A Direct Approach to Data Fusion

Abstract

The generic data fusion problem is to make inferences about the joint distribution of two sets of variables without any direct observations of the joint distribution. Instead, information is only available about each set separately along with some other set of common variables. The standard approach to data fusion creates a fused data set with the variables of interest and the common variables. Our approach directly estimates the joint distribution of just the variables of interest. For the case of either discrete or continuous variables, our approach yields a solution that can be implemented with standard statistical models and software. In typical marketing applications, the common variables are psycho-graphic or demographic variables and the variables to be fused involve media viewing and product purchase. For this example, our approach will directly estimate the joint distribution of media viewing and product purchase without including the common variables. This is the object required for marketing decisions. In marketing applications, fusion of discrete variables is required. We develop a method for relaxing the assumption of conditional independence for this case. We illustrate our approach with product purchase and media viewing data from a large survey of British consumers.

Keywords: Data fusion, predictive distributions, Bayesian analysis, media planning and buying

JEL Classification: C1, C8, M3