Determining Dimensionality of Binary Variables: A Monte Carlo Simulation Study
Objective: The present study aimed to evaluate four criteria—Kaiser, empirical Kaiser, parallel analysis, and profile likelihood for determining the dimensionality of binary variables.
Methods: A large scale Monte Carlo simulation was conducted to evaluate these criteria across combinations of correlation matrices (Pearson r or tetra choric 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%), dimension (1, 3, 5, 10), and items per dimension (3, 5, 10).
Results: Parallel analysis performed best out of the four criteria, recovering dimensionality in 87.9% of replications when using principal component analysis with Pearson correlations.
Conclusion: Our findings suggested that dimensionality of a binary variable data matrix is best determined by parallel analysis using the combination of principal component analysis with a correlation matrix based on Pearson r. We provided recommendations for selecting criteria in different study conditions.
Ting Dai1*, Adam Davey2