Rotation to a partially specified target matrix in exploratory factor analysis in practice

The purpose of the present study was to explore the influence of the number of targets specified on the quality of exploratory factor analysis solutions with a complex underlying structure and incomplete substantive measurement theory. We extended previous research in this area by (a) exploring this phenomenon in situations in which both the common factor model and the targeted pattern matrix contained specification errors and (b) comparing the performance of target rotation to an easier-to-use default rotation criterion (i.e., geomin) under conditions commonly observed in practice. A Monte Carlo study manipulated target error, number of targets, model error, overdetermination, communality, and sample size. Outcomes included bias (i.e., accuracy) and variability (i.e., stability) with regard to the rotated pattern matrix. The effects of target error were negligible for both accuracy and stability, whereas small effects were observed for the number of targets for both outcomes. Further, target rotation outperformed geomin rotation with regard to accuracy but generally performed worse than geomin rotation with regard to stability. These findings underscore the potential importance (or caution, in the case of stability) of using extant, even if incomplete and somewhat inaccurate, substantive measurement theory to inform the rotation criterion in a nonmechanical way.