Utility of Dependence: Uncertainty Reduction and Departure from Independence

• Activity Number: 398
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Marketing
• Author(s): Nima Y Jalali*+ and Ehsan Soofi and Nader Ebrahimi
• Companies: University of Wisconsin-Milwaukee and University of Wisconsin-Milwaukee and Northern Illinois University
• Keywords: Copula ; elliptical distributions ; Kendall's tau ; mutual information ; Spearman's rank correlation ; utility

Abstract

Modeling and measuring dependence are important in statistics and marketing. We formulate dependence in terms of the utility of predicting a variable. This approach, which integrates ideas from the literature on dependence with the Bayesian expected utility of data for uncertainty reduction, leads to an information measure, known as the mutual information M which quantifies the departure of a dependent model from the independence. Because modeling dependence often involves different families of models, "it is important to measure dependence on a common metric" (Smith et al. 2010). Currently the popular choices are Kendall's tau and Spearman's rank correlation; their invariance under monotone transformations makes them applicable to copulas, which recently has also been suggested for modeling dependence in marketing problems (Danaher and Smith 2010). We illustrate that M provides a suitable common metric for dependence within and between families of models, in contrast with the traditional indices which fail to measure dependence even for some important models such as the elliptical families. We present applications for regression, random utility models and copula transformations.