ABSTRACT In exploratory factor analysis (EFA), cross-loadings frequently occur in empirical research, but its effects on determining the number of factors to retain are seldom known. In this paper, we analyzed whether and how cross-loadings affected the performance of the parallel analysis (PA), the empirical Kaiser criterion (EKC), the likelihood ratio test (LRT), the comparative fit index (CFI), the Tucker-Lewis index (TLI), and the root mean square error of approximation (RMSEA) in determining the number of factors to retain. A large-scale simulation study was also conducted. A few conclusions can be drawn: (1) overall, PA provides the most accurate performance, especially when data are non-normally distributed; (2) cross-loadings noticeably affect the performance of PA, CFI, and TLI with different patterns, and they virtually have no effect on EKC, LRT, and RMSEA; (3) no method is immune to the sizable detrimental effect of normality assumption violation. Several recommendations were provided.

中文翻译：

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交叉加载对确定要保留的因子数量的影响

摘要 在探索性因子分析 (EFA) 中，交叉加载经常出现在实证研究中，但它对确定要保留的因子数量的影响很少为人所知。在本文中，我们分析了交叉加载是否以及如何影响并行分析 (PA)、经验凯撒准则 (EKC)、似然比检验 (LRT)、比较拟合指数 (CFI)、Tucker- Lewis 指数 (TLI) 和近似均方根误差 (RMSEA)，用于确定要保留的因子数。还进行了大规模的模拟研究。可以得出几个结论：（1）总体而言，PA 提供了最准确的性能，尤其是在数据非正态分布时；(2) 交叉负载显着影响不同模式的 PA、CFI 和 TLI 的性能，它们对 EKC、LRT 和 RMSEA 几乎没有影响；(3) 没有任何方法可以免受正态性假设违反的相当大的不利影响。提供了几项建议。