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On the Comparison of Group Performance with Categorical Data

Author

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  • Carmen Herrero
  • Antonio Villar
Abstract
There are many different evaluation problems that involve several groups (societies, firms or institutions) whose members can be classified into ordered categories, pursuant to their characteristics or their achievements. This paper addresses these types of problems and provides an evaluation criterion based on the distribution of the agents across categories. The starting point is that of dominance relations in pair-wise comparisons. We say that group i dominates group j when the expected category of a member of i is higher than the expected category of a member of j. We introduce the notion of relative advantage of a group to extend this principle to multi-group comparisons and show that there is a unique evaluation function that ranks all groups consistently in terms of this criterion. This function associates to each evaluation problem the (unique) dominant eigenvector of a matrix whose entries describe the dominance relations between groups in pair-wise comparisons. The working of the model is illustrated by means of three different applications.

Suggested Citation

  • Carmen Herrero & Antonio Villar, 2013. "On the Comparison of Group Performance with Categorical Data," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-7, December.
    • Handle: RePEc:plo:pone00:0084784
    DOI: 10.1371/journal.pone.0084784
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    References listed on IDEAS

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    14. 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.
    15. Buhong Zheng, 2011. "A new approach to measure socioeconomic inequality in health," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 555-577, December.
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    Cited by:

    1. Albarrán, Pedro & Herrero, Carmen & Ruiz-Castillo, Javier & Villar, Antonio, 2017. "The Herrero-Villar approach to citation impact," Journal of Informetrics, Elsevier, vol. 11(2), pages 625-640.
    2. Ramón José Torregrosa Montaner, 2015. "Medición y evolución del sentimiento autonómico en España," Working Papers. Serie EC 2015-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Iñaki Permanyer & Diederik Boertien, 2019. "A century of change in global education variability and gender differences in education," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-22, February.
    4. Ildefonso Méndez Martínez & Antonio Villar Notario & Carmen Herrero Blanco, 2013. "Analysis of group performance with categorical data when agents are heterogeneous: The case of compulsory education in the OECD," Working Papers. Serie AD 2013-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    5. Héctor Pifarré i Arolas & Christian Dudel, 2019. "An Ordinal Measure of Population Health," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 143(3), pages 1219-1243, June.
    6. Herrero, Carmen & Mendez, Ildefonso & Villar, Antonio, 2014. "Analysis of group performance with categorical data when agents are heterogeneous: The evaluation of scholastic performance in the OECD through PISA," Economics of Education Review, Elsevier, vol. 40(C), pages 140-151.
    7. Carmen Herrero & Antonio Villar, 2018. "The Balanced Worth: A Procedure to Evaluate Performance in Terms of Ordered Attributes," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 140(3), pages 1279-1300, December.
    8. Tugce Cuhadaroglu, 2013. "My Group Beats Your Group: Evaluating Non-Income Inequalities," Discussion Paper Series, School of Economics and Finance 201308, School of Economics and Finance, University of St Andrews.
    9. Torregrosa Montaner, Ramón J., 2015. "Medición y evolución de la identidad nacionalista en España," INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, Asociación Española de Ciencia Regional, issue 33, pages 53-70.
    10. Cristina Pita & Ramón J. Torregrosa, 2023. "The Education-Job Satisfaction Paradox in the Public Sector," Public Organization Review, Springer, vol. 23(4), pages 1717-1735, December.
    11. Carmen Herrero & Antonio Villar, 2020. "Opportunity advantage: a new approach to comparing income distributions," Working Papers 516, ECINEQ, Society for the Study of Economic Inequality.

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    More about this item

    JEL classification:

    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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