I have a question regarding shared effects in my model. My formula is as follows:
fomula = ... + f(r.Y, model="iid", hyper = list(theta = list(initial=log(L.Y),fixed=TRUE))) + f(b.Y, copy="r.Y", hyper = list(beta = list(initial = tau, fixed = TRUE))).
In this setup, Y appears in both Model 1 and Model 2, and they are meant to share the same random effect. I have Y in model 1 and tau*Y in model 2. I expected r.Y and b.Y to have the same values. However, I noticed that the estimates of r.Y and b.Y differ.
I came across the explanation that "the main difference between the copy and replicate features is that with the copy effect, the values of the random effects are the same, but copied effects can be scaled by a parameter." I’m wondering if the difference in estimates is due to b.Y being scaled, and if so, what parameter is responsible for this scaling?
Additionally, which of the two—r.Y or b.Y—should be considered the true estimate of Y?
Thank you for your help.