Xia Yan, Green Samuel B, Xu Yuning, Thompson Marilyn S
Arizona State University, Tempe, AZ, USA.
Educ Psychol Meas. 2019 Feb;79(1):85-107. doi: 10.1177/0013164418754611. Epub 2018 Feb 7.
Past research suggests revised parallel analysis (R-PA) tends to yield relatively accurate results in determining the number of factors in exploratory factor analysis. R-PA can be interpreted as a series of hypothesis tests. At each step in the series, a null hypothesis is tested that an additional factor accounts for zero common variance among measures in the population. Integration of an effect size statistic-the proportion of common variance (PCV)-into this testing process should allow for a more nuanced interpretation of R-PA results. In this article, we initially assessed the psychometric qualities of three PCV statistics that can be used in conjunction with principal axis factor analysis: the standard PCV statistic and two modifications of it. Based on analyses of generated data, the modification that considered only positive eigenvalues ( ) overall yielded the best results. Next, we examined PCV using minimum rank factor analysis, a method that avoids the extraction of negative eigenvalues. PCV with minimum rank factor analysis generally did not perform as well as , even with a relatively large sample size of 5,000. Finally, we investigated the use of in combination with R-PA and concluded that practitioners can gain additional information from and make more nuanced decision about the number of factors when R-PA fails to retain the correct number of factors.
以往的研究表明，在探索性因素分析中确定因素数量时，修正平行分析（R-PA）往往能得出相对准确的结果。R-PA可以被解释为一系列的假设检验。在这个系列的每一步，都要检验一个零假设，即额外的一个因素在总体测量中所解释的共同方差为零。将效应量统计量——共同方差比例（PCV）——纳入这个检验过程，应该能够对R-PA结果进行更细致入微的解释。在本文中，我们首先评估了三种可与主轴因素分析结合使用的PCV统计量的心理测量特性：标准PCV统计量及其两种修正形式。基于对生成数据的分析，总体上仅考虑正特征值（ ）的修正形式产生了最佳结果。接下来，我们使用最小秩因素分析来检验PCV，这是一种避免提取负特征值的方法。即使样本量相对较大达到5000，使用最小秩因素分析的PCV总体表现也不如 。最后，我们研究了将 与R-PA结合使用的情况，并得出结论，当R-PA未能保留正确的因素数量时，从业者可以从 中获得更多信息，并对因素数量做出更细致入微的决策。
