Multi-rater delta: extending the delta nominal measure of agreement between two raters to many raters

The need to measure the degree of agreement among R raters who independently classify n subjects within K nominal categories is frequent in many scientific areas. The most popular measures are Cohen's kappa (R = 2), Fleiss' kappa, Conger's kappa and Hubert's kappa (R >= 2) coefficients, which have several limitations. In 2004, the delta coefficient was defined for the case of R = 2, which did not have the limitations of Cohen's kappa coefficient. This article extends the coefficient delta from R = 2 raters to R >= 2 (coefficient multi-rater delta), demonstrating that it can be expressed in the kappa format and has the same advantages as the coefficient delta with regard to the type kappa classic coefficients: (i) it refers to the proportion of replies that are concordant not by chance; (ii) allow to obtain a parameter that faithfully measures the degree of agreement in each category; and (iii) it is not affected by the marginal imbalance.