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Simple Moment Estimates of the κ‐Coefficient and its Variance

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  • Stuart R. Lipsitz
  • Nan M. Laird
  • Troyen A. Brennan

Abstract

Estimating equations are used to develop simple non‐iterative estimates of the K‐coefficient that can be used when there are more than two random raters and/or unbalanced data (each subject is not judged by every rater). We show that there is a simple way to estimate the variance of any estimate of the κ‐coefficient that is a solution to an estimating equation. Two non‐iterative estimates that are shown to be solutions to estimating equations are Fleiss's estimate and Schouten's estimate. Also, assuming that the underlying data are beta‐binomial, we compare the asymptotic relative efficiency of the non‐iterative estimators of κ relative to the iterative maximum likelihood estimator (MLE) of K from the beta‐binomial distribution. Fleiss's estimator was found to have high efficiency. Finally, simulations are used to compare the finite sample performance of these estimators as well as the MLE from the beta‐binomial distribution. In the simulations, the Newton‐Raphson algorithm for the MLE from the beta‐binomial model did not always converge in small samples, which also supports the use of a non‐iterative estimate in small samples. The estimators are also compared by using a psychiatric data set given by Fleiss.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:43:y:1994:i:2:p:309-323
    DOI: 10.2307/2986022
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    Cited by:

    1. Barbara Więckowska & Katarzyna B. Kubiak & Paulina Jóźwiak & Wacław Moryson & Barbara Stawińska-Witoszyńska, 2022. "Cohen’s Kappa Coefficient as a Measure to Assess Classification Improvement following the Addition of a New Marker to a Regression Model," IJERPH, MDPI, vol. 19(16), pages 1-15, August.
    2. 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.
    3. Matthijs Warrens, 2010. "A Formal Proof of a Paradox Associated with Cohen’s Kappa," Journal of Classification, Springer;The Classification Society, vol. 27(3), pages 322-332, November.
    4. Guangyong Zou & Allan Donner, 2004. "Confidence Interval Estimation of the Intraclass Correlation Coefficient for Binary Outcome Data," Biometrics, The International Biometric Society, vol. 60(3), pages 807-811, September.
    5. 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.
    6. Huiman X. Barnhart & John M. Williamson, 2002. "Weighted Least-Squares Approach for Comparing Correlated Kappa," Biometrics, The International Biometric Society, vol. 58(4), pages 1012-1019, December.

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