I am working on a 2 level SEM model with continuous observed variables loading onto a latent variable specified at Level 1 and 2, with numerous binary (e.g., sex) and continuous covariates (e.g., income) regressed on various predictors of the latent variable at both levels.
I have several questions regarding the 95CI and Effect size calculations.
1. Does Mplus offer an option to request confidence intervals for the standardized path coefficients?
2. Can effect sizes be calculated for individual unstandardized estimates and/or the R2? If “yes”, can you point me to a formula or reference that would illustrate the appropriate steps to calculate these?
1. The CINTERVAL option is for raw coefficients. You can use MODEL CONSTRAINT to create new parameters that are the standardized coefficients and then the CINTERVAL option will give confidence intervals for them.
2. If you ask for STANDARDIZED in the OUTPUT command, you will get R-square. You cannot get effect sizes automatically. See any standard statistics text for how to compute these.
I found a formula that explains how to calculate the effect size of a level 2 variable for multilevel analyses:
delta = 2 x B x SDpredictor/residual var at student level
However, I was wondering how you would calculate this with the output in Mplus when trying to calculate the effect size of a cross-level interaction? The B you can get from the regression of your random slope on your class-level variable (the B for the interaction effect), but how do you get the SD of your predictor when there is no actual predictor (i.e., you create a cross-level interaction by including a random slope and regressing it on your class-level variable, but you do not actually create a new predictor)? Or I am thinking in the wrong way?