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Decomposing R2 with the Owen value

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  • Hüttner, Frank
  • Sunder, Marco

Abstract

We provide an axiomatization-based justification for applying the Owen value to decompose R2 in OLS models if prior knowledge can be used to form groups of regressor variables. The assumptions made by the axioms are not only plausible with respect to the variables but also clarify the meaning of the exogenous grouping of variables.

Suggested Citation

  • Hüttner, Frank & Sunder, Marco, 2011. "Decomposing R2 with the Owen value," Working Papers 100, University of Leipzig, Faculty of Economics and Management Science.
  • Handle: RePEc:zbw:leiwps:100
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    References listed on IDEAS

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    1. repec:spr:compst:v:66:y:2007:i:2:p:255-261 is not listed on IDEAS
    2. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 227-240.
    3. Groemping, Ulrike, 2006. "Relative Importance for Linear Regression in R: The Package relaimpo," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 17(i01).
    4. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    5. Anger, Silke & Heineck, Guido, 2010. "Cognitive Abilities and Earnings – First Evidence for Germany," EconStor Open Access Articles, ZBW - German National Library of Economics, pages 699-702.
    6. Gert G. Wagner & Joachim R. Frick & Jürgen Schupp, 2007. "The German Socio-Economic Panel Study (SOEP) – Scope, Evolution and Enhancements," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 127(1), pages 139-169.
    7. Osnat Israeli, 2007. "A Shapley-based decomposition of the R-Square of a linear regression," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(2), pages 199-212, August.
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    More about this item

    Keywords

    Shapley value; Owen value; OLS; variance decomposition; German Socio-Economic Panel;

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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