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 available only for 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. This article develops an approach that directly estimates the joint distribution of just the variables of interest. For the case of either discrete or continuous variables, the approach yields a solution that can be implemented with standard statistical models and software. In typical marketing applications, the common variables are psychographic or demographic variables, and the variables to be fused involve media viewing and product purchase. For this example, the approach directly estimates 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. The authors develop a method for relaxing the assumption of conditional independence for this case. They illustrate their approach with product-purchase and media-viewing data from a large survey of British consumers.