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

Juan M. Muñoz-Pichardo, Emilio D. Lozano-Aguilera, Antonio Pascual-Acosta and Ana M. Muñoz-Reyes
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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

Mathematics, 2021, vol. 9, issue 14, 1-16

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.

Keywords: ordinal data; multiple ordinal dependence; Kendall’s tau measure; ordinal logistic regression; happiness index; life satisfaction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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