A critical assumption in exploratory factor analysis (EFA) is that manifest variables are no longer correlated after the influences of the common factors are controlled. The assumption may not be valid in some EFA applications; for example, questionnaire items share other characteristics in addition to their relations to common factors. We present a computationally efficient and robust method to estimate EFA with correlated residuals. We provide details on the implementation of the method with both ordinary least squares estimation and maximum likelihood estimation. We demonstrate the method using empirical data and conduct a simulation study to explore its statistical properties. The results are (a) that the new method encountered much fewer convergence problems than the existing method; (b) that the EFA model with correlated residuals produced a more satisfactory model fit than the conventional EFA model; and (c) that the EFA model with correlated residuals and the conventional EFA model produced very similar estimates for factor loadings. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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一种计算高效且稳健的方法，用于估计具有相关残差的探索性因素分析模型。


探索性因素分析（EFA）的一个关键假设是，在控制公共因素的影响后，显性变量不再相关。该假设在某些全民教育应用中可能无效；例如，除了与共同因素的关系之外，调查问卷项目还具有其他特征。我们提出了一种计算高效且稳健的方法来估计具有相关残差的 EFA。我们提供了使用普通最小二乘估计和最大似然估计来实现该方法的详细信息。我们使用经验数据演示该方法，并进行模拟研究以探索其统计特性。结果是：（a）新方法遇到的收敛问题比现有方法少得多； (b) 具有相关残差的 EFA 模型比传统 EFA 模型产生了更令人满意的模型拟合； (c) 具有相关残差的 EFA 模型和传统 EFA 模型对因子载荷的估计非常相似。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。