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Multiple Ordinal Correlation Based on Kendall’s Tau Measure: A Proposal

Author

Listed:
  • Juan M. Muñoz-Pichardo

    (Department of Estadística e I.O., Universidad de Sevilla, 410112 Seville, Spain)

  • Emilio D. Lozano-Aguilera

    (Department of Statistics and O.R., University of Jaén, 23071 Jaén, Spain)

  • Antonio Pascual-Acosta

    (Department of Estadística e I.O., Universidad de Sevilla, 410112 Seville, Spain)

  • Ana M. Muñoz-Reyes

    (Department of Estadística e I.O., Universidad de Sevilla, 410112 Seville, Spain)

Abstract

The joint analysis of various ordinal variables is necessary in many experimental studies within research fields such as sociology and psychology. Therefore, the necessary measures of multiple ordinal dependence must be easy to interpret and facilitate the interpretation of multivariate models that fit ordinal data. The main objective of this article is to propose a multiple ordinal correlation measure based on a bivariate correlation measure: Kendall’s tau. A sample version of the measure is proposed for its estimation. Furthermore, a confidence interval and a multiple ordinal independence test are proposed. The measure is applied to various simulations, covering a wide range of multiple ordinal dependency scenarios, in order to illustrate the adequacy of the measure and the proposed inferential techniques. Finally, the measure is applied to a real-world study based on a social survey of the levels of life satisfaction and the happiness index of a population.

Suggested Citation

  • Juan M. Muñoz-Pichardo & Emilio D. Lozano-Aguilera & Antonio Pascual-Acosta & Ana M. Muñoz-Reyes, 2021. "Multiple Ordinal Correlation Based on Kendall’s Tau Measure: A Proposal," Mathematics, MDPI, vol. 9(14), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1616-:d:590954
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    References listed on IDEAS

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    1. Henry Chow, 2005. "Life Satisfaction Among University Students in a Canadian Prairie City: a Multivariate Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 70(2), pages 139-150, January.
    2. J. M. Muñoz-Pichardo & R. Pino-Mejías & J. García-Heras & F. Ruiz-Muñoz & M. Luz González-Regalado, 2021. "A multivariate Poisson regression model for count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(13-15), pages 2525-2541, November.
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