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A Note on the Linearly and Quadratically Weighted Kappa Coefficients

Published online by Cambridge University Press:  01 January 2025

Pingke Li Open the ORCID record for Pingke Li [Opens in a new window]
Pingke Li*
Affiliation:
Tsinghua University
*
Correspondence should be made to Pingke Li, Department of Industrial Engineering, Tsinghua University, Beijing, 100084, China. Email: pkli@tsinghua.edu.cn
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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.

Keywords

inter-rater agreementweighted kapparank-one representationcomplete positivity
Type
Original Paper
Information
Psychometrika , Volume 81 , Issue 3 , September 2016 , pp. 795 - 801
Copyright
Copyright 2016 © The Psychometric Society

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