Abstract
Examining interactions among predictors is an important part of a developing research program. Estimating interactions using latent variables provides additional power to detect effects over testing interactions in regression. However, when predictors are modeled as latent variables, estimating and testing interactions requires additional steps beyond the models used for regression. We review methods of estimating and testing latent variable interactions with a focus on product indicator methods. Product indicator methods of examining latent interactions provide an accurate method to estimate and test latent interactions and can be implemented in any latent variable modeling software package. Significant latent interactions require additional steps (plotting and probing) to interpret interaction effects. We demonstrate how these methods can be easily implemented using functions in the semTools package with models fit using the lavaan package in R, and we illustrate how these methods work using an applied example concerning teacher stress and testing.
Highlights
Phenomena are rarely influenced by only one variable; rather, it is often the case that the effect of one variable on another depends on the level of third variable or even two other variables
We provide details about implementing product–indicator methods but here we list some advantages of using product indicators, foremost of which is that they can be applied in any structural equation model (SEM) software package using standard estimation procedures
0.055–0.062, CFI = 0.957, TLI = 0.944, and SRMR = 0.039, with the test value negatively related to Teacher instructional practices (TIP), b = −0.12, SE = 0.02, and p < 0.001 and sources of stress positively related to TIP, b = 0.72, SE = 0.03, and p < 0.001
Summary
Phenomena are rarely influenced by only one variable; rather, it is often the case that the effect of one variable on another depends on the level of third variable or even two other variables. Interactions, or moderation, occurs when the strength or sign of a relationship between two variables, x and y, depends on the value of a third variable, z. Moderation is represented with a statistical interaction by calculating the product of the two predictors of interest and including the product as an additional predictor in the model. A structural equation model (SEM) can include regressions among latent variables (e.g., common factors or growth factors), which are unobserved. Without observing individual subjects’ values (factor scores), it is not possible to multiply latent factor scores to calculate a product term to be included in the model, and other methods must be implemented [6,7,8,9,10]
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