Data Fusion in Several Algorithms

• Activity Number: 429
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Marketing
• Author(s): Stan Lipovetsky*+
• Companies: GfK Custom Research North America
• Keywords: data fusion ; distances ; weighting ; dual canonical correlations and PLS ; ridge-regression ; regression with dummies

Abstract

Data fusion consists of the process of integrating several datasets with some common variables, and other variables available only in partial datasets. The main problem of data fusion can be described as follows. From one source, having X0 and Y0 datasets (with N0 observations by multiple x and y variables, n and m of those, respectively), and from another source, having X1 data (with N1 observations by the same n x-variables), we need to estimate the missing portion of the Y1 data (of size N1 by m variables) in order to combine all the data into one set. Several algorithms are considered in this work, including estimation of weights proportional to the distances from each i-th observation in the X1 "recipients" dataset to all observations in the X0 "donors" dataset. Or we can use a sample balancing technique with the maximum effective base performed by applying ridge-regression for the Gifi system of binaries obtained from the x-variables for the best fit of the "donors" X0 data to the margins defined by each respondent in the "recipients" X1 dataset. Then the weighted regressions of each y in the Y0 dataset by all variables in the X0 are constructed. For each i-th observation in the dataset X0, these regressions are used for predicting the y-variables in the Y1 "recipients" dataset. If X and Y are the same n variables from different sources, the dual partial least squares technique and a special regression model with dummies defining each of the three available sets are used for prediction of the Y1 data.