title: A Note on the Linearly and Quadratically Weighted Kappa Coefficients.
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.
authors.affiliation: Department of Industrial Engineering, Tsinghua University, Beijing, 100084, China. pkli@tsinghua.edu.cn.
authors.forename: Pingke
authors.identifier: 0000-0003-2244-3139
authors.initials: P
authors.lastname: Li
mesh_terms: D006801:Humans; D015588:Observer Variation; D011594:Psychometrics; D015203:Reproducibility of Results; D013223:Statistics as Topic
keywords: complete positivity; inter-rater agreement; rank-one representation; weighted kappa