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Local Concordance and Some Applications

Author

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  • Silvia Terzi

    (RomaTre University)

  • Luca Moroni

    (RomaTre University)

Abstract

One of the main issues when analyzing multidimensional phenomena such as well being is how to define a composite indicator. However a sometimes neglected collateral issue is how to take into account the joint distribution of the single components, and connected with this issue the question should be: how to compute the association among the single components of a multidimensional concept. This is precisely the aim of this paper. We suggest a counting based approach to detect positive association amongst the single components of multivariate phenomena, in particular among the best performing units and vice-versa among the worst performing units. Taking moves from Kendall’s notion of concordance/agreement and from his well known concordance coefficient W (Kendall and Babington Smith in Ann Math Stat 10:275–287, 1939), we introduce the concept of local concordance and derive a local concordance coefficient and a local concordance curve. Our intent is to have, not an overall measure of concordance, i.e. not a global indicator, but instead local concordance coefficients to detect different degrees of concordance in the head, tail or centre of the multivariate distribution of the components of a well being indicator. The local concordance curve can have many different applications. When referred to the components of a well being indicator (and thus to inequality), the local concordance coefficient obtained from the first (last) window can be seen as a measure of concentration of high-level (or low-level) attributes. We apply this approach to exploit whether different aspects of social vulnerability are equally or unequally distributed among censuary areas of a same region.

Suggested Citation

  • Silvia Terzi & Luca Moroni, 2022. "Local Concordance and Some Applications," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 161(2), pages 457-470, June.
    • Handle: RePEc:spr:soinre:v:161:y:2022:i:2:d:10.1007_s11205-020-02312-z
    DOI: 10.1007/s11205-020-02312-z
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    References listed on IDEAS

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    1. Koen Decancq & María Ana Lugo, 2012. "Inequality of Wellbeing: A Multidimensional Approach," Economica, London School of Economics and Political Science, vol. 79(316), pages 721-746, October.
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    4. Sabina Alkire & James Foster, 2011. "Understandings and misunderstandings of multidimensional poverty measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(2), pages 289-314, June.
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    6. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
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    8. Matteo Mazziotta & Adriano Pareto, 2018. "Measuring Well-Being Over Time: The Adjusted Mazziotta–Pareto Index Versus Other Non-compensatory Indices," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(3), pages 967-976, April.
    9. Silvia Terzi, 2013. "How to Integrate Macro and Micro Perspectives: An Example on Human Development and Multidimensional Poverty," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 114(3), pages 935-945, December.
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    13. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    14. Susan L. Cutter & Bryan J. Boruff & W. Lynn Shirley, 2003. "Social Vulnerability to Environmental Hazards," Social Science Quarterly, Southwestern Social Science Association, vol. 84(2), pages 242-261, June.
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    2. Giovanna Scarcilli, 2024. "Studying the evolution of cumulative deprivation among European countries with a copula-based approach," Working Papers 667, ECINEQ, Society for the Study of Economic Inequality.

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