Reliability measurement for polytomous ordinal items: the empirical polychoric ordinal Alpha

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 empirical polychoric correlation coefficient. It builds upon the theoretical framework of the classic polychoric correlation coefficient, but relaxes its fundamental assumption that the ordinal variables have a specific underlying continuous joint distributions. The proposed index, defined by the means of the empirical copula, is a non parametric reliability measure particularly suitable for ordinal data. A simulation study is conducted in order to compare the proposed index to classical reliability measures.