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A Note on the Linearly and Quadratically Weighted Kappa Coefficients
1Department of Industrial Engineering, Tsinghua University, Beijing, 100084, China. pkli@tsinghua.edu.cn.
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.
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