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

Anneke Cleopatra Weide · André Beauducel

51 citations0/0 files storedFrontiers in Psychology

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Psychometric Methodologies and Testing Statistical Methods and Applications Advanced Statistical Methods and Models

Abstract

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.

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References

1999Evaluating the use of exploratory factor analysis in psychological research.1958The Varimax Criterion for Analytic Rotation in Factor Analysis 1999Sample size in factor analysis.1968Modern Factor Analysis 1988Relation of sample size to the stability of component patterns.2004Psychometric Properties of the HEXACO Personality Inventory 2005Minimum Sample Size Recommendations for Conducting Factor Analyses 2006FACTOR: A computer program to fit the exploratory factor analysis model

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