st: gllamm and u-shaped cumulative logits over time

[Thomas Herold <thomasherold@gmx.net>]

Dear statalist users,

I am working on a longitudinal dataset dealing with depression, measured 
as ordinal variable (1: none, 2: mild, 3:moderate, 4: severe). There are 
5 measurement points (t0-t4) and two different groups (T0=conventional 
treatment GP, T1=new treatment). I want to find out whether the 
treatment has an influence on the development of the depression score. I 
would normally use the -gllamm- command with the model (without a random 
slope) looking something like this:

gllamm depr week treatment interact, i(id) link(ologit) adapt eform

, where week is the time tx-t0 and interact=week*treatment.

But here is my problem: The development over time (and over time by 
group) is not linear but clearly (!) u-shaped. There is a short-term 
effect in both groups, i.e. the depression scores decline considerably 
from t0 to t1. However, in the long run (t1-t4), the scores in both 
groups increase again and often even exceed the initial value at t0. For 
obvious reasons, the above model fits the data very poorly.

Any help would be much appreciated.

Best,
Thomas
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