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I'm currently working on a DSEMCFA for my dissertation and I'm trying to figure out how to interpret the random innovation variance, seeing as it is log transformed. A larger innovation result (Mean = ~3) when exponentiated is actually a very small number. But when the innovation result is smaller (Mean =~ .3), this exponentiates to a larger number. Because of this relationship, I'm not sure how to interpret the credible intervals or the covariance between the innovation variance and phi. Any help would be appreciated! 


If you have a model like this %within% V  Y; phi  Y on Y&1; %between% V with phi; Y with V Phi; [Y V phi]; then the residual variance of Y on the within level is subject specific, V and Phi are random effects. You can obtain factor scores for these and the parameters are subject specific. If the factor score for a particular cluster is V=3, then the residual variance for Y on the within level is EXP(V), i.e. abut 20. If V=0.3 the residual variance for Y for that cluster would be 1.3. You might find the option output:residual(cluster) tech4(cluster); useful in seeing that as well as plots. Both S and Phi are cluster specific parameters and the distribution of these parameters form the estimates on the between level. The interpretation of V with Phi is just like the interpretation for any other between level parameter, it would be interpreted the same way as Y with Phi, i.e., the interpretation does not get affected by what the implications are for the within level residuals. 


Ah, I think I get it! I realized that I did not include in my original post that the values were actually negative (so V=3 and .3), which then exponentiated to a smaller and larger positive number, respectively. But I see now that even though V approaches 0 as it gets less negative, EXP(V) is actually growing, so the correlations between V and phi are still interpretable. I also would love some input on getting ICCs for DSEMCFA. I saw another post about ICCs in a standard DSEM; can that same method be applied to a DSEM factor analysis? Additionally, would be interested in hearing what plots you think might be most useful for a DSEMCFA. 


For ICC see https://www.statmodel.com/download/ICCinDSEM.pdf You can get all the available plots using this command plot: type is plot3; factors=all; savedata: file=1.dat; save=fs(200); There is a lot but among those you can plot observed v.s. estimated within level cluster specific variances, as well as time series plots. 


Thanks! I saw that thread and it is helpful. My advisor believes that these are the residual variances (i.e. what is "leftover" after accounting for the factor model). Is this accurate? Or is the residual output the accurate and complete variances for the items while removing the bias of things like phi and V? 


I am not sure I understand the question but if you scatter plot Y(variance over within) v.s. Y(estimated cluster variance) these will represent for each cluster the observed and estimated quantity for the within level total variance(not just residual variance). 


Thank you! I apologize for my poorly worded question, but I was able to confirm that the residual output does give me what I need for the ICCs. Thank you for your help! 

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