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An Alternative Interpretation of the Linearly Weighted Kappa Coefficients for Ordinal Data

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  • Tarald O. Kvålseth

    (University of Minnesota)

Abstract

When two (or more) observers are independently categorizing a set of observations, Cohen’s kappa has become the most notable measure of interobserver agreement. When the categories are ordinal, a weighted form of kappa becomes desirable. The two most popular weighting schemes are the quadratic weights and linear weights. Quadratic weights have been justified by the fact that the corresponding weighted kappa is asymptotically equivalent to an intraclass correlation coefficient. This paper deals with linear weights and shows that the corresponding weighted kappa is equivalent to the unweighted kappa when cumulative probabilities are substituted for probabilities. A numerical example is provided.

Suggested Citation

  • Tarald O. Kvålseth, 2018. "An Alternative Interpretation of the Linearly Weighted Kappa Coefficients for Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 618-627, September.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:3:d:10.1007_s11336-018-9621-1
    DOI: 10.1007/s11336-018-9621-1
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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, 2012. "Some Paradoxical Results for the Quadratically Weighted Kappa," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 315-323, April.
    3. 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.
    4. Matthijs Warrens, 2014. "Corrected Zegers-ten Berge Coefficients Are Special Cases of Cohen’s Weighted Kappa," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 179-193, July.
    5. 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.
    6. Helena Kraemer, 1979. "Ramifications of a population model forκ as a coefficient of reliability," Psychometrika, Springer;The Psychometric Society, vol. 44(4), pages 461-472, December.
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