estimates of direct utility models occur when error correlations are ignored. Furthermore, we provide practical guidance to empirical researchers by examining strengths and weaknesses of the two suggested approaches. We find that the Gaussian copula approach is flexible but computationally demanding. On the other hand, the proposed FGM copula approach substantially reduces computational complexity, while fully utilizing the maximum range of correlations that is theoretically attainable by the generalized FGM copulas. We apply the proposed approaches to various contexts including grocery scanner panel, experimental, and conjoint datasets and demonstrate that overlooking the correlations may bias managerial metrics and result in suboptimal decisions (e.g., optimal package configuration, monetary equivalents of attribute levels).