Iteratively re-weighted random-coefficient models and Shapley value regression

Article type: Research Article

Authors: Lipovetsky, Stan

Affiliations: GfK Custom Research North America, 8401 Golden Valley Road, Minneapolis, MN 55427, USA. E-mail: stan.lipovetsky@gfk.com

Abstract: In this article, random-coefficient regression models are considered in an iteratively re-weighted approach. In Hildreth-Houck model for one-cluster data and in the yield analysis, the decomposition of residuals by predictors is used to estimate random regression coefficients for each observation. In a sample balance model, the random regression coefficients are obtained by adjusting predictions. However, in all the models, multicollinearity distorts the estimates of fixed coefficients in the linear aggregate. To overcome this problem and to obtain the robust estimates of the predictors, the Shapley value regression is implemented. It is based on a cooperative game approach in estimating the incremental share of each predictor, and provides consistent and interpretable results for both fixed- and random-coefficient models. This technique proved to be very convenient and useful for practical analysis of the importance of the predictors for each observation.

Keywords: Random-coefficient regression, Hildreth-Houck model, yield analysis, sample balance, multicollinearity, cooperative games, Shapley value

DOI: 10.3233/MAS-2007-2403

Journal: Model Assisted Statistics and Applications, vol. 2, no. 4, pp. 201-212, 2007