Covariates in Growth Mixture Modeling
Message/Author
 Andrea Dalton posted on Thursday, February 11, 2010 - 2:45 pm
In a growth mixture model with covariates, why is it important to regress covariates on BOTH the growth factors and the categorical latent variable used to represent class membership? I am thinking of the following basic example for a 2-class model (User's Guide, 8.1):

MODEL: %OVERALL%
i s | y1@0 y2@1 y3@2 y4@3;
i s ON x;
c#1 ON x;

If x is used to determine class membership based on its effect on i and s, then why would it also give information about the odds of belonging to class 1 vs. class 2?

I understand from my reading that it's very important to regress covariates on both the growth factors and the latent classes, but I can't see why. It looks like double-counting.
 Bengt O. Muthen posted on Friday, February 12, 2010 - 8:21 am
The way I think about this is that the most important path is from x to c. This says that class membership probability is a function of x, which in turn implies that the means of i and s are influenced by x since those means change over classes (this is like an indirect effect). The regression of i and s on x is saying that even within a given class is there influence from x. For instance, a high x value for a subject may make it more likely for the subject to be in a c class that has a high i mean (that's c on x). But within that high class, it may also be true that the higher the x value is for a subject the higher the subject's i value (that's i on x). Conceptually, you can think of i on x as a partial (residual) effect, holding c on x constant.

This also speaks for the possibility that i s on x can vary across classes because it may not be the case that x has this same extra influence in all classes.
 Andrea Dalton posted on Friday, February 12, 2010 - 8:44 am
Thanks for the reply - this makes sense, except that when I run this model, the regression coefficients and standard errors for i s ON x are identical across classes! Is this the result of a default setting that can be changed? Do I have to specify that I want i s ON x estimated differently for each class?
 Linda K. Muthen posted on Friday, February 12, 2010 - 9:28 am
The default is for these parameters to be held equal across classes. To relax this equality, you need to mention the regressions in the class-specific parts of the MODEL command.
 Sheila Frankfurt posted on Friday, October 01, 2010 - 8:21 am
Hi Linda,

I've been looking through the Mplus manual and the discussion board for the syntax to relax this equality. I'm not having any luck finding this, though. How exactly do I relax this constraint? For example, here is my syntax now for a 4 class LCGA model with one covariate:

Title: latent class growth analysis on bsi hostility with covariates
Variable: names are id hos1 hos2 hos3 hos4 x1 x2 x3;
usevar=hos1-hos4 x3;
IDVARIABLE = id;
missing = all(999);
CLASSES = c(4);
SAVEDATA: FILE IS hos_four_priorvic_output;
save=cprobabilities;
Analysis: type = MIXTURE missing;
STARTS = 10 2;
STITERATIONS = 10;
Model: %Overall%
i s|hos1@0 hos2@2 hos3@6 hos4@12;
i-s@0;
i s ON x3;
c#1 ON x3;
c#2 ON x3;
c#3 ON x3;
Output: sampstat standardized tech1 tech4 tech8 tech11 tech14;
PLOT: SERIES = hos1-hos4 (s);
TYPE=PLOT3;

Thank you very much for all your help!
 Linda K. Muthen posted on Saturday, October 02, 2010 - 10:49 am
You relax equality constraints by mentioning the parameter in a class-specific part of the MODEL command, for example,

%c#1%
c ON x3;
 Sheila Frankfurt posted on Sunday, October 03, 2010 - 8:13 pm
Hi Linda,

Thank you very much for your help! I have another question about how to relax the equality constraint in the model. I added this syntax to the model:

Title: latent class growth analysis on bsi hostility with covariates
Variable: names are id hos1 hos2 hos3 hos4 x1 x2 x3;
usevar=hos1-hos4 x1;
IDVARIABLE = id;
missing = all(999);
CLASSES = c(2);
SAVEDATA: FILE IS hos_two_childage_output;
save=cprobabilities;
Analysis: type = MIXTURE missing;
STARTS = 10 2;
STITERATIONS = 10;
Model: %Overall%
i s|hos1@0 hos2@1.5 hos3@5.5 hos4@11.5;
i-s@0;
i s ON x1;
c#1 ON x1;
%c#1%
Output: sampstat standardized tech1 tech4 tech8 tech11 tech14;
PLOT: SERIES = hos1-hos4 (s);
TYPE=PLOT3;

However, when I run it, I ON X1 and S ON X1 in the model results output doesn't vary between classes, which is what I'm trying model when I relax the equality constraint. Am I doing something wrong?

Thank you again for your help!!!
Sheila
 Linda K. Muthen posted on Sunday, October 03, 2010 - 9:07 pm
You need to specify after %c#1% the statements that you want to vary like I showed above. If you can't figure this out, please send your input, data, output, and license number to support@statmodel.com.
 Sheila Frankfurt posted on Friday, October 08, 2010 - 12:11 pm
Hi Dr. Muthen,

I am still having problems relaxing the equality constraints in my model. I have sent my question to support@statmodel.com

Thank you very much!
Sheila