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The Cicchetti–Allison weighting matrix is positive definite

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  • Warrens, Matthijs J.

Abstract

Application of Cohen’s weighted kappa for inter-rater agreement requires the specification of a weighting matrix. An explicit formula for the determinants of the principal minors of the weighting matrix with Cicchetti–Allison weights is derived. Since all determinants are strictly positive, it follows that the Cicchetti–Allison weighting matrix is positive definite.

Suggested Citation

  • Warrens, Matthijs J., 2013. "The Cicchetti–Allison weighting matrix is positive definite," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 180-182.
  • Handle: RePEc:eee:csdana:v:59:y:2013:i:c:p:180-182 DOI: 10.1016/j.csda.2012.09.019
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    References listed on IDEAS

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    1. Yang, Jingyun & Chinchilli, Vernon M., 2011. "Fixed-effects modeling of Cohen's weighted kappa for bivariate multinomial data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1061-1070, February.
    2. Matthijs Warrens, 2010. "Inequalities Between Kappa and Kappa-Like Statistics for k×k Tables," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 176-185, March.
    3. Matthijs Warrens, 2011. "Cohen’s Linearly Weighted Kappa is a Weighted Average of 2×2 Kappas," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 471-486, July.
    4. Matthijs Warrens, 2012. "Some Paradoxical Results for the Quadratically Weighted Kappa," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 315-323, April.
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    Cited by:

    1. Sophie Vanbelle, 2016. "A New Interpretation of the Weighted Kappa Coefficients," Psychometrika, Springer;The Psychometric Society, vol. 81(2), pages 399-410, June.
    2. Pingke Li, 2016. "A Note on the Linearly and Quadratically Weighted Kappa Coefficients," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 795-801, September.

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