Coding of slope coefficients in condi...
Message/Author
 Tor Neilands posted on Monday, December 15, 2014 - 8:54 pm
I've fitted the following conditional LCGM to 4 time points:

int slope | baseline@1 twenty_h@0 thirty_h@0 forty_ho@0 ;
baseline twenty_h thirty_h forty_ho (1) ;
int slope ON ncogen1 ;
ncogen2 ON int slope ncogen1;

I understand that this coding allows for a decrease in the slope from baseline to the post-baseline measurements and then all post-BL measurements are the same.

As I understand it, the random intercept term in this model refers to the (conditional) post-BL status. We are also interested in the (conditional) BL status, which I tried to obtain by recoding the slope coefficients to:

int slope | baseline@0 twenty_h@-1 thirty_h@-1 forty_ho@-1 ;

I was expecting that the the model chi-square and slope results would be the same across the models (which they are for unconditional versions of the two models), but they aren't. Can anyone tell me why the results are different across these two models and what I would need to do to obtain estimates of the regression of initial status on the ncogen1 covariate and the regression of the ncogen2 distal outcome onto initial status from the first model? Thanks!
 Tihomir Asparouhov posted on Tuesday, December 16, 2014 - 3:50 pm
Your expectations are correct but you need to add "int with slope;" in both models.
 Tor Neilands posted on Tuesday, December 16, 2014 - 11:03 pm
Thanks! The log-likelihoods, chi-square, mean slope, etc. are now the same for the two models as expected. I have one remaining confusion: Why are the regressions of the distal outcome identical for the intercept-as-predictor, but different for the slope-as-predictor?

NCOGEN2 ON
INT -0.019 0.010
SLOPE 0.001 0.007

NCOGEN2 ON
INT -0.019 0.010
SLOPE 0.020 0.012

I would have thought that with the intercept latent variable representing different status points, the regressions of NCOGEN2 on INT would differ, but the regressions of NCOGEN2 on SLOPE would be the same since the slope is the same in the two models.
 Tihomir Asparouhov posted on Thursday, December 18, 2014 - 10:12 am
It is a direct reparameterization.

In the first model

NCOGEN2 ON
INT (a)
SLOPE (b);

In the second model

NCOGEN2 ON
INT1 (a1)
SLOPE1 (b1);

INT1=INT+SLOPE
SLOPE1=SLOPE

a1=a
b1=b-a

The fact that the slope stays the same doesn't mean that the coefficient for it stays the same. Since it is a multiple regression the coefficient depends on the covariances with the other predictors and that changes.
 Tor Neilands posted on Thursday, January 08, 2015 - 8:28 pm
Please excuse my tardiness in thanking you for this extremely clear and helpful response. It is very much appreciated!

With best wishes for a happy 2015,

Tor Neilands
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