Causal Effects Based on Latent Variable Models

Building on the stochastic theory of causal effects and latent state-trait theory, this article shows how a comprehensive analysis of the effects of interventions can be conducted based on latent variable models. The proposed approach offers new ways to evaluate the differential effects of interventions for substantive researchers in experimental and observational studies while allowing for complex measurement models. The key definitions and assumptions of the stochastic theory of causal effects are first introduced and then four statistical models that can be used to estimate various types of causal effects with latent state-trait models are developed and illustrated: The multistate effect model with and without method factors, the true-change effect model, and the multitrait effect model. All effect models with latent variables are implemented based on multigroup structural equation modeling with the EffectLiteR approach. Particular emphasis is placed on the development of models with interactions that allow for interindividual differences in treatment effects based on latent variables. Open source software code is provided for all models.