Nguyen Hoang V, Waller Niels G
Department of Psychology, University of Minnesota, Twin-Cities.
Psychol Methods. 2023 Oct;28(5):1122-1141. doi: 10.1037/met0000467. Epub 2022 Jan 6.
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. (PsycInfo Database Record (c) 2023 APA, all rights reserved).
在探索性因素分析中，因素旋转算法从不同的起始点开始时可能会收敛到局部解（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，调查了五种因素旋转算法（方差最大化、斜交旋转、熵法和广义最小残差法（正交和斜交））局部解的发生率及其相关因素。我们总共模拟了16000个数据集，并进行了超过5700万次因素旋转，以检验（a）因素载荷大小、（b）因素指标数量、（c）因素交叉载荷、（d）因素相关大小、（e）因素载荷标准化、（f）样本大小和（g）模型近似误差对因素旋转中局部解频率的影响。我们还在一个包含54个人格项目的开源数据集的探索性因素分析中研究了局部解。在三项研究中，所有五种算法在某些条件下都会收敛到局部解，其中广义最小残差法（正交和斜交）产生的局部解数量最多。后续分析表明，当因素旋转产生多个解时，具有最大超平面计数（而不是最低复杂度值）的因素模式在均方误差上通常最接近总体因素模式。（《心理学文摘数据库记录》（c）2023美国心理学会，保留所有权利）
