Department of Psychology, The College of New Jersey, Ewing, NJ 08628, USA.
Psychol Assess. 2012 Jun;24(2):282-92. doi: 10.1037/a0025697. Epub 2011 Oct 3.
Exploratory factor analysis (EFA) is used routinely in the development and validation of assessment instruments. One of the most significant challenges when one is performing EFA is determining how many factors to retain. Parallel analysis (PA) is an effective stopping rule that compares the eigenvalues of randomly generated data with those for the actual data. PA takes into account sampling error, and at present it is widely considered the best available method. We introduce a variant of PA that goes even further by reproducing the observed correlation matrix rather than generating random data. Comparison data (CD) with known factorial structure are first generated using 1 factor, and then the number of factors is increased until the reproduction of the observed eigenvalues fails to improve significantly. We evaluated the performance of PA, CD with known factorial structure, and 7 other techniques in a simulation study spanning a wide range of challenging data conditions. In terms of accuracy and robustness across data conditions, the CD technique outperformed all other methods, including a nontrivial superiority to PA. We provide program code to implement the CD technique, which requires no more specialized knowledge or skills than performing PA.
探索性因素分析（EFA）是开发和验证评估工具时常用的方法。在进行 EFA 时，最具挑战性的问题之一是确定要保留多少个因素。平行分析（PA）是一种有效的停止规则，它将随机生成的数据的特征值与实际数据的特征值进行比较。PA 考虑到了抽样误差，目前被广泛认为是最好的可用方法。我们引入了一种 PA 的变体，它更进一步，通过再现观察到的相关矩阵而不是生成随机数据。首先使用 1 个因子生成具有已知因子结构的比较数据（CD），然后增加因子的数量，直到观察到的特征值的再现无法显著提高为止。我们在涵盖广泛具有挑战性的数据条件的模拟研究中评估了 PA、具有已知因子结构的 CD 和其他 7 种技术的性能。在数据条件的准确性和稳健性方面，CD 技术优于所有其他方法，包括相对于 PA 的实质性优势。我们提供了实现 CD 技术的程序代码，该技术不需要比执行 PA 更多的专门知识或技能。
