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A Note on the Linearly and Quadratically Weighted Kappa Coefficients

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  • Pingke Li

    (Tsinghua University)

Abstract

The linearly and quadratically weighted kappa coefficients are popular statistics in measuring inter-rater agreement on an ordinal scale. It has been recently demonstrated that the linearly weighted kappa is a weighted average of the kappa coefficients of the embedded 2 by 2 agreement matrices, while the quadratically weighted kappa is insensitive to the agreement matrices that are row or column reflection symmetric. A rank-one matrix decomposition approach to the weighting schemes is presented in this note such that these phenomena can be demonstrated in a concise manner.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-016-9501-5
    DOI: 10.1007/s11336-016-9501-5
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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. 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. Warrens, Matthijs J., 2013. "The Cicchetti–Allison weighting matrix is positive definite," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 180-182.
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    Cited by:

    1. 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.
    2. Fabio Rapallo, 2022. "Analysis of the Weighted Kappa and Its Maximum with Markov Moves," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1270-1289, December.

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