st: gllamm model with random slopes in time varying covariates

[Michael Ingre <Michael.Ingre@ipm.ki.se>]

Dear Statalist

I would like to regress individual differences in change over time in 
time varying covariates on individual differences in change over time 
in of my dependent variable. This calls for a random coefficient model 
with -gllamm- where random effects (slope in covariates) are regressed 
on another random effect (slope in the dependent variable).

The reason for trying this model is that I want to show that individual 
differences in the change over time (slope) in the dependent variable 
is "explained" by individual differences in the change over time 
(slope) in my covariates.

I have no problem with defining a model with a random intercept and 
slope for the dependent variable. And regressing a random effect on 
another random effect is also quite straightforward.

My problem is the slope for the covariates. I first thought that 
defining a random effect that multiply the interaction covariate*time 
would do the trick. But now I'm not sure any more. The model (I'm not 
sure of any more) is described below:

. gen const                = 1
. gen cov1_time            = cov1*time	
. gen cov2_time            = cov2*time
	
. eq int:      const
. eq slope0:   time
. eq slope1:   cov1_time
. eq slope2:   cov2_time

. matrix b = (0,1,1,1\ 0,0,0,0\0,0,0,0\0,0,0,0)

. gllamm y time cov1 cov2 , i(id) link(ident) fam(gauss) nrf(4) ///
.   eq(slope0 intercept slope1 slope2) nocorrel bmatrix(b) trace dots 
adapt

This is complicated stuff for me. I'm now questioning the meaning of my 
slope1 and slope2. They multiply the random effect with the interaction 
cov*time. But does this mean that they describe individual differences 
in change in covariates over time? Or what do they mean?

In the case I am on the right track: Should I include the interaction 
cov*time as a fixed effect also?

The answer I'm afraid of is that I need to model three parallel growth 
curve models to answer my question (6 random effects 3 intercepts and 3 
slopes).

Please, help me out. I cant think straight anymore (!!!)

Thanks for your time!

Michael

WARNING: Don't try this at home, unless you have a supercomputer or 
lots of time!

------------------------------------------------
Michael Ingre , PhD student & Research Associate
Department of Psychology, Stockholm University &
National Institute for Psychosocial Medicine IPM
Box 230, 171 77 Stockholm, Sweden

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