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.

Bonanomi, A., Cantaluppi, G., Nai Ruscone, M., Osmetti, S. A., A new estimator of Zumbo’s Ordinal Alpha: a copula approach, <<QUALITY & QUANTITY>>, 2015; 2015 (49 (3)): 941-953. [doi:10.1007/s11135-014-0114-8] [http://hdl.handle.net/10807/65749]

A new estimator of Zumbo’s Ordinal Alpha: a copula approach

Bonanomi, Andrea;Cantaluppi, Gabriele;Nai Ruscone, Marta;Osmetti, Silvia Angela
2014

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.
Inglese
Bonanomi, A., Cantaluppi, G., Nai Ruscone, M., Osmetti, S. A., A new estimator of Zumbo’s Ordinal Alpha: a copula approach, <<QUALITY & QUANTITY>>, 2015; 2015 (49 (3)): 941-953. [doi:10.1007/s11135-014-0114-8] [http://hdl.handle.net/10807/65749]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/65749
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