Robust Oblique Target-rotation for Small Samples

Introduction: Oblique Target-rotation in the context of exploratory factor analysis is a relevant method for the investigation of the oblique simple structure. It was argued that minimizing single cross-loadings by means of target rotation may lead to large effects of sampling error on the target rotated factor solutions.

Method: In order to minimize effects of sampling error on results of Target-rotation we propose to compute the mean cross-loadings for each block of salient loadings of the independent clusters model and to perform Target-rotation for the block-wise mean cross-loadings. The resulting transformation-matrix is than applied to the complete unrotated loading matrix in order to produce mean Target-rotated factors.

Results: A simulation study based on correlated independent clusters model and zero-mean cross-loading models revealed that mean oblique Target-rotation resulted in smaller bias of factor inter-correlations than conventional Target-rotation based on single loadings, especially when sample size was small and when the number of factors was large. An empirical example revealed that the similarity of Target-rotated factors computed for small subsamples with Target-rotated factors of the total sample was more pronounced for mean Target-rotation than for conventional Target-rotation.

Discussion: Mean Target-rotation can be recommended in the context of oblique factor models based on simple structure, especially for small samples. An R-script and an SPSS-script for this form of Target-rotation are provided in the Supplementary Material.