In exploratory factor analysis, factor rotation algorithms can converge to local solutions (i.e., local minima) when they are initiated from different starting points. To better understand this problem, we performed three studies that investigated the prevalence and correlates of local solutions with five factor rotation algorithms: varimax, oblimin, entropy, and geomin (orthogonal and oblique). In total, we simulated 16,000 data sets and performed more than 57 million factor rotations to examine the influence of (a) factor loading size, (b) number of factor indicators, (c) factor cross loadings, (d) factor correlation size, (e) factor loading standardization, (f) sample size, and (g) model approximation error on the frequency of local solutions in factor rotation. We also examined local solutions in an exploratory factor analysis of an open source data set that included 54 personality items. Across three studies, all five algorithms converged to local solutions under some conditions with geomin (orthogonal and oblique) producing the highest number of local solutions. Follow-up analyses showed that, when factor rotations produced multiple solutions, the factor pattern with the maximum hyperplane count (rather than the lowest complexity value) was typically closest in mean squared error to the population factor pattern.

中文翻译：

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探索性因子分析中的局部最小值和因子旋转。

在探索性因子分析中，当因子旋转算法从不同的起点开始时，它们可以收敛到局部解（即局部最小值）。为了更好地理解这个问题，我们进行了三项研究，调查了使用五种因子旋转算法的局部解决方案的普遍性和相关性：varimax、oblimin、entropy 和 geomin（正交和倾斜）。我们总共模拟了 16,000 个数据集并执行了超过 5700 万次因子旋转，以检查 (a) 因子载荷大小、(b) 因子指标数量、(c) 因子交叉载荷、(d) 因子相关大小、 (e) 因子加载标准化，(f) 样本量，以及 (g) 因子旋转中局部解的频率的模型近似误差。我们还在对包含 54 个个性项目的开源数据集进行探索性因素分析时检查了本地解决方案。在三项研究中，所有五种算法都在某些条件下收敛到局部解，geomin（正交和倾斜）产生最多数量的局部解。后续分析表明，当因子旋转产生多个解时，具有最大超平面数（而不是最低复杂度值）的因子模式通常在均方误差上最接近总体因子模式。