Varimax rotation based on gradient projection is a feasible alternative to SPSS
- 1University of Bonn, Germany
Gradient projection rotation (GPR) is an openly-available and promising tool for factor and component rotation. We compare GPR towards the Varimax criterion in principal component analysis to the built-in Varimax procedure in SPSS. In a simulation study, we tested whether GPR-Varimax yielded multiple local solutions by creating population simple structure with a single optimum and with two optima, a global and a local one (double-optimum condition). The other conditions comprised the number of components (k = 3, 6, 9, 12), the number of variables per component (k/m = 4, 6, 8), the number of iterations per rotation (i = 25, 250), and whether loadings were Kaiser normalized before rotation or not. GPR-Varimax was conducted with unrotated and multiple (q = 1, 10, 50, 100) random start loadings. We found equal results for GPR-Varimax and SPSS-Varimax in most conditions. The few very small differences in favor of SPSS-Varimax did not occur with Kaiser normalized loadings and 250 iterations per rotation. Selecting the best solution out of multiple random starts in GPR-Varimax increased proximity to population components in the double-optimum condition with Kaiser normalized loadings, for which GPR-Varimax recovered population structure better than SPSS-Varimax. We also included an empirical example and found that GPR-Varimax and SPSS-Varimax yielded highly similar solutions for orthogonal simple structure in a real data set. We suggest that GPR-Varimax can be used as an alternative to Varimax rotation in SPSS. Users of GPR-Varimax should allow for at least 250 iterations, normalize loadings before rotation, and select the best solution from at least 10 random starts to ensure optimal results.
Keywords: Gradient projection, Varimax, Factor rotation, Component rotation, Principal Component Analysis, Local optima, Random start loadings
Received: 14 Sep 2018;
Accepted: 07 Mar 2019.
Edited by:Holmes Finch, Ball State University, United States
Reviewed by:Paul T. Barrett, Independent researcher
AHMET ADEMOGLU, Boğaziçi University, Turkey
Guangjian Zhang, University of Notre Dame, United States
Copyright: © 2019 Weide and Beauducel. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Ms. Anneke C. Weide, University of Bonn, Bonn, Germany, firstname.lastname@example.org