Causal Parameter Moderation: Applying Moderated Nonlinear Factor Analysis to Causal Inference With Latent Outcomes

When studying latent outcomes in causal inference, causal effects can occur not only on the mean of the latent variable but also on all parts of the measurement model: the mean and residual variance of the latent variable, as well as the item parameters. This article proposes causal parameter moderation, the application of moderated nonlinear factor analysis (MNLFA) to causal inference with latent outcomes. The proposed approach can handle an arbitrary number of continuous or categorical covariates, making it well-suited to handling heterogenous treatment effects. Causal parameter moderation is compared to item-level heterogenous treatment effect (IL-HTE) models. The models are best suited to handle different types of differential item functioning (DIF), and thus the circumstances under which each is appropriate differ: IL-HTE models assume a normal distribution of DIF across all items, so they do not substantially correct bias introduced by a subset of items being extra-sensitive to treatment. The proposed MNLFA approach is shown to handle this scenario more effectively. The approach is demonstrated in a reanalysis of data from a randomized controlled trial of a reading intervention’s effects on science vocabulary, where there is substantial evidence of both a main effect on the latent variable and additional effects on a subset of items.