Shapley Value Regression and the Resolution of Multicollinearity
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Keywords

Multicollinearity
Shapley value
Regression
Computer program
Fortran.

How to Cite

MISHRA, S. K. (2016). Shapley Value Regression and the Resolution of Multicollinearity. Journal of Economics Bibliography, 3(3), 498–515. https://doi.org/10.1453/jeb.v3i3.850

Abstract

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 develops a Fortran computer program that executes it. It also retrieve regression coefficients from the Shapley value. 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..

Keywords. Multicollinearity,  Shapley value, regression, computer program,  Fortran.

JEL. C63, C71.
https://doi.org/10.1453/jeb.v3i3.850
PDF

References

Arumairajan, S., & Wijekoon, P. (2013). Improvement of the preliminary test estimator when stochastic restrictions are available in linear regression model. Scientific Research, 3(4), 283-292. doi. 10.4236/ojs.2013.34033

Belsley, D.A., Kuh, E. & 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. Journal of Applied Statistics, 39(9), 1893-1909. doi. 10.1080/02664763.2012.690857

Gómez, R.S., Pérez, J.G., Martín, M.D.M.L. & García, C.G. (2016). Collinearity diagnostic applied in ridge estimation through the variance inflation factor. Journal of Applied Statistics, 43(10), 1831-1849. doi. 10.1080/02664763.2015.1120712

Hart, S. (1989). Shapley Value. In Eatwell, J., Milgate, M., and Newman, P (eds.). The New Palgrave: Game Theory. Norton, p.210-216.

Huang, C.C.L., Jou, Y.J., & Cho, H.J. (2015). A new multicollinearity diagnostic for generalized linear models. Journal of Applied Statistics, 43(11), 2029-2043. doi. 10.1080/02664763.2015.1126239

Lipovetsky, S. (2006). Entropy criterion in logistic regression and Shapley value of predictors. Journal of Modern Applied Statistical Methods, 5(1), 95-106.

Macedo, P., Scotto, M., & 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), 981-993. doi. 10.1080/03610911003695719

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. [Retrieved from].

Mishra, S.K. (2007). Performance of differential evolution method in least squares fitting of some typical nonlinear curves. Journal of Quantitative Economics, 5(1), 140-177.

Mishra, S.K. (2013). Global optimization of some difficult benchmark functions by host-parasite coevolutionary algorithm. Economics Bulletin, 33(1), 1-18.

Özkale, M.R. (2012). Combining the unrestricted estimators into a single estimator and a simulation study on the unrestricted estimators. Journal of Statistical Computation and Simulation, 82(5): 653-688. doi. 10.1080/00949655.2010.550293

Özkale, M.R. (2014). The relative efficiency of the restricted estimators in linear regression models. Journal of Applied Statistics, 41(5), 998-1027. doi. 10.1080/02664763.2013.859234

Ročková, V., & George, E.I. (2014). Negotiating multicollinearity with spike-and-slab priors. Metron, 72(2), 217-229. doi. 10.1007/s40300-014-0047-y

Shapley, L.S. (1953). A Value for n-person Games. In Kuhn, H.W. and Tucker, A.W. (eds.). Contributions to the theory of games. Annals of Mathematical Studies 28. Princeton University Press, p.307-317.

Woods, H., Steinour, H.H., & Starke, H.R. (1932). Effect of composition of Portland cement on heat evolved during hardening. Industrial and Engineering Chemistry, 24(11), 1207-1214. doi. 10.1021/ie50275a002

Wu, X. (2009). A weighted generalized maximum entropy estimator with a data-driven weight. Entropy, 11(4), 917-930. doi. 10.3390/e11040917

York, R. (2012). Residualization is not the answer: Rethinking how to address multicollinearity. Social Science Research, 41(6), 1379–1386. doi. 10.1016/j.ssresearch.2012.05.014

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