Wy serves as the weight.
The weighted kappa coefficient is seldom used because the weights have to be theoretically and, if possible, empirically founded. Moreover, if the data are metrical, the weighted kappa equals the intra-class correlation if all subsequent weights are equidistant (see Berry & Mielke, 1988; Fleiss & Cohen, 1973). If all categories can be ordered on a single dimension representing different levels of this dimension, models of item response theory can be used to ascertain convergent validity (see Rost & Walter, chap. 18, this volume). Weighted kappa can, thus, be used if categories cannot be ordered on a single dimension and if some categories have more in common than others (for a more detailed discussion, see Landis & Koch, 1975a, 1975b).
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