# How add a fixed offset term to account for a known effect in a repeated measures mixed model?

I'm running a lmer with a continuous outcome TestY measured in each visit a participant makes to the study i.e. a longitudinal repeated measures analysis. The outcome is a tablet-based test and the value used is z-scored.

I'm interested in the role of a specific categorical predictor Group and it's interaction with time.

Overall, TestY declines with time. However, it is known that this sample of study participants actually have an increase - due to a learning effect - between first and second time they take the test. Thus, it would be important to adjust for this known effect, which seems to be possible by adding a fixed offset term.

Let's say the known effect is that between 1st and 2nd visit we have a +0.33 between these visits. But that's it, no adjustments for future visits would be of interest (follow-up goes like to mean 6 visits).

My lmer looks like this:

lmer(TestY ~ Group + Group:Time_bl + covariates + (1 + Time_bl | ptID))


Question: Does anyone has some light to shed on how could I possibly account for this .33 increase between first and second visit?

It seems I'd probably have to add VisitNumber to the model, but I can't imagine how to code this offset term only between first and second visit.