Class varying (co)variance paramters ...
Message/Author
 Anonymous posted on Saturday, September 03, 2005 - 11:44 am
Dear Bengt and Linda:
I am attempting to fit a GGMM for 166 salespeople's monthly sales performance, with 6 observations on each salesperson. Based on your chapter in Collins and Sayer (2001), Bengt, I first attempted to separately fit one-class linear, quadratic, and freely estimated solutions to the growth curve, and found all fit stats suggesting the quadratic curve to be the best solution. However, when I attempt to fit a 2- or 3-class solution with the quadratic curve, I get an error message about the PSI (residual covariance) matrix involving the quadratic growth factor. Instead, reverting to the freely estimated lambda coefficients yields convergence, with a 3-class freely estimated solution finding greatest support. My questions are:

1. Does this make sense? Why am I not able to obtain multi-class solutions for the quadratic constrained model?
2. My understandng of MPlus is that by default, Mplus estimates class-varying means for the growth factors and keeps elements of the (co)variance matrix class-invariant; my attempts to estimate class-varying (co)variance parameters using the i s or i with s commands separately as well as together, however, have been unsuccessful thus far. I get a matrix inversion error message.
3. Your chapter in Collins and Sayer (2001) states that GGMM differs from LCGA only in that the growth factor covariance matrix is fixed to 0 (no within-class trajectory variation is allowed) in the latter. I gathered that MPLUS allows for such within-class variation with a RANDOM statement appended to the end of the TYPE=MIXTURE command. When I did this, however, I did not see any change in ANY of the parameter estimates. What am I doing wrong?

FYI, here's the relevant part of my code:

ANALYSIS: TYPE = MIXTURE;
STARTS = 20 2;

MODEL: %OVERALL%
i s | lsales0@0 lsales1@1 lsales2@2 lsales3*3 lsales4*4 lsales5*5;
!i s ON mthsdel cooper;

%c#1%
i s ;
!i with s;
!lsales0-lsales5;

%c#2%
i s ;
!i with s;
!lsales0-lsales5;

!%c#3%
!i s ;
!i with s;
!lsales0-lsales5;

Your insights would be greatly appreciated.
 BMuthen posted on Monday, September 05, 2005 - 2:52 pm
1. When you use a mixture model, part of the variation in the growth factors is absorbed by the different classes having different growth factor means and there is therefore less variation left within class. Depending on your psi matrix message, you might consider fixing the quadratic growth factor variance to zero.

2. See number 1.

3. You don't have to have RANDOM. If your outcomes are categorical, TYPE=MIXTURE; gives LCGA by default and you may have to add ALGORITHM = INTEGRATION; to get growth factor variances estimated. If this is not sufficient information, please send your input, data, output, and license number to support@statmodel.com. It is difficult to answer data dependent questions. These are more appropriate for Mplus support.