Mishra, SK (2016): Shapley value regression and the resolution of multicollinearity.

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Abstract
Multicollinearity in empirical data violates the assumption of independence among the regressors in a linear regression model that often leads to failure in rejecting a false null hypothesis. It also may assign wrong sign to coefficients. Shapley value regression is perhaps the best methods to combat this problem. The present paper simplifies the algorithm of Shapley value decomposition of R2 and provides a computer program that executes it. However, Shapley value regression becomes increasingly impracticable as the number of regressor variables exceeds 10, although, in practice, a good regression model may not have more than ten regressors.
Item Type:  MPRA Paper 

Original Title:  Shapley value regression and the resolution of multicollinearity 
Language:  English 
Keywords:  Multicollinearity, Shapley value, regression, computational algorithm, computer program, Fortran 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games 
Item ID:  72116 
Depositing User:  Sudhanshu Kumar Mishra 
Date Deposited:  20 Jun 2016 14:09 
Last Modified:  26 Sep 2019 11:29 
References:  Arumairajan, S. and Wijekoon, P. (2013). Improvement of the Preliminary Test Estimator When Stochastic Restrictions are Available in Linear Regression Model. Scientific Research, 3(4): 283292. Belsley, D.A., Kuh, E. and Welsch, R.E. (1980). Regression diagnostics, identifying influential data and sources of collinearity, Wiley, New York. Chen, G.J. (2012). A simple way to deal with multicollinearity. J. of Applied Statistics, 39(9): 18931909. Gómez, R.S., Pérez, J.G., Martín, M.D.M.L. and García, C.G. (2016). Collinearity diagnostic applied in ridge estimation through the variance inflation factor. J. of Applied Statistics, 43(10): 18311849. Hart, S. (1989). Shapley Value. In Eatwell, J., Milgate, M., and Newman, P (eds.). The New Palgrave: Game Theory. Norton: 210216. Huang, C.C.L., Jou, Y.J. and Cho, H.J. (2015). A new multicollinearity diagnostic for generalized linear models. J. of Applied Statistics (online): 115. Lipovetsky, S. (2006). Entropy criterion in logistic regression and Shapley value of predictors. J. of Modern Applied Statistical Methods, 5(1): 95106. Macedo, P., Scotto, M. and Silva, E. (2010). A general class of estimators for the linear regression model affected by collinearity and outliers. Communications in Statistics  Simulation and Computation, 39(5):981993. Mishra, S.K. (2004a). Multicollinearity and maximum entropy leuven estimator. Economics Bulletin, 3(25): 1−11. Mishra, S.K. (2004b). Estimation under multicollinearity: Application of restricted Liu and maximum entropy estimators to the Portland cement dataset. Social Science Research Network, http://ssrn.com/abstract=559861. Mishra, S.K. (2007). Performance of differential evolution method in least squares fitting of some typical nonlinear curves. J. of Quantitative Economics, 5(1): 140177. Mishra, S.K. (2013). Global optimization of some difficult benchmark functions by hostparasite coevolutionary algorithm. Economics Bulletin, 33(1): 118. Özkale, M.R. (2012). Combining the unrestricted estimators into a single estimator and a simulation study on the unrestricted estimators. J. of Statistical Computation and Simulation, 82(5): 653688. Özkale, M.R. (2014). The relative efficiency of the restricted estimators in linear regression models. Journal of Applied Statistics, 41(5): 9981027. Ročková, V. and George, E.I. (2014). Negotiating multicollinearity with spikeandslab priors. Metron, 72(2): 217229. Shapley, L.S. (1953). A Value for nperson Games. In Kuhn, H.W. and Tucker, A.W. (eds.). Contributions to the theory of games. Annals of Mathematical Studies 28. Princeton University Press: 307317. Woods, H., Steinour, H.H. and Starke, H.R. (1932). Effect of composition of Portland cement on heat evolved during hardening. Industrial and Engineering Chemistry, 24(11): 12071214. Wu, X. (2009). A weighted generalized maximum entropy estimator with a datadriven weight. Entropy, 11(4): 917930. York, R. (2012). Residualization is not the answer: Rethinking how to address multicollinearity. Social Science Research, 41(6): 1379–1386. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/72116 