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Interpretation of the coefficient of determination of an ANOVA model as a measure of polarization

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  • Federico Palacios-González
  • Rosa Mar�a Garc�a-Fernández

Abstract

In this paper, it is demonstrated that coefficient of determination of an ANOVA linear model provides a measure of polarization. Taking as the starting point the link between polarization and dispersion, we reformulate the measure of polarization of Zhang and Kanbur using the decomposition of the variance instead of the decomposition of the Theil index. We show that the proposed measure is equivalent to the coefficient of determination of an ANOVA linear model that explains, for example, the income of the households as a function of any population characteristic such as education, gender, occupation, etc. This result provides an alternative way to analyse polarization by sub-populations characteristics and at the same time allows us to compare sub-populations via the estimated coefficients of the ANOVA model.

Suggested Citation

  • Federico Palacios-González & Rosa Mar�a Garc�a-Fernández, 2012. "Interpretation of the coefficient of determination of an ANOVA model as a measure of polarization," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1543-1555, January.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:7:p:1543-1555
    DOI: 10.1080/02664763.2012.658361
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    1. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-851, July.
    2. You‐Qiang Wang & Kai‐Yuen Tsui, 2000. "Polarization Orderings and New Classes of Polarization Indices," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 2(3), pages 349-363, July.
    3. X. Zhang & R. Kanbur, 2001. "What Difference Do Polarisation Measures Make? An Application to China," Journal of Development Studies, Taylor & Francis Journals, vol. 37(3), pages 85-98.
    4. Wang, You-Qiang & Tsui, Kai-Yuen, 2000. "Polarization Orderings and New Classes of Polarization Indices," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 2(3), pages 349-363.
    5. Mohammad Hussain, 2009. "The sensitivity of income polarization," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(3), pages 207-223, September.
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