I have been working on revisions on a paper using DSEM, and one of the reviewers has asked us for a metric of effect size for our DSEM parameter estimates, but I am not having much luck figuring out the best way to address this. Specifically, the paper presents a two-level random effects model for which we are estimating random within-person parameters at level one (e.g., variance, mean) and then regressing these random effects on between-person covariates at level 2. All within-person random effects are based off of items with the same (ordinal) scale.
Should we be looking at unstandardized coefficients (or some transformation of these), standardized coefficients, one-tailed p-values, or some other statistic for effect sizes? Or is this not possible in DSEM? Thank you for your time.
Thank you for this! We have actually already used standardized coefficients, and use latent mean centering for variable decomposition across within- and between-person levels (along with centering of observed between-person variables), consistent with the Schuurman et al paper. We are stuck on how to interpret the standardized coefficients (or R squared values) in a way that allows comparisons to other studies or to standard measures of effect size (pearson r, Cohen's d, etc). Is there a way to do this that you or others might be aware of? Whether in MPlus or using some external formula or equation. Thank you!
Perhaps looking at the more detailed version of that would help output:stdyx(cluster); This will give you the standardized model for each cluster separately. The interpretation of that is the same as in single level SEM and standard regression. I think the Schuurman paper has the insights that you are seeking. What might also help you is comparing the standardized coefficients for the DSEM model against the two-level model (i.e. when you drop all autocorrelations).
1. Multilevel models don't have auto-correlation. DSEM standardized coefficients include the auto-correlation.
2. The easiest way is to test the significance of the auto-correlation parameters. If you have just one you can use the credibility interval. If you need to test multiple coefficients you can use the Model Test command in Mplus.