Weide Anneke Cleopatra, Beauducel André
Department of Methods and Evaluation, Institute of Psychology, University of Bonn, Bonn, Germany.
Front Psychol. 2019 Mar 26;10:645. doi: 10.3389/fpsyg.2019.00645. eCollection 2019.
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 ( = 3, 6, 9, and 12), the number of variables per component ( = 4, 6, and 8), the number of iterations per rotation ( = 25 and 250), and whether loadings were Kaiser normalized before rotation or not. GPR-Varimax was conducted with unrotated and multiple ( = 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.
梯度投影旋转（GPR）是一种可公开获取且很有前景的因子和成分旋转工具。我们将主成分分析中针对方差最大化准则的GPR与SPSS中内置的方差最大化程序进行比较。在一项模拟研究中，我们通过创建具有单个最优解以及两个最优解（一个全局最优解和一个局部最优解，即双最优条件）的总体简单结构，来测试GPR - 方差最大化是否会产生多个局部解。其他条件包括成分数量（= 3、6、9和12）、每个成分的变量数量（= 4、6和8）、每次旋转的迭代次数（= 25和250），以及旋转前载荷是否进行了Kaiser标准化。GPR - 方差最大化使用未旋转的以及多个（= 1、10、50和100）随机起始载荷进行。我们发现在大多数条件下，GPR - 方差最大化和SPSS - 方差最大化的结果相同。当使用Kaiser标准化载荷和每次旋转250次迭代时，有利于SPSS - 方差最大化的那些极小差异就消除了。在GPR - 方差最大化中从多个随机起始中选择最佳解，在具有Kaiser标准化载荷的双最优条件下会增加与总体成分的接近程度，在这种情况下GPR - 方差最大化比SPSS - 方差最大化能更好地恢复总体结构。我们还纳入了一个实证例子，发现在一个真实数据集中，GPR - 方差最大化和SPSS - 方差最大化对于正交简单结构产生了高度相似的解。我们建议GPR - 方差最大化可作为SPSS中方差最大化旋转的替代方法。GPR - 方差最大化的用户应允许至少进行250次迭代，在旋转前对载荷进行标准化，并从至少10个随机起始中选择最佳解以确保获得最优结果。
