An alternative method for evaluating congruence coefficients with procrustes rotation: A bootstrap procedure

Comparing factor structures across samples has long been an important topic in psychological research. Traditionally, the congruence coefficient is used to measure the degree of similarity between 2 factor matrices. However, as the congruence coefficients do not have known sampling distributions, it is difficult to assess factor replicability statistically. In this study, a bootstrap procedure was proposed to test factor invariance by examining the statistical significance of 3 types of congruence coefficients. A Monte Carlo study evaluated the performance of the proposed bootstrap procedure. Results provide strong support for this procedure as a powerful tool to assess factor replicability across groups. Two real examples demonstrate the usefulness of the proposed method.