R-squared change in structural equation models with latent variables and missing data.

Researchers frequently wish to make incremental validity claims, suggesting that a construct of interest significantly predicts a given outcome when controlling for other overlapping constructs and potential confounders. Once the significance of such an effect has been established, it is good practice to also assess and report its magnitude. In OLS regression, this is easily accomplished by calculating the change in R-squared, ΔR, between one's full model and a reduced model that omits all but the target predictor(s) of interest. Because observed variable regression methods ignore measurement error, however, their estimates are prone to bias and inflated type I error rates. As a result, researchers are increasingly encouraged to switch from observed variable modeling conducted in the regression framework to latent variable modeling conducted in the structural equation modeling (SEM) framework. Standard SEM software packages provide overall R measures for each outcome, yet calculation of ΔR is not intuitive in models with latent variables. Omitting all indicators of a latent factor in a reduced model will alter the overidentifying constraints imposed on the model, affecting parameter estimation and fit. Furthermore, omitting variables in a reduced model may affect estimation under missing data, particularly when conditioning on those variables is essential to meeting the MAR assumption. In this article, I describe four approaches to calculating ΔR in SEMs with latent variables and missing data, compare their performance via simulation, describe a set of extensions to the methods, and provide a set of R functions for calculating ΔR in SEM.