A recommendation for applied researchers to substantiate the claim that ordinal variables are the product of underlying bivariate normal distributions

Abstract

A simulation study was carried out to study the behaviour of the polychoric correlation coefficient in data not compliant with the assumption of underlying continuous variables. Such data can produce relatively high estimated polychoric correlations (in the order of.62). Applied researchers are prone to accept these artefacts as input for elaborate modelling (e.g., structural equation models) and inferences about reality justified by sheer magnitude of the correlations. In order to prevent this questionable research practice, it is recommended that in applications of the polychoric correlation coefficient, data is tested with goodness-of-fit of the BND, that such statistic is reported in published applications, and that the polychoric correlation is not applied when the test is significant.