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 Michael Lap posted on Monday, March 12, 2018 - 8:12 am

I have run LCGA and identified 4 class trajectories. How can I find out if their latent class means differ from each other (class 1 from class 2, class 2 from class 3 etc.). Is there some kind of a post-hoc test available and how to request it? Thank you!
 Michael Lap posted on Monday, March 12, 2018 - 11:33 am
To clarify- in a 3-trajectory class solution, in the output, there is a section: Parameterization using Reference Class 1

which contains

C#2 -3.899 0.996 -3.916 0.000
C#3 0.325 0.587 0.554 0.580

Does it mean that Class 2 intercept is different from Class 1 but Class 3 intercept is not?
And if yes, does it mean that Class 1 and 3 the trajectories of cannot be reliably distinguished?
 Bengt O. Muthen posted on Monday, March 12, 2018 - 3:29 pm
You are probably referring to the means of the intercept and slope growth factors [i] and [s]. If so, simply label them for each class in the Model command and do test of their differences in Model Test.

As for c#2 and c#3, they have to do with class sizes and not trajectory differences.
 Michael Lap posted on Monday, March 12, 2018 - 5:12 pm
Thank you, Bengt.
1) Where can I find an example of the Model test?
2) "As for c#2 and c#3, they have to do with class sizes and not trajectory differences."
Does it mean that in my case, the size of Class 3 (number of cases) is not different from the size of Class 1? But Class 2 and Class 1 are different in terms of their sizes?
Thank you, I appreciate your help.
 Bengt O. Muthen posted on Monday, March 12, 2018 - 5:51 pm
1) Look up Model Test in the UG index.

2) Yes (assuming you have no C on X).
 Michael Lap posted on Monday, March 12, 2018 - 6:37 pm
Thank you, Bengt.
I did check the Users guide. The only example I could find was on factor analysis. However, in another thread on GMM I found the following syntax:

[tcdel16] (m1);

[tcdel16] (m2);

[tcdel16] (m3);


The syntax is used for distal outcomes, which I don't have.

How should this syntax be modified to suit LCGA with 4 classes and covariates (predictors of class membership)?

2) if I have 4-5 covariates (x's) - then how the interpretation would change?
 Bengt O. Muthen posted on Tuesday, March 13, 2018 - 11:42 am
I would not go about the analysis that way. I would first focus on whether C or C-1 classes is required by looking at BIC. If say 2 classes has a much better BIC than 1 class, I would report the 2-class solution. I would not bother with testing if [i1], [s1] are different from [i2], [s2] - referring the the means of the intercept and slope growth factors in the case of no covariates. But if you want to, simply say

[i1] (i1);
[s1] (s1);
[i2] (i2);
[s2] (s2);

Model Test:
0 = i2-i1;
0 = s2-s1;

With covariates, these parameters would refer to intercepts in the regressions on the covariates and would therefore be less informative about trajectory differences.
 Michael Lap posted on Wednesday, March 14, 2018 - 12:34 pm
Thank you very much, Bengt.
Actually, the number of class trajectories was finalized based on the BIC, entropy, and Lo-Mendel-Rubin statistic. By using the Model test, I was hoping to make sure that all detected class trajectories do indeed differ from each other (intercepts and slopes). However, as you said, the Model test is less informative in the situation with covariates in the model.
 Livia Sacchi posted on Monday, June 03, 2019 - 4:02 am
Dear Drs. Muthen,
I am running a 3-class GMM CI with predictors and covariates. I am using the 3-step approach with adjustment for classification errors.

Referring to Micheal's post (the 4th from the top) and your related reply "Yes (assuming you have no C on X).", I was wondering if you could help me interpreting the size of classes when covariates are included in the model.

In my model, when Class 1 is the reference one, and when age, education, sex, smoking habit and alcohol habit are included, I obtain these values:

C#2 -4.649 3.890 -1.195 0.232
C#3 1.658 3.155 0.525 0.599

Both estimates are non significant. However, class sizes are different when checking the counts and proportion table.

Thank you for your help.
 Tihomir Asparouhov posted on Monday, June 03, 2019 - 5:00 pm
If you want to estimate the class counts in the situation with covariate it would be best to use the output


Unfortunately these don't come with confidence interval yet.

Looking at the intercepts alone is not very useful because in evaluating class counts you would need to include the entire multinomial regression with the covariates. In addition the posterior class probabilities vary across observations because the covariates vary.

For a particular set of covariates you can obtain CI for the posterior class probablities using the multinomial regression formula in model constraints. For the entire population, as an approximation, one can use the average covariate value (see output:tech7) instead of actual covariate values. This can yield good confidence interval estimates for the class counts.
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