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Message/Author
 Pablo Mora posted on Monday, June 20, 2005 - 7:22 am
I have lots of questions regarding mixture modeling. First, Iíll give the context of my study. I have a sample of over 700 participants who were assessed over three times (baseline, 3, and 6 months). I am interested in determining whether I can find classes in trajectories for a number of variables. I know that many of these variables (e.g., symptoms) follow a quadratic trajectory, at time 1 most participant report a high number of symptoms, at time 2, there is a dramatic drop in symptom reporting, and at time 3 levels are similar to the levels reported in time

Now my questions
General
1. Given that my variable(s) change in a quadratic fashion I think I should try to model a quadratic change. Is this correct? What are the implications of not doing so?
2. Related to the previous question, I am new to GMM so I played with a linear trend only and got similar estimated values and trajectories (graphs) for the groups. Why does this happen? Should I not get different estimates and graphs if I only use a linear change variable?
3. I am also puzzled by the different results I get when I change the values within groups (e.g., starting values). I know there are ways to compare models in order to determine which ones are the best; however, the number of models I could estimate by specifying values for the different classes is almost infinite. So whatís the best way to delimit the number of models I run and compare given that the only thing I know is the overall trajectory of the sample? (or what and when is enough?)
Specific about syntax
4. Just want to make sure that I am understanding the syntax:
i) Is this the right way to specify a quadratic trajectory for the full model and a linear for class 1?
%overall%
i by physxs@1 physxs2@1 physxs3@1;
s by physxs@0 physxs2@1 physxs3@2;
s2 by physxs@0 physxs2@1 physxs3@4;
[physxs@0 physxs2@0 physxs3@0 i s s2];
%c#1%
s2@0;
s2 with s@0;
s2 with i@0;
ii) If I had only a linear trajectory specified, what would a command like the following do?
%c#1%
s*; (will this allow a higher order slope?)

Output.
5. Iíve seen the following errors messages in my outputs as well as in examples from the statmodel website and from the lab material from Bengt Muthenís class. What do they mean exactly?

i) Does the following error mean that my model is no good therefore I need to keep working on a better solution?

WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN CLASS 1 IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE
THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE I.

ii) Based on the TECH1 output the parameter mentioned (i.e., 5) is ďS,Ē how can I deal with the following error in order to prevent the error situation?

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ILL-CONDITIONED FISHER INFORMATION MATRIX. CHANGE YOUR MODEL AND/OR STARTING VALUES.
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-POSITIVE DEFINITE FISHER INFORMATION MATRIX. THIS MAY BE DUE TO THE STARTING VALUES
BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS -0.836D-17.
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THIS IS OFTEN DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. CHANGE YOUR MODEL AND/OR
STARTING VALUES. PROBLEM INVOLVING PARAMETER 5.

iii) Whatís the meaning of this? What can I do to fix this? (Parameter 9 is alpha/C#1)

ONE OR MORE MULTINOMIAL LOGIT PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT DISTRIBUTION OF THE CATEGORICAL LATENT VARIABLES AND ANY INDEPENDENT VARIABLES. THE FOLLOWING PARAMETERS WERE FIXED: 9

Thank you very much for your help
 Linda K. Muthen posted on Monday, June 20, 2005 - 8:27 am
1. If your theory and data point to a quadratic growth curve, then you should try this model.

2. If it is the wrong growth shape, then I would not pay attention to the findings.

3. You should use random starts as provided in Version 3. See the STARTS option of the ANALYSIS command.

4. i. It looks correct but it's simpler to use the new growth language. See Chapter 16.

ii. This would relax the equality of the slope growth factor variance for Class 1.

5. i. Yes, that message means your model has a problem.

ii. and iii. You need to send your output, data, and license number to support@statmodel.com. This is a data-model dependent problem.
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