A Bootstrap Generalization of Modified Parallel Analysis for IRT Dimensionality Assessment

This article introduces a bootstrap generalization to the Modified Parallel Analysis (MPA) method of test dimensionality assessment using factor analysis. This methodology, based on the use of Marginal Maximum Likelihood nonlinear factor analysis, provides for the calculation of a test statistic based on a parametric bootstrap using the MPA methodology for generation of synthetic datasets. Performance of the bootstrap test was compared with the likelihood ratio difference test and the DIMTEST procedure using a Monte Carlo simulation. The bootstrap test was found to exhibit much better control of the Type I error rate than the likelihood ratio difference test, and comparable power to DIMTEST under most conditions. A major conclusion to be taken from this research is that under many real-world conditions, the bootstrap MPA test presents a useful alternative for practitioners using Marginal Maximum Likelihood factor analysis to test for multidimensional testing data.