The Polychoric Ordinal Alpha, measuring the reliability of a set of polytomous ordinal items

We aim at proposing a new reliability measurement for polytomous ordinal items. Conventionally, reliability coefficients, such as Cronbach Alpha, are calculated using the Pearson correlation matrix. We suggest a modification of the classical Cronbach Alpha for ordinal variables, by using the polychoric correlation coefficient. In particular we consider the extension of polychoric correlation coefficient via copula approach. It builds upon the theoretical framework of the classic polychoric correlation coefficient, but relaxes its fundamental assumption that the ordinal variables have a underlying multinormal distributions. A simulation study is conducted in order to compare the proposed index to classical reliability measures.