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On Measuring Polarization For Ordinal Data: An Approach Based On The Decomposition Of The Leti Index

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  • Mussini Mauro

    (Department of Economics, University of Verona, ; Verona, ; Italy)

Abstract

This paper deals with the measurement of polarization for ordinal data. Polarization in the distribution of an ordinal variable is measured by using the decomposition of the Leti heterogeneity index. The ratio of the between-group component of the index to the within-group component is used to measure the degree of polarization for an ordinal variable. This polarization measure does not require imposing cardinality on ordered categories to quantify the degree of polarization in the distribution of an ordinal variable. We address the practical issue of identifying groups by using classification trees for ordinal variables. This tree-based approach uncovers the most homogeneous groups from observed data, discovering the patterns of polarization in a data-driven way. An application to Italian survey data on self-reported health status is shown.

Suggested Citation

  • Mussini Mauro, 2018. "On Measuring Polarization For Ordinal Data: An Approach Based On The Decomposition Of The Leti Index," Statistics in Transition New Series, Statistics Poland, vol. 19(2), pages 277-296, June.
    • Handle: RePEc:vrs:stintr:v:19:y:2018:i:2:p:277-296:n:9
    DOI: 10.21307/stattrans-2018-016
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    References listed on IDEAS

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    1. Benedicte Apouey, 2007. "Measuring health polarization with self‐assessed health data," Health Economics, John Wiley & Sons, Ltd., vol. 16(9), pages 875-894, September.
    2. Deutsch, Joseph & Fusco, Alessio & Silber, Jacques, 2013. "The BIP Trilogy (bipolarization, inequality and polarization): One saga but three different stories," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 7, pages 1-33.
    3. Walter Bossert & William Schworm, 2008. "A Class of Two‐Group Polarization Measures," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(6), pages 1169-1187, December.
    4. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-851, July.
    5. Raffaella Piccarreta, 2008. "Classification trees for ordinal variables," Computational Statistics, Springer, vol. 23(3), pages 407-427, July.
    6. Jenkins, Stephen P., 1995. "Did the middle class shrink during the 1980s? UK evidence from kernel density estimates," Economics Letters, Elsevier, vol. 49(4), pages 407-413, October.
    7. James Foster & Michael Wolfson, 2010. "Polarization and the decline of the middle class: Canada and the U.S," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(2), pages 247-273, June.
    8. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    9. 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.
    10. Iñaki Permanyer & Conchita D'Ambrosio, 2015. "Measuring Social Polarization with Ordinal and Categorical Data," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(3), pages 311-327, June.
    11. Chiara Gigliarano & Karl Mosler, 2009. "Constructing indices of multivariate polarization," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(4), pages 435-460, December.
    12. Mauro Mussini, 2016. "On Measuring Income Polarization: An Approach Based On Regression Trees," Statistics in Transition New Series, Polish Statistical Association, vol. 17(2), pages 221-236, June.
    13. 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.
    14. Shlomo Yitzhaki, 2010. "Is There Room For Polarization?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(1), pages 7-22, March.
    15. Mauro Mussini, 2016. "On Measuring Income Polarization: An Approach Based On Regression Trees," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(2), pages 221-236, June.
    16. repec:bla:jpbect:v:2:y:2000:i:3:p:349-63 is not listed on IDEAS
    17. Alessio Fusco & Jacques Silber, 2014. "On social polarization and ordinal variables: the case of self-assessed health," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 15(8), pages 841-851, November.
    18. Galimberti, Giuliano & Soffritti, Gabriele & Maso, Matteo Di, 2012. "Classification Trees for Ordinal Responses in R: The rpartScore Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i10).
    19. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
    20. Kakwani, Nanak & Wagstaff, Adam & van Doorslaer, Eddy, 1997. "Socioeconomic inequalities in health: Measurement, computation, and statistical inference," Journal of Econometrics, Elsevier, vol. 77(1), pages 87-103, March.
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    More about this item

    Keywords

    polarization; ordinal data; Leti index; classification trees.;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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