Moderation with a latent class variable: A tutorial and example

Moderation analyses allow a more nuanced understanding of the relationship between a predictor and an outcome. A limitation of traditional moderation analysis arises when addressing the hypothesis when using a moderator that does not account for unobserved heterogeneity in the population. This limitation can be addressed by extending moderation analyses to include a latent class analysis with auxiliary variables (as predictors and/or outcomes) where the moderator is the latent class variable. This tutorial specifies this extended moderation model with a latent class variable using the three-step manual approach (Asparouhov & Muthén, Structural Equation Modeling: A Multidisciplinary Journal, 21, 329-341, 2014). Data from the Longitudinal Survey of American Life illustrates this approach within the context of science attitudes. Specifically, a latent class variable (science attitudes) is hypothesized to moderate the relationship between a predictor (science achievement) and an outcome (interest in science issues), while controlling for demographic variables.