A Note on the Interpretation of Weighted Kappa and its Relations to Other Rater Agreement Statistics for Metric Scales

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Conditional inequalities between Cohen's kappa and weighted kappas (2013, background): “For r = 1 we have the linear weights wij(1) = |i − j| [5,28] and for r = 2 the quadratic weights wij(2) = (i − j)2 [11,23].”
A note on the linearly weighted kappa coefficient for ordinal scales (2009, methodology): “For126 instance, Fleiss and Cohen (1973) and Schuster (2004) showed that using the127 weights vij = (i − j)2, the weighted kappa coefficient can be interpreted as128 an intraclass correlation coefficient in a two-way analysis of variance setting.129 In this article, we focused on the linearly…”
Some Paradoxical Results for the Quadratically Weighted Kappa (2012, methodology): “Some support for the quadratically weighted kappa, denoted by κq , was presented in Fleiss and Cohen (1973) and Schuster (2004).”
Variance Estimation of Nominal-Scale Inter-Rater Reliability with Random Selection of Raters (2008, background): “Other authors, such as Schuster (2004) or Schuster and Smith (2006), addressed the inter-rater reliability problem within the framework of theoretical statistical models and have been able to gain further insight into the nature of agreement among raters.”