It is straightforward to model "direct" changes using a mixed-effects model. Let's assume we have 3 correlated measures over time from a subject,
y1, y2 and y3. One can model these three outcome variables directly by regressing against time (independent variable) in both random and fixed effects. However, I wonder how I could approach a problem in which I have
y1 - y2,
y3-y1. In this case I do not have access to direct measures (
y1,y2 or y3), but pairwise changes over time (that I call "indirect"). Perhaps I can use the interval between
y3-y1 as both random and fixed effects, but with this approach the meaning of time is quite different.
So the question is: how would you organise your data frame for this scenario? How would you define time? My aim is to calculate annual changes with the mixed effects model for example.