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 Thomas Rodebaugh posted on Thursday, June 21, 2018 - 3:37 pm
When latent variables are included, Mplus provides R-squared estimates--which is great. However, I'm confused about a specific result. I have a model in which Mplus estimates the R-squared of a dependent variable as ranging between 0.004 and 0.871. However, this R-squared is a result of a single regression coefficient, and the STDYX estimate CI for that coefficient is -0.902 to 0.912. How can it be that the R-squared has a credible interval that doesn't contain zero when the coefficient's interval does? (For that matter, it's centered on zero!) My first thought is that the R-squared isn't being permitted to have a CI that goes below zero, since the R-squared can't go below zero--but, although that lets me interpret this output, that would make interpreting the R-squared CI difficult in some circumstances (e.g., multiple predictors that you might expect to combine to predict significantly/credibly even if no one predictor does).

This occurs in a two-level random model that terminates normally and for which the PSR is good after 2X the original number of fbiterations.

Any thoughts much appreciated.
 Tihomir Asparouhov posted on Thursday, June 21, 2018 - 5:37 pm
Your first thought is correct. The posterior distribution consists of only positive values so by definition CI will not contain 0.

You can construct ML style CINT from the point estimate and the standard error
estimate +- 1.96 SE
and that would work well most of the time.

You can use also DIC for some more complex testing.
 Thomas Rodebaugh posted on Friday, June 22, 2018 - 9:42 am
That's very helpful. Thanks! With the DIC: Would the idea be to drop the paths and see if the DIC is worse?
 Tihomir Asparouhov posted on Friday, June 22, 2018 - 1:14 pm
 Thomas Rodebaugh posted on Tuesday, June 26, 2018 - 9:08 am
Thanks for confirming!
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