Modeling Multivariate Distributions Using Copulas: Applications in Marketing

Abstract

In this research we introduce a new class of multivariate probability models to the marketing literature. Known as “copula models,” they have a number of attractive features. First, they permit the combination of any univariate marginal distributions that need not come from the same distributional family. Second, a particular class of copula models, called “elliptical copula,” has the property that they increase in complexity at a much slower rate than existing multivariate probability models as the number of dimensions increase. Third, they are very general, encompassing a number of existing multivariate models and providing a framework for generating many more. These advantages give copula models a greater potential for use in empirical analysis than existing probability models used in marketing. We exploit and extend recent developments in Bayesian estimation to propose an approach that allows reliable estimation of elliptical copula models in high dimensions. Rather than focusing on a single marketing problem, we demonstrate the versatility and accuracy of copula models with four examples to show the flexibility of the method. In every case, the copula model either handles a situation that could not be modeled previously or gives improved accuracy compared with prior models.