SEM estimation choices

[SRL]

Hello,

I have clustered data with non-normally distributed dependent variable.
I am running multiple group comparison model in SEM path analysis.
It would be nice if I can use vce(cluster) option with ADF estimation, but STATA won't let me.
So I tried
Model 1) running SEM with ADF estimation
pro: address non-normality issue, detailed goodness of fit statistics available
con: clustered error not addressed
Model 2) running SEM with ML estimation with clustered errors
pro: address the clustered nature of data
con: non-normality issue not addressed, only residual goodness of fit available

I hit a stumbling block as the results differ drastically depending on the estimation method.
Any suggestions on which issue is more important or what the decision rule needs to be?

Thanks

[ben earnhart]

Is this SEM (Stata 12) or GSEM (Stata 13)? I've been curious what they can and cannot do. If it's SEM, check out GSEM. If you're already using GSEM, consider Mplus.

[SRL]

I am using SEM in stata 13 with group comparisons. I was wondering if they can be done in SEM as GSEM does not allow group-comparison (or as easily...)

[ben earnhart]

One thing you might do is to see what the ICCs are for some of your more normally distributed variables. Low ICCs, and it would help bolster an argument for model 1. This isn't to say that ICCs couldn't be low for some variables and high for others, but it's a bit of an argument. High ICCs *and* non-normality, you might need to use Mplus. Hopefully somebody will chime in with more extensive experience with SEM in Stata (I know SEMs in general, but mainly from Lisrel and Mplus). The limits on what SEM and GSEM can and cannot do sometimes seem strange to me.

ps. Have you ran it under ML w/out clustering? If taking into account clustering doesn't change things much, then another argument for ADF. Again, weak, but it's something.

[Dick Campbell]

I am not sure what kind of a non-normal outcome you have. If it is a dichotomy or ordinal variable, you have to use GSEM or something like it, but you may be able to get closer to normality with some transformation if you have a continuous but non-normal outcome. In any case, the SEM literature shows quite clearly that chi-square goodness of fit tests and other related statistics are biased when you violate the MVN assumption. Your differing results for the two estimation methods show that.

SEM users often use a GROUPS approach when simpler approaches will do. If you are testing the equivalence of specific coefficients you may be able to get what you need with interactions.

[SRL]

Thanks for your inputs.

Ben Earnhart)
I did have high ICC.
Per your postscript, what motivated me to post this discussion in the first place. The result from ML w/o clustering is very similar to ADF (similar, but not exactly same; some of the mediator had differential effect. nevertheless, the main effect was similar for the variable of interest).
I was wanting to carry this out in STATA, but maybe it is time for me to learn Mplus...

Dick Campbell)
Ideally, I am trying to emulate blogit in SEM/GSEM framework; I have a series of binary variables for each observation. To my knowledge, this extension of grouped logistic is not available in GSEM, so I constructed percentage measures and ran SEM.