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When latent variables are included, Mplus provides Rsquared estimateswhich is great. However, I'm confused about a specific result. I have a model in which Mplus estimates the Rsquared of a dependent variable as ranging between 0.004 and 0.871. However, this Rsquared 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 Rsquared 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 Rsquared isn't being permitted to have a CI that goes below zero, since the Rsquared can't go below zerobut, although that lets me interpret this output, that would make interpreting the Rsquared 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 twolevel random model that terminates normally and for which the PSR is good after 2X the original number of fbiterations. Any thoughts much appreciated. 


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. 


That's very helpful. Thanks! With the DIC: Would the idea be to drop the paths and see if the DIC is worse? 


Yes 


Thanks for confirming! 

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