Rotation to a Partially Specified Target Matrix in Exploratory Factor Analysis: How Many Targets?

The purpose of this 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. Three Monte Carlo studies were performed based on the ratio of the number of observed variables to the number of underlying factors. Within each study, communality, sample size, and the number of targets were manipulated. Outcomes included a measure of congruence and a measure of variability with regard to the rotated pattern matrix. The magnitude of the main effect for the influence of the number of targets on congruence and variability ranged from moderate to large. The magnitude of the interaction between the number of targets and level of communality ranged from small to moderate with regard to congruence and variability. Consistent with theoretical expectations, the minimum number of targets to specify to be reasonably assured of obtaining an accurate solution varied across study conditions.