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Mplus Discussion > Growth Modeling of Longitudinal Data >
 Scott posted on Sunday, October 07, 2007 - 3:33 pm
I am running growth mixture modeling analyses, specifying specific groups (e.g., male vs. female; sexual offender vs. index offender vs. nonoffender). My DVs are indexes of self report delinquency across 7 assessment waves. How would I compare the trajectories across these different groups? Would I need to calculate t tests by hand for the intercepts, linear slopes, & quadratic slopes to see if the trajectories are different, or is there some other method? I have been using MLR estimation.

 Linda K. Muthen posted on Monday, October 08, 2007 - 5:48 am
Growth mixture modeling involves classes based on unobserved heterogeneity. Are all of your groups observed?
 Scott posted on Monday, October 08, 2007 - 6:47 pm
Yes, they are observed. What would this be called then? Just growth model? In the User's Guide, there is an explanation for GMM for known classes (multiple group analysis). Is this somehow different? If so, would I use the grouping option of the VARIABLE command and then use TYPE=GENERAL MISSING (there are MAR data) and ML option under the ANALYSIS command?
 Linda K. Muthen posted on Tuesday, October 09, 2007 - 6:00 am
In the user's guide example, there are two categorical latent variables. One is used for KNOWNCLASS, the other is not. In your case, you are doing a multiple group growth model. All groups are defined by observed variables. Yes, you would use the GROUPING option and TYPE=GENERAL MISSING H1;
 Scott posted on Tuesday, October 09, 2007 - 8:06 pm
For a 2 group model, what should I look at in terms of output to see if the groups differ from each other? Is this an omnibus test (in other words, how would I know what groups differ from other groups if I had 3 or more groups)? Here is an excerpt of the stats:

Chi-Square Test of Model Fit
Value 1073.940
Degrees of Freedom 198
P-Value 0.0000

Chi-Square Contributions From Each Group

Chi-Square Test of Model Fit for the Baseline Model
Value 5302.518
Degrees of Freedom 176
P-Value 0.0000

CFI 0.829
TLI 0.848

H0 Value -10506.506
H1 Value -9969.536

Information Criteria
Number of Free Parameters 46
AIC 21105.012
BIC 21355.849
Sample-Size Adjusted BIC 21209.712

Estimate 0.072
90 Percent C.I. 0.067 0.076

Value 0.210
 Linda K. Muthen posted on Wednesday, October 10, 2007 - 7:22 am
The first step with multiple group growth modeling is to fit the growth model in each group separately. If the same growth model does not fit in both groups, it does not make sense to analyze the groups together and compare growth factors means, variances, and covariances.
 Scott posted on Wednesday, October 10, 2007 - 7:54 pm
I have tried to fit the growth model in each group, but the fit statistics do not reveal good fitting models (I have tried linear, quadratic, and cubic growth curves)--e.g., RMSEA > .10, CFI/TLI < .90, sig chi sq. Do you have suggestions on what I could do to get adequate model fit?
 Linda K. Muthen posted on Thursday, October 11, 2007 - 5:59 am
Have you looked at modification indices to see where the misfit is?
 Michael Spaeth posted on Thursday, October 11, 2007 - 12:29 pm
Don't want to make a new thread and i think my question is comparable to scott's problems. I want to evaluate a primary prevention programme dealing with alcohol use in young adolescents. I have a pre-test and three follow ups. I expect heterogeneity regarding the trajectories and differential programme effects for those.

I plan the following analysis:

1.) single class LGCA seperately for control and treatment group to get a clue
2.) multi group LCGA analyses to test for overall effects of the programme, also checking for treatment baseline interaction
3.) LGMM seperately for treatment and control group
4.) LGMM with treatment group as dummy coded covariate with slopes regressed on it

Regarding point 4... Obviously it is not possible in this model to test for treatment/initial status interaction...!? Would you recommend a model pretty much like Example 8.8 in the manual (gmm with multiple group)? Or is this "too much"!? Can i use the above mentioned covariate model instead, when i have found no interaction in point 2?

a little bit off topic... Because we measure alcohol consume (continous variable) at an very early age at time 1 and time 2 (10 years old) we have many zero values. Is that a problem? how can i handle that?

Many thanks!
 Linda K. Muthen posted on Thursday, October 11, 2007 - 3:26 pm
Your analysis plan sounds reasonable.

If your trajectories differ more in the intercept of the trajectories rather than in the slope and the treatment effect is allowed to vary across classes, you are testing for a treatment/initial status interaction.

For models with a preponderance of zeros, you could consider two-part modeling. See Example 6.16 and the reference mentioned there.
 Michael Spaeth posted on Friday, October 12, 2007 - 2:11 am
Thanks so much!

regarding the zeros... Exists there any threshold for this problem so that it is not ingorable? the problems with zero becomes more and more weaker within the last two measurement points. Is this a problem for model 6.16?
I've heard of adding a constant and doing a log transformation of those raw scores to overcome the problem of nonnormal distributions. Is that an alternative?

If not, seems a little bit complicated to me, to combine 6.16 with my analysis steps 3 and 4. Exists there any example or paper doing that!?

Thanks for helping very interested beginners in LGCA! :-)
 Linda K. Muthen posted on Friday, October 12, 2007 - 10:13 am
I don't think a log transformation would avoid the piling up of values. I would say you should have at least 20 percent zeros for two-part modeling. Following is a cross-sectional paper that goes through the steps of two-part modeling that may help you:

Kim, Y.K. & Muthén, B. (2007). Two-part factor mixture modeling: Application to an aggressive behavior measurement instrument.

It can be downloaded from the website.
 Michael Spaeth posted on Monday, October 15, 2007 - 10:23 am
Once again, thanks for these helpful recommendations.
1.) I went through the above mentioned article and was wondering how to apply the two-part modeling issue within my longitudinal LGMM Study. The only related article i had found was the Brown et al. paper from your website. But this study only deals with two-part LGM (single class analysis). Exists there any example/paper integrating the two-part modeling in the LGMM framework?
2.) Based on your recommendation to have at least 20 percent zeros for two part modeling. Imagine we measure alcohol consumption in a longitudinal study at the age of ten till the age of 16. At the age of 14, 15 or 16 there might be less zeros in the sample, may be 19 percent or less. Would be piecewise modeling an alternative? (First piece with two-part modeling, second piece without) Or exist there other ways to handle that problem?

Thanks so far!
 Linda K. Muthen posted on Tuesday, October 16, 2007 - 12:27 pm
1. I don't know of any paper but the one I suggested. You would have to generalize from there.
2. I would stick with two-part.
 EFried posted on Monday, March 26, 2012 - 7:38 am
Running GMMs with categorical outcome variables, does one use (apart from BIC, tech11 & tech14) the Chi-Square test "for ordered categorical outcomes" or "for MCAR under unrestricted LC indicator model" to determine model fit?

Thank you
 Linda K. Muthen posted on Monday, March 26, 2012 - 8:09 am
The MCAR test is not a test of model fit.

The two chi-square tests can be used if the number of indicators is eight or less and if the two tests agree.
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