Latent distal regressed onto GGMM
Message/Author
 Keri Jowers posted on Thursday, March 12, 2009 - 3:41 pm
I have a 4-class LCA of distal risk variables that I want to regress onto a 2-class GGMM. Run independently, the LCA and the GGMM run without warnings. However, when I do the regression step, I get a warning that the psi matrix is non-positive definite with regards to the slope. When I look at the tech 4 output, the correlation between intercept and slope is, in fact, greater than 1 (1.121). Why would this be, and what is the best way to handle it? Constraining either the intercept or slope would be changing the measurement model, so I wouldn't think this would be the solution. Thanks in advance for your help!
 Bengt O. Muthen posted on Thursday, March 12, 2009 - 4:46 pm
The fact that you encounter this problem when adding the two model parts suggests that the outcomes of the GMM and the outcomes of the LCA are related to each other in a different way than you have specified. So for instance if you are saying

clca on cgmm;

you may miss the fact that you should also have, say,

clca on i;

where i is the growth factor intercept at the last time point. If that is the case, then the estimation tries to compensate for the left-out relationship and then gets the non-pos-def problem. - There may be other types of relationships left out; this is just an example.
 Keri Jowers posted on Thursday, March 12, 2009 - 4:58 pm

i might be doing something completely wrong... here is a sample of my input:

Model:
%overall%
i s | tocsum1@0 tocsum2@.5 tocsum3@1.5 tocsum4@2.5;
c2#1 on c1#1;
c2#1 on c1#2;
c2#1 on c1#3;
Model c1:
%c1#1%
[set start values as in original LCA]
%c1#2%
[set start values as in original LCA]
%c1#3%
[set start values as in original LCA]
%c1#4%
[set start values as in original LCA]
Model c2:
%c2#1%
[set start values as in original GGMM]
%c2#2%
[set start values as in original GGMM}

Is this completely off base? I was thinking that the "on" commands under the %overall% statement would perform the regression.
 Bengt O. Muthen posted on Thursday, March 12, 2009 - 5:08 pm
It performs the regression of c2 on c1 and therefore says that all the relationship between the 2 sets of outcomes has go through these 2 c variables - that may be too restrictive.

It looks like c1 is the LCA variable and c2 the GMM variable. Do you intend for c1 to influence c2 as you have specified? Your initial question stated it in the opposite direction.

An easy generalization is that say c1 influences the GMM growth factor means as well, not only c2.
 Keri Jowers posted on Thursday, March 12, 2009 - 5:35 pm
Exactly true about switching the on statements to c1 on c2 -- I've been staring at my screen too long today!

So, if I want to say that c1 influences the GMM growth factor means, too, I would simply add the following to the %overall% statement, right?

c2#1 on i;
c2#1 on s;

Thanks!
 Keri Jowers posted on Thursday, March 12, 2009 - 5:36 pm
i mean:
c1#1 on i;
c1#1 on s;
 Bengt O. Muthen posted on Thursday, March 12, 2009 - 6:02 pm
c1 influencing the growth factors i and s would have c1 on the right-hand-side of ON, not the way you have it.

But I was thinking of the approach of deleting Model c2 for the GMM part - this would imply that the growth factor means vary across both c1 and c2 classes, not only across c2 classes.
 Keri Jowers posted on Thursday, March 12, 2009 - 6:27 pm
So sorry for the repeated posts! I'm not understanding something in your last statement. How do I delete Model c2 for the GMM part and have the model understand that I'm regressing the LCA (that's no longer specified) onto the GMM? And it completely makes sense to allow the growth factor means to vary across c1 and c2 classes. I'm just stuck on how to accomplish that.
 Bengt O. Muthen posted on Friday, March 13, 2009 - 11:09 am
The Mplus default in mixture modeling is that latent variable means vary across all the classes. Your Model c2 replaced that with having the growth factor means vary across only the c2 GMM classes. So if you remove those Model c2 lines you will get the default. Keeping Model c1, the LCA indicator means vary across the c1 LCA classes. But GMM growth factor means vary across all the classes, which implies that the growth factors are influenced not only by the c2 GMM classes but also by the c1 LCA classes. You can see all of this happening by requesting and looking at TECH1 - you find the growth factor means in the alpha array (see UG for an explanation of the different parameter arrays).
 Keri Jowers posted on Friday, March 13, 2009 - 2:00 pm
and that wouldn't be considered changing the gmm measurement model? or at least, it would be a justifiable reason for doing so? the reasoning totally makes sense.
 Keri Jowers posted on Friday, March 13, 2009 - 2:21 pm
whew! i used your original suggestion of clca on i (and s), which resulted in no warnings! thank you so much! i'm still interested in knowing how this isn't essentially altering the gmm measurement model, though.
 Bengt O. Muthen posted on Friday, March 13, 2009 - 2:42 pm
Your GMM measurement model is determined by the

i s | ...

statement, so things are ok.
 Keri Jowers posted on Friday, March 13, 2009 - 3:31 pm
thanks! your help is much appreciated!