Global Evaluation of Reliability for a Structural Equation Model with Latent Variables and Ordinal Observations

We present a review of the main reliability measures. We first introduce the Classical Test Theory and define reliability within this framework. Some reliability estimates are considered, among which is Cronbach's $\alpha$, the most popular reliability index, which relies on the assumptions of unidimensionality and parallelism. The latter assumptions are relaxed by considering estimates of reliability in the frameworks of Factor Analysis and Structural Equation Models with Latent Variables, where the construct usually consists of more than one single dimension. In particular we make use of the Average Variance Explained indicators to assess a global evaluation of reliability. In case of test items of the ordinal nature we consider polychoric correlations instead of Pearson's ones when computing reliability measures.