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Mplus Discussion > Structural Equation Modeling >
 Brian S. Connelly posted on Tuesday, June 16, 2009 - 8:42 am
I am doing a set of comparisons of two nested SEM models in which a second predictor of a latent criterion variable is added to a model specifying only a single predictor. Specifically:
Model 1:
Predictor 1: common factor across 3 rating sources

Model 2:
Predictor 1: common factor across 3 rating sources
Predictor 2: residual variance in 1 of the rating sources

The goal is to test whether what 1 of the raters uniquely perceives predicts the criterion above and beyond what is predicted by the common variance in ratings. For some of these comparisons, the estimate of variance explained in the criterion reduces in Model 2 from that in Model 1. This is at odds with the way I think about R-squared values in OLS, where adding a second predictor should yield an R-square at least equal to the single predictor alone. Do you have any insight about what might be causing this?
 Linda K. Muthen posted on Wednesday, June 17, 2009 - 9:14 am
Adding a predictor can cause a misspecified model in which case anything can happen to R-square.
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