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 Star David posted on Sunday, August 08, 2010 - 7:38 am
hello,

I'm trying to find a model of the development of children's indirect aggression with LCGA. I've test the liner model and the quadric model as well as the cubic model with 1 2 3 and 4 classes separately, and I find the 3-class quadric model is the best fitting model (with no warning) among all above. My first question is: Is that correct for me to find the best model in an order as I described above?
When I trying the 4-class quadric model, I find a BIC lower than the 3-class model but with a warning as below:
ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE
INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY DUE TO THE
MODEL IS NOT IDENTIFIED, OR DUE TO A LARGE OR A SMALL PARAMETER
ON THE LOGIT SCALE. THE FOLLOWING PARAMETERS WERE FIXED:
7 8
Here is my second question: under what condition the problem would happen, and what should I do to solve it? And should I accept the 4-class model or not considering the lower BIC and the warning?

Thank you very much!
 Linda K. Muthen posted on Sunday, August 08, 2010 - 11:12 am
We usually start with one class to find the best-fitting growth model and then look for the proper number of classes. It may be that for some classes, you will see that some growth factor variance should be fixed at zero.

Regarding the parameters that are fixed, it depends on what they are. Please send the full output as an attachment and your license number to support@statmodel.com.
 Star David posted on Sunday, August 08, 2010 - 6:29 pm
"It may be that for some classes, you will see that some growth factor variance should be fixed at zero.
", with my understanding, LCGA allow no variance of growth factor,is it? Then how should I fix "some growth factor" at zero, which seems to mean that some are not zero?

I will send it soon.

Thanks for your help!
 Linda K. Muthen posted on Monday, August 09, 2010 - 8:54 am
You are correct. There are no growth factor variances and covariances with LCGA. With LCGA you would fix means of the growth factors to zero in classes where they are very small.
 Star David posted on Monday, August 09, 2010 - 11:14 pm
Thank you very much! your answer makes me more clear about LCGA.

I have an additional question: Since GMM allows variances of growth factor, which is an advantage compared with LCGA. Then how do we choose the proper method (GMM or LCGA)? Dose it depend on our data and theory?

I have such a question because I have seen some researches using LCGA first and then let some of the growth factor to be freely estimated. And I also have seen some researches using GMM, leting all the parameters to be freely estimated first and then fix those which are not significant according to the output. I really want to figure it out what's the differences between these two approaches and which one is better?
 Linda K. Muthen posted on Tuesday, August 10, 2010 - 9:56 am
The difference between the two approaches is that GMM estimates means, variances, and covariances of growth factors. LCGA estiamtes only means of growth factors. I think it is more likely that there is variability on the growth factors within classes. I think it is a rare case when all individuals within a class are the same. I would use GMM and if the growth factor variances are estimated at zero or are not significantly different from zero, I would just leave that as is. I would not fix growth factor variances to zero unless they are estimated as negative, small, and not significant.

You might find the following paper which is available on the website of interest:

Muthén, B. & Asparouhov, T. (2009). Growth mixture modeling: Analysis with non-Gaussian random effects. In Fitzmaurice, G., Davidian, M., Verbeke, G. & Molenberghs, G. (eds.), Longitudinal Data Analysis, pp. 143-165. Boca Raton: Chapman & Hall/CRC Press.

See in particular the crime curve example.
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