Factor retention in ordered categorical variables: Benefits and costs of polychoric correlations in eigenvalue-based testing.

An essential step in exploratory factor analysis is to determine the optimal number of factors. The Next Eigenvalue Sufficiency Test (NEST; Achim, 2017) is a recent proposal to determine the number of factors based on significance tests of the statistical contributions of candidate factors indicated by eigenvalues of sample correlation matrices. Previous simulation studies have shown NEST to recover the optimal number of factors in simulated datasets with high accuracy. However, these studies have focused on continuous variables. The present work addresses the performance of NEST for ordinal data. It has been debated whether factor models - and thus also the optimal number of factors - for ordinal variables should be computed for Pearson correlation matrices, which are known to underestimate correlations for ordinal datasets, or for polychoric correlation matrices, which are known to be instable. The central research question is to what extent the problems associated with Pearson correlations and polychoric correlations deteriorate NEST for ordinal datasets. Implementations of NEST tailored to ordinal datasets by utilizing polychoric correlations are proposed. In a simulation, the proposed implementations were compared to the original implementation of NEST which computes Pearson correlations even for ordinal datasets. The simulation shows that substituting polychoric correlations for Pearson correlations improves the accuracy of NEST for binary variables and large sample sizes (N = 500). However, the simulation also shows that the original implementation using Pearson correlations was the most accurate implementation for Likert-type variables with four response categories when item difficulties were homogeneous.