Precluding Interpretational Confounding in Factor Analysis with a Covariate or Outcome via Measurement and Uncertainty Preserving Parametric Modeling

In latent variable models, interpretational confounding occurs when the inclusion of a covariate or outcome when fitting the model alters the results for the measurement model. Commonly used estimation procedures do not preclude this possibility. Multi-stage estimation approaches preclude interpretational confounding, but most are limited in that they do not properly propagate uncertainty from earlier stages to later stages. This work introduces a measurement and uncertainty preserving approach to factor analytic models with covariates or outcomes, which additionally supports procedures for conducting diagnostic model-data fit analyses. These are examined in simulation studies, where they perform favorably relative to existing strategies, and illustrated with analyses of real data. Functions for conducting the analyses in freely available software are provided.

在潜变量模型中，当拟合模型时纳入协变量或结果变量会改变测量模型的结果时，便会出现解释性混淆。当前常用的估计方法均无法排除此类情况的发生。多阶段估计方法虽可规避解释性混淆，但多数此类方法存在局限：无法将早期阶段的不确定性正确传递至后续阶段。本研究提出了一种适用于带协变量或结果变量的因子分析模型的方法，该方法可保留测量特性与不确定性，同时支持开展模型-数据拟合诊断分析的相关流程。我们通过模拟研究对该方法及相关流程进行了检验，结果显示其表现优于现有同类策略，并通过真实数据分析案例对其应用进行了演示。此外，本文还提供了可在开源软件中执行上述分析的函数代码。