I have a straightforward path model with a single endogenous variable and multiple observed predictors – in other words, a regression. (I'm doing it as a path model to be able to easily test mediation later). For now, I really need to know how to test for significance in R2 as I add predictors – the same as you get with the F-change statistic in OLS. If there's no straightforward way, is there perhaps a formula I could do by hand? Thanks in advance!

# Solved – A way to compute significance of R-squared change across models in a path model, or specifically lavaan

model comparisonpath-modelr-squaredregressionstructural-equation-modeling

## Best Answer

If I understand correctly, you would like to compare alternative

`SEM`

models. In this case, I believe that you have to use thescaled chi-square difference test statistic(withSatorra-Bentler correction): see http://www.statmodel.com/chidiff.shtml and (the original paper) http://link.springer.com/article/10.1007%2Fs11336-009-9135-y. You can perform this test by using`lavaan`

's function`anova()`

, which automatically detects the presence of nested models and applies the correction.For a non-nested models comparison, you could use either one of the following R packages:

`nonnest2`

(http://cran.r-project.org/web/packages/nonnest2) and`simsem`

(http://cran.r-project.org/web/packages/simsem). Both packages support`lavaan`

classes' objects. For`simsem`

, in addition to the documentation, you can take a look at non-nested models comparison examples here.