부산대학교 도서관

We aim to propose a new estimator of the reliability index for polytomous ordinal items, introduced by Zumbo et al. (J Mod Appl Stat Methods 6:21-29, 2007 (See CR16)), who suggested a modification of the classical Cronbach's [Formula omitted] indicator to be used in presence of ordinal variables. Zumbo et al. introduced an underlying variable conceptualization of the Cronbach's reliability index and suggested that one can estimate this underlying variable index, Zumbo's Ordinal Alpha, using ML estimation of the polychoric correlations. Our proposal relaxes the assumption made by Zumbo et al., that the ordinal variables have an underlying multinormal distribution, by using a copula framework. The proposed estimator builds upon the Spearman grade correlation coefficient on a transformation of the ordinal variables, calculated by the copula function. An empirical version of our proposal, defined by means of the empirical copula, is also presented. Some examples and simulation studies are presented.
Author(s): Andrea Bonanomi [sup.1], Gabriele Cantaluppi [sup.1], Marta Nai Ruscone [sup.1], Silvia Angela Osmetti [sup.1] Author Affiliations: (1) grid.8142.f, 0000000109413192, Department of Statistical Sciences, Università Cattolica del Sacro Cuore, , [...]