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.

Empirical growth benchmarks, as introduced by Hill, Bloom, Black, and Lipsey (2008), are a well-known way to contextualize effect sizes in education research. Past work on these benchmarks, both positive and negative, has largely avoided confronting the role of vertical scales, yet technical issues with vertical scales trouble the use of such benchmarks. This article introduces vertical scales and outlines their role in the creation of empirical benchmarks for growth. I then outline three strands of recent vertical scale research that call into question the grounds for relying on these benchmarks. I conclude with recommendations for researchers looking to contextualize observed effects of educational interventions without confounding their effects with vertical scaling artifacts.