Determining Dimensionality of a Set of Binary Indicators: A Simulation Study

• In Event: Research Methodologies in Education

Abstract

Abstract
We conducted a large-scale simulation to evaluate several criteria (i.e., Kaiser’s criterion, empirical Kaiser’s criterion, parallel analysis, and profile likelihood) for determining the dimensionality of binary variables given combinations of correlation matrices (Pearson r or tetrachoric ρ) and analysis methods (principal component analysis or exploratory factor analysis); and combinations of study characteristics—sample sizes (100, 250, 1000), variable splits (10%/90%, 25%/75%, 50%/50%), underlying dimensions (1, 3, 5, 10), and items per dimension (3, 5, 10) with 1000 replications per condition. Parallel analysis outperformed the other criteria (recovering dimensionality in 87.9% of replications) when using PCA with Pearson correlations—the most effective matrix-analysis combination. Guidance for selecting criteria were provided.

Authors

• Ting Dai, University of Illinois at Chicago
  Presenting Author

• Adam Davey, University of Delaware
  Non-Presenting Author