Mishra, SK (2016): A note on construction of a composite index by optimization of Shapley value shares of the constituent variables.

PDF
MPRA_paper_72330.pdf Download (189kB)  Preview 
Abstract
This paper proposes a method to construct composite index, which is a linear combination of several variables, by deriving weights on the criterion of Shapley value (from cooperative game theory) that a constituent variable has in making the composite index. In practice it is found oftentimes that the most common method of principal component analysis has a tendency to ignore (or poorly weigh) those constituent variables that do not have strong correlation with the sister variables. This elitist nature of PCA forces a compromise upon the analyst’s desire and need to incorporate those weakly correlated (but theoretically and practically important) variables into the composite index. In that case, one must construct a composite index that is more inclusive in nature. The Shapley value based composite index meets that requirement.
Item Type:  MPRA Paper 

Original Title:  A note on construction of a composite index by optimization of Shapley value shares of the constituent variables 
Language:  English 
Keywords:  Shapley value, Composite index, Principal Component Analysis, Inclusive indices, Global optimization 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C43  Index Numbers and Aggregation C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis 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:  72330 
Depositing User:  Sudhanshu Kumar Mishra 
Date Deposited:  02 Jul 2016 12:39 
Last Modified:  01 Oct 2019 13:25 
References:  Adelman, I. And Morris, C.T. (1967). Society, Politics and Economic Development: A Quantitative Approach, John Hopkins Press, Baltimore. Booysen, F. (2002). An overview and evaluation of composite indices of development. Social Indicators Research, 59(2): 115151. Chattopadhyay, R. N. and Pal, M.N. (1972). Some Comparative Studies on the Construction of Composite Indices. Indian J. of Regional Science, 4(2): 13242. Hart, S. (1989). Shapley Value. In Eatwell, J., Milgate, M., and Newman, P. (eds.). The New Palgrave: Game Theory. Norton: 210216. Hotelling, H. (1933a). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24(6): 417–441. Hotelling, H. (1933b). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24(7): 498–520. Lipovetsky, S. (2006). Entropy criterion in logistic regression and Shapley value of predictors. J. of Modern Applied Statistical Methods, 5(1): 95106. KOF (2012): KOF Index of Globalization, http://globalization.kof.ethz.ch/. Visited on April 2, 2012. Mishra, S. K. (2007a). Construction of an Index By Maximization of the Sum of its Absolute Correlation Coefficients With the Constituent Variables, SSRN: http://ssrn.com/abstract=989088 Mishra, S.K. (2007b). A Comparative Study of Various Inclusive Indices and the Index Constructed By the Principal Components Analysis. SSRN: http://ssrn.com/abstract=990831. Mishra, S.K. (2009). On Construction of Robust Composite Indices by Linear Aggregation. ICFAI University Journal of Computational Mathematics, 2(3): 2444. Mishra, S.K. (2012). A Comparative Study of Trends in Globalization Using Different Synthetic Indicators. SSRN: http://ssrn.com/abstract=2038127. Mishra, S.K. (2013). Global optimization of some difficult benchmark functions by hostparasite coevolutionary algorithm. Economics Bulletin, 33(1): 118. Mishra, S.K. (2016). Shapley value regression and the resolution of multicollinearity SSRN: http://ssrn.com/abstract=2797224. Montero, J.M., Chasco, C. and Lanaz, B. (2010). Building an environmental quality index for a big city: a spatial interpolation approach combined with a distance indicator. J. Geogr. Syst. 12: 435459. Munda, G. and Nardo, M. (2005). Constructing Consistent Composite Indicators: The Issue of Weights”, EUR 21834 EN, Institute for the Protection and Security of the citizen, European Commission, Luxembourg. Nardo M., Saisana M., Saltelli A., Tarantola S., Hoffman A. and Giovannini E. (2005). Handbook on constructing composite indicators: methodology and user guide. OECD Statistic Working Papers, OECD, Paris. http://www.oecd.org/findDocument/0,2350,en_2649_201185_1_119684_1_1_1,00.html OECD (2003). Composite Indicators of Country Performance: A Critical Assessment, DST/IND(2003) 5, Paris. Pearson, K. (1901). On Lines and Planes of Closest Fit to Systems of Points in Space. Philosophical Magazine, 2 (11): 559–572. Saltelli, A. (2007). Composite indicators between analysis and advocacy. Social Indicators Research, 81(1): 6577. Salzman, J. (2003). Methodological Choices Encountered in the Construction of Composite Indices of Economic and Social WellBeing, Center for the Study of Living Standards Ottawa, Ontario, Canada, http://www.csls.ca/events/cea2003/salzmantypolcea2003.pdf Sarker, S., Biswas, B. & Soundrs, P.J. (2006). DistributionAugmented Human Development Index: A Principal Component Analysis, GSP, College of Business, Utah State Univ., USA. www.usu.edu/cob/econ/graduatestudents/documents/papers/developmentpaper.pdf. (visited on April1 24, 2007). Somarriba, N. and Pena, B. (2009). Synthetic Indicators of Quality of Life in Europe. Soc. Indic. Res. 94:115–133. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/72330 