Performance of Parallel Analysis in Retrieving Unidimensionality in the Presence of Binary Data

Parallel analysis has been shown to be suitable for dimensionality assessment in factor analysis of continuous variables. There have also been attempts to demonstrate that it may be used to uncover the factorial structure of binary variables conforming to the unidimensional normal ogive model. This article provides both theoretical and empirical evidence that this is not appropriate. Results of a simulation study indicate that sample size, item discrimination, and type of correlation coefficient (Pearson vs. tetrachoric correlation) considerably influence the performance of parallel analysis. Reliability of parallel analysis with binary variables is found to be notably poor for Pearson correlations and also limited for tetrachoric correlations.