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.