The work describes developments in the multiple regression performed for building models resistant to multicollinearity, having meaningful robust solution for individual parameters, convenient for interpretation of the results, and good for prediction. A tool from the cooperative game theory, the Shapley Value analysis, have been tried for estimation of regression coefficients and relative usefulness of the predictors in a model. This approach has been checked and successfully applied in various real-life projects in data analysts for commercial companies. It is useful for decision makers in economics, management, marketing research, and any other practical fields.
FragnelliV., & Sánchez-SorianoJ., eds. (2020). Handbook of the Shapley Value, Chapman and Hall/CRC, Boca Raton, FL.
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LipovetskyS. (2006). Entropy Criterion in Logistic Regression and Shapley Value of Predictors, Journal of Modern Applied Statistical Methods, 5, 121-132.
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LipovetskyS. (2007). Iteratively Re-weighted Random-Coefficient Models and Shapley Regression, Model Assisted Statistics and Applications, 2, 201–212.
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LipovetskyS. (2009). Linear Regression with Special Coefficient Features Attained via Parameterization in Exponential, Logistic, and Multinomial – Logit Forms, Mathematical and Computer Modelling, 49, 1427-1435.
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LipovetskyS. (2010). Meaningful regression coefficients built by data gradients, Advances in Adaptive Data Analysis, 2, 451-462.
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LipovetskyS. (2012). Interpretation of Shapley Value Regression Coefficients as Approximation for Coefficients Derived by Elasticity Criterion, JSM’12, Proceedings of the Joint Statistical Meeting of the American Statistical Association, July-August, 3302-3307, San Diego, CA.
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LipovetskyS. (2013). How Good is Best? Multivariate Case of Ehrenberg-Weisberg Analysis of Residual Errors in Competing Regressions, Journal of Modern Applied Statistical Methods, 12(2), 242-255.
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LipovetskyS. (2016). Combined Granger-Koyck Causality Distributed Lag Modeling, International Journal of Operations and Quantitative Management, 22(4), 317-333.
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LipovetskyS. (2017). Prediction of Percent Change in Linear Regression by Correlated Variables, Journal of Modern Applied Statistical Methods, 16(2), 347-358.
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LipovetskyS. (2020). Personalized Key Drivers for Individual Responses in Regression Modeling, International Journal of Risk and Contingency Management, 9(3), 15-30.
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LipovetskyS., & ConklinM. (2001). Analysis of Regression in Game Theory Approach, Applied Stochastic Models in Business and Industry, 17, 319-330.
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LipovetskyS., & ConklinM. (2004a). Decision Making by Variable Contribution in Discriminant, Logit, and Regression Analyses, Information Technology and Decision Making, 3, 265-279.
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LipovetskyS., & ConklinM. (2004b). Enhance-Synergism and Suppression Effects in Multiple Regression, International Journal of Mathematical Education in Science and Technology, 35, 391-402.
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LipovetskyS., & ConklinM. (2005). Incremental Net Effects in Multiple Regression, International Journal of Mathematical Education in Science and Technology, 36, 361-373.
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LipovetskyS., & ConklinM. (2010a). Reply to the paper “Do not adjust coefficients in Shapley value regression”, Applied Stochastic Models in Business and Industry, 26, 203-204.
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LipovetskyS., & ConklinM. (2010b). Meaningful Regression Analysis in Adjusted Coefficients Shapley Value Model, Model Assisted Statistics and Applications, 5(4), 251-264.
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LipovetskyS., & ConklinM. (2014). Predictor Relative Importance and Matching Regression Parameters, Journal of Applied Statistics, 42, 1017-1031.
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LipovetskyS., & NowakowskaE. (2013). Modeling with Structurally Missing Data by OLS and Shapley Value Regressions, International Journal of Operations and Quantitative Management, 19(3), 169-178.
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