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Abstract

We all know what latent variable models are. We use them all the time. Well, not all the time. In our paper, we show that investigators who start their work with latent variable models usually abandon such models when testing for interactions. For example, they might use SEM to show that latent-X and latent-Z both predict latent-Y, but then they use moderated regression with scale scores to test the X by Z interaction. Given that latent variable models are even more useful for multiplicative models than they are for additive models, this doesn’t make a lot of sense. By contrast, we show that papers that test only additive models tend to stick with SEM throughout. The reason for this paradox is almost certainly discomfort with methods for testing latent interactions. In an attempt to address this issue, we update the review of procedures contained in Cortina, Chen, and Dunlap (2001) and develop new R code for implementing some of the best procedures for testing latent interactions.

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