On chance and factor congruence following orthogonal procrustes rotation

Procrustes methods of factor rotation have been criticized for producing excessively high coefficients of congruence when attempting to tit one factor pattern matrix into the space of a targeted pattern. A Monte Carlo study was designed to evaluate some of the conditions contributing to this problem when using Schonemann's orthogonal Procrustes transformation. It was found that the expected size of the factor congruence coefficient varied with (a) the number of variables in the analysis, (b) the number of salient variables defining a factor, and (c) the size of the salient variables' factor pattern coefficients. The number of factors extracted also had some influence on congruence but only in interaction with the size of the salient pattern values. The results of this simulation study, which include a prediction equation, can be used by researchers to appraise levels of factor congruence they find with real data.