How to Determine the Number of Factors to Retain in Exploratory Factor Analysis: A Comparison of Extraction Methods Under Realistic Conditions
How to Determine the Number of Factors to Retain in Exploratory Factor Analysis: A Comparison of Extraction Methods Under Realistic Conditions
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DOI：
10.1037/met0000200
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发表时间：
2019-08-01
影响因子：
7
通讯作者：
Moshagen, Morten
中科院分区：
文献类型：
--
作者：
Auerswald, Max;Moshagen, Morten
探索性因素分析通常用于确定多个观察变量的潜在因素。已经提出了许多标准来确定应该保留多少因素。在这项研究中，我们提出了一个广泛的蒙特卡罗模拟，以研究在不同样本量、每个因素的指标数量、负载大小、观察变量的潜在多变量分布下提取标准的性能，以及在一维、正交和相关因素模型中，交叉负载和次要因素的存在如何影响提取标准的性能。我们将传统的平行分析（PA）、Kaiser- guttman标准和顺序chi(2)模型检验（SMT）的几种变体与最近提出的4种方法进行了比较：修订PA、比较数据（CD）、Hull方法和经验Kaiser标准（EKC）。没有一个单一的提取标准对每个因素模型都是最好的。在一维和正交模型中，传统的PA、EKC和Hull即使在小样本中也始终显示出较高的命中率。具有相关因子的模型更具挑战性，其中CD和SMT优于其他方法，特别是在较短尺度下。虽然交叉加载的存在通常会增加准确性，但非正态性实际上对大多数标准没有影响。我们建议研究人员使用SMT和Hull、EKC或传统PA的组合，因为如果这些方法收敛，因子的数量几乎总是正确检索的。当这种组合规则的结果不确定时，传统的PA、CD和EKC表现相对较好。然而，分歧也表明因素将更难检测，将样本量要求增加到N >= 500。
Exploratory factor analyses are commonly used to determine the underlying factors of multiple observed variables. Many criteria have been suggested to determine how many factors should be retained. In this study, we present an extensive Monte Carlo simulation to investigate the performance of extraction criteria under varying sample sizes, numbers of indicators per factor, loading magnitudes, underlying multivariate distributions of observed variables, as well as how the performance of the extraction criteria are influenced by the presence of cross-loadings and minor factors for unidimensional, orthogonal, and correlated factor models. We compared several variants of traditional parallel analysis (PA), the Kaiser-Guttman Criterion, and sequential chi(2) model tests (SMT) with 4 recently suggested methods: revised PA, comparison data (CD), the Hull method, and the Empirical Kaiser Criterion (EKC). No single extraction criterion performed best for every factor model. In unidimensional and orthogonal models, traditional PA, EKC, and Hull consistently displayed high hit rates even in small samples. Models with correlated factors were more challenging, where CD and SMT outperformed other methods, especially for shorter scales. Whereas the presence of cross-loadings generally increased accuracy, non-normality had virtually no effect on most criteria. We suggest researchers use a combination of SMT and either Hull, the EKC, or traditional PA, because the number of factors was almost always correctly retrieved if those methods converged. When the results of this combination rule are inconclusive, traditional PA, CD, and the EKC performed comparatively well. However, disagreement also suggests that factors will be harder to detect, increasing sample size requirements to N >= 500.