I’m modeling responses to a task in fairly straightforward way. Each person has multiple responses and they are expected to vary as different task factors change. I am allowing each person to have a different mean response, and for the effect of each task factor to vary by person as well. I also have some person-level variables that are constant within person. They are theoretically downstream consequences of the psychological processes being measured by the task, so I do not want to include them as independent variables that predict variation in the group terms / random effects. Rather, I want to use the random effects as latent variables to predict the individual-level variables.
The task might be modeled as:
response ~ 1 + factorA + factorB + (1 + factorA + factorB | id)
I would like to be able to regress
indiv_diff on the id-varying intercept and parameters for factorA and factorB simultaneously. So if, e.g., 1_id is a vector of individually varying intercepts, I’d like to be able to include the formulas
1_id ~ indiv_diff,
factorA_id ~ indiv_diff, etc, with each of those variables having length equal to the unique values of grouping variable
Is this (a) possible, and (b) ridiculous? For example, maybe I should just be using
indiv_diff without regard to where it lies on the theoretical causal diagram and use the following equation:
response ~ 1 + factorA + factorB + indiv_diff + factorA:indiv_diff + factorB:indiv_diff + (1 + factorA + factorB | id)
Thanks for your input!