%A Weide,Anneke Cleopatra
%A Beauducel,AndrĂ©
%D 2019
%J Frontiers in Psychology
%C
%F
%G English
%K Gradient projection,Varimax,Factor rotation,Component rotation,Principal Component Analysis,Local optima,Random start loadings
%Q
%R 10.3389/fpsyg.2019.00645
%W
%L
%N 645
%M
%P
%7
%8 2019-March-26
%9 Methods
%#
%! Varimax rotation by gradient projection
%*
%<
%T Varimax Rotation Based on Gradient Projection Is a Feasible Alternative to SPSS
%U https://www.frontiersin.org/article/10.3389/fpsyg.2019.00645
%V 10
%0 JOURNAL ARTICLE
%@ 1664-1078
%X Gradient projection rotation (GPR) is an openly available and promising tool for factor and component rotation. We compare GPR toward 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, and 12), the number of variables per component (m/k = 4, 6, and 8), the number of iterations per rotation (i = 25 and 250), and whether loadings were Kaiser normalized before rotation or not. GPR-Varimax was conducted with unrotated and multiple (q = 1, 10, 50, and 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 were eliminated when Kaiser-normalized loadings and 250 iterations per rotation were used. 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.