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A new measure of nominal-ordinal association

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  • Raffaella Piccarreta

Abstract

A new measure for evaluating the strength of the association between a nominal variable and an ordered categorical response variable is introduced. The introduction of a new measure is justified by analysing the characteristics of a measure of the nominal-ordinal association proposed by Agresti (1981), especially with respect to the problem of the 'choice' of a predictive variable. The sample-based version of the index is studied, and its asymptotic standard error and asymptotic distribution are derived. Simulations are considered to evaluate the adequacy of the asymptotic approximation determined, following Goodman & Kruskal (1963).

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  • Raffaella Piccarreta, 2001. "A new measure of nominal-ordinal association," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 107-120.
    • Handle: RePEc:taf:japsta:v:28:y:2001:i:1:p:107-120
    DOI: 10.1080/02664760120011635
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    References listed on IDEAS

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    1. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
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    Cited by:

    1. M. Perakis & P. Maravelakis & S. Psarakis & E. Xekalaki & J. Panaretos, 2005. "On Certain Indices for Ordinal Data with Unequally Weighted Classes," Quality & Quantity: International Journal of Methodology, Springer, vol. 39(5), pages 515-536, October.
    2. Raffaella Piccarreta, 2008. "Classification trees for ordinal variables," Computational Statistics, Springer, vol. 23(3), pages 407-427, July.
    3. Rosaria Lombardo & Eric Beh & Antonello D'Ambra, 2011. "Studying the dependence between ordinal-nominal categorical variables via orthogonal polynomials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2119-2132.
    4. Janitza, Silke & Tutz, Gerhard & Boulesteix, Anne-Laure, 2016. "Random forest for ordinal responses: Prediction and variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 57-73.
    5. Giuseppe Bove & Pier Luigi Conti & Daniela Marella, 2021. "A measure of interrater absolute agreement for ordinal categorical data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 927-945, September.
    6. Podani, János & Patonai, Katalin & Szabó, Péter & Szilágyi, András, 2022. "Coefficients of association between nominal and fully ranked ordinal variables with applications to ecological network analysis," Ecological Modelling, Elsevier, vol. 466(C).

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