Mplus Discussion >> Piecewise GMM with individually varying times

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Piecewise GMM with individually varyi...

Mplus Discussion > Latent Variable Mixture Modeling >

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Bruce A. Cooper posted on Thursday, March 13, 2014 - 3:53 pm

I'm running GMM for a symptom variable for six assessments. First is immediately following treatment, 2nd is at an expected high point for maximum symptoms, 3rd is after symptoms are reduced, and just prior to next treatment. The second set of three assessments repeats this pattern. I think a piecewise model will fit this data best with two quadratic curves like ^ ^ . I confirmed this pattern fit the data best with a pw latent growth model using isq (compared to simple linear, LQ, & LQC), and have gotten GMM solutions with the pw model. I have individually varying times of assessement available. Is it possible to estimate a piecewise model like this also using IVT of assessment for LG and GMM models?
Thanks!
Bruce

Linda K. Muthen posted on Friday, March 14, 2014 - 4:31 pm

The AT option is available for GMM models.

Bruce A. Cooper posted on Friday, March 14, 2014 - 5:23 pm

Thanks, Linda!
I know how to do that, but I'm puzzled about how to set up a piecewise model to identify two series, while also using the AT command for the varying times. Right now, my code for a pw latent growth model without the AT command is:

i s1 q1 | y0@0 y1@1 y2@2 y3@2 y4@2 y5@2 ;
i s2 q2 | y0@0 y1@0 y2@0 y3@1 y4@2 y5@3 ;

Do I still just add the AT t1-t6 at the end of each line? (I tried it and it didn't work, so if that's the correct procedure I'm doing something wrong.)
Thanks, Bruce

Linda K. Muthen posted on Sunday, March 16, 2014 - 11:56 am

See Example 6.12 which uses the AT option. See the TSCORES option and the data set which shows how the TSCORE variables are scored. To use AT with a piecewise model, you would have to generalize the time scores from the piecewise model to the TSCORE variables.

Jon Heron posted on Monday, March 17, 2014 - 8:06 am

Hi Bruce

I banged my head against this for ages and finally found a solution. This was for LGM but I expect it extends to GMM readily enough. There's a trick to it.

Here's my post:

http://www.statmodel.com/discussion/messages/14/478.html?1332152261
(scroll down to March 19th 2012)

cheers, Jon

Bruce A. Cooper posted on Monday, March 17, 2014 - 12:34 pm

Thanks Linda & Jon -

This is terrific solution, Jon - Thanks!

Best,
Bruce

Bruce A. Cooper posted on Monday, March 17, 2014 - 3:16 pm

Hi Linda & Jon -
If I may take advantage of your suggestion, Jon ...
I tried the model with the improved syntax you provided, and it worked (!) but the model did not fit as well conceptually as the regular pw model with "averaged" assessment times. :-(
Oh, well.
But, what do you think about using a factor approach to allow the program to provide the means across time?
I tried:

MODEL: i BY rg0-rg5@1 ;
s BY rg0@0 rg1@1 rg2* rg3* rg4* rg5* ;
rg0-rg4 PWITH rg1-rg5 ;
[ rg0-rg5@0 ] ;
[ i s ] ;
s@0 ;
i WITH s@0 ;

and the pattern of means for S BY ... was just what I expected for these symptoms, with a piecewise-like ^^ pattern with 2 quadratic frowns!
Any thoughts would be great!
Thanks, Bruce

Jon Heron posted on Wednesday, March 19, 2014 - 2:05 am

Hi Bruce

not sure what I feel about a free-curve approach. Have you read this?
http://www.ncbi.nlm.nih.gov/pubmed/23880389

Can you obtain your frown-model by fitting a high-order polynomial?

I'm also wondering whether you might benefit from splitting your data into more time points - I recently managed to fit a 4 time point "AT-model" as a 50 time point model with no age variability. There you have a simple way of building in some of the additional information on actual age.