A Copula-Based Direct Utility Approach with Various Correlations

A direct utility approach can handle multiple discrete/continuous choice outcomes. However, there is a trade-off between allowing correlations between unobserved perceived qualities of two alternatives and computational burden. If we allow the correlations, then we have to do numerical integrations for getting likelihoods, whereas if we give up the correlations, then we can get closed form likelihood. Thus, we suggest a new copula-based direct utility approach that not only allows the correlations but also provides closed form of likelihood. Empirically, we find the existence of the correlations between unobserved qualities of two alternatives. Ignoring the correlations may cause the misunderstanding of the joint-purchases.