AUTHOR=Weide Anneke Cleopatra , Beauducel André 

TITLE=Varimax Rotation Based on Gradient Projection Is a Feasible Alternative to SPSS

JOURNAL=Frontiers in Psychology

VOLUME=10

YEAR=2019

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2019.00645

DOI=10.3389/fpsyg.2019.00645

ISSN=1664-1078

ABSTRACT=<p>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 (<italic>k</italic> = 3, 6, 9, and 12), the number of variables per component (<italic>m/k</italic> = 4, 6, and 8), the number of iterations per rotation (<italic>i</italic> = 25 and 250), and whether loadings were Kaiser normalized before rotation or not. GPR-Varimax was conducted with unrotated and multiple (<italic>q</italic> = 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.</p>