Unrestricted factor analysis of multidimensional test items based on an objectively refined target matrix

A common difficulty in the factor analysis of items designed to measure psychological constructs is that the factor structures obtained using exploratory factor analysis tend to be rejected if they are tested statistically with a confirmatory factor model. An alternative to confirmatory factor analysis is unrestricted factor analysis based on Procrustes rotation, which minimizes the distance from a target matrix proposed by the researcher. In the present article, we focus on the situation in which researchers propose a partially specified target matrix but are prepared to allow their initial target to be refined. Here we discuss RETAM as a new procedure for objectively refining target matrices. To date, it has been recommended that this kind of refinement be guided by human judgment. However, our approach is objective, because the threshold value is computed automatically (not decided on by the researcher) and there is no need to manually compute a number of factor rotations every time. The new procedure was tested in an extensive simulation study, and the results suggest that it may be a useful procedure in factor analysis applications based on incomplete measurement theory. Its feasibility in practice is illustrated with an empirical example from the personality domain. Finally, RETAM is implemented in a well-known noncommercial program for performing unrestricted factor analysis.