Robust oblique Target-rotation for small samples

• Published in: Frontiers in psychology Vol. 14; p. 1285212
• Main Authors: Beauducel, André, Hilger, Norbert
• Format: Journal Article
• Language: English
• Published: Switzerland Frontiers Media S.A 27.11.2023
• Subjects: exploratory factor analysis; factor inter-correlation; factor-rotation; independent clusters model; Psychology; Target-rotation; exploratory factor analysis; factor-rotation; independent clusters model; Target-rotation; factor inter-correlation
• ISSN: 1664-1078; 1664-1078
• DOI: 10.3389/fpsyg.2023.1285212

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. 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. 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. 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.