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Title: A new estimator of Zumbo's Ordinal Alpha: a copula approach
Authors: Bonanomi, Andrea
Cantaluppi, Gabriele
Nai Ruscone, Marta
Osmetti, Silvia Angela
Issue Date: 2015
Publisher: Springer
Bibliographic citation: Bonanomi Andrea, et al. (2015), A new estimator of Zumbo's Ordinal Alpha: a copula approach. In: Quality and quantity, vol. 49, n. 3, May 2015, p. 941-953. ISSN 0033-5177. DOI 10.1007/s11135-014-0114-8.
Abstract: 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), who suggested a modification of the classical Cronbach's α 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.
Journal/Book: Quality and quantity
ISSN: 0033-5177
Appears in Collections:Contributo in rivista

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