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A Unified Treatment of Agreement Coefficients and their Asymptotic Results: the Formula of the Weighted Mean of Weighted Ratios

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  • Haruhiko Ogasawara

    (Otaru University of Commerce 3-5-21)

Abstract

A unified treatment of agreement coefficients for multiple raters is shown, where the chance-expected proportions of the Bennett et al.-type, Scott-type, its new variation, and Cohen-type are dealt with using full or lower-order agreement among raters. When only pairwise agreement is used for multiple raters, chance corrections of the Gwet-type and its new variation are also considered. For the unified treatment, Conger’s two formulas of the ratio of means and the mean of ratios are combined into a parent formula of the weighted mean of weighted ratios. The corresponding unified expressions of their new asymptotic results are presented.

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  • Haruhiko Ogasawara, 2021. "A Unified Treatment of Agreement Coefficients and their Asymptotic Results: the Formula of the Weighted Mean of Weighted Ratios," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 390-422, July.
    • Handle: RePEc:spr:jclass:v:38:y:2021:i:2:d:10.1007_s00357-020-09366-1
    DOI: 10.1007/s00357-020-09366-1
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    References listed on IDEAS

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    1. Haruhiko Ogasawara, 2020. "Asymptotic cumulants of the minimum phi-divergence estimator for categorical data under possible model misspecification," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(10), pages 2448-2465, May.
    2. Louis Guttman, 1946. "The test-retest reliability of qualitative data," Psychometrika, Springer;The Psychometric Society, vol. 11(2), pages 81-95, June.
    3. Kilem Gwet, 2008. "Variance Estimation of Nominal-Scale Inter-Rater Reliability with Random Selection of Raters," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 407-430, September.
    4. Stuart R. Lipsitz & Nan M. Laird & Troyen A. Brennan, 1994. "Simple Moment Estimates of the κ‐Coefficient and its Variance," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 309-323, June.
    5. Ogasawara, Haruhiko, 2012. "Cornish-Fisher expansions using sample cumulants and monotonic transformations," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 1-18, January.
    6. Ogasawara, Haruhiko, 2010. "Asymptotic expansions for the pivots using log-likelihood derivatives with an application in item response theory," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2149-2167, October.
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