Standard common factor models, such as the linear normal factor model, rely on strict parametric assumptions, which require rigorous model-data fit assessment to prevent fallacious inferences. However, overall goodness-of-fit diagnostics conventionally used in factor analysis do not offer diagnostic information on where the misfit originates. In the current work, we propose a new fit assessment framework for common factor models by extending the theory of generalized residuals (Haberman & Sinharay, 2013). This framework allows for the flexible adaptation of test statistics to identify various sources of misfit. In addition, the resulting goodness-of-fit tests provide more informative diagnostics, as the evaluation is performed conditionally on latent variables. Several examples of test statistics suitable for assessing various model assumptions are presented within this framework, and their performance is evaluated by simulation studies and a real data example.

翻译：标准的公共因子模型，如线性正态因子模型，依赖于严格的参数假设，这需要严谨的模型-数据拟合评估以防止错误的推断。然而，因子分析中传统使用的整体拟合优度诊断方法无法提供关于拟合不良来源的诊断信息。在当前工作中，我们通过扩展广义残差理论（Haberman & Sinharay, 2013），提出了一种用于公共因子模型的新拟合评估框架。该框架允许灵活调整检验统计量，以识别各种拟合不良的来源。此外，由于评估是在潜变量条件下进行的，所得的拟合优度检验能提供更具信息量的诊断。本文在该框架内提出了几个适用于评估不同模型假设的检验统计量示例，并通过模拟研究和真实数据案例评估了其性能。