What are the assumptions of a random slope model? In particular I am interested in knowing the assumptions about level-1 and level-2 residuals and what are their expected theoretical distributions.
My model in R is this,
OUTCOME ~ DAY+MEDICINE+DAY*MEDICINE, random = ~ 1 + DAY| ID_SUBJECT
Where I have two days (DAY = 1, 2) for each subject. What theoretical distribution should I expect for the residuals considering that for each subject I have a pair of residuals, for DAY=1 and DAY=2?
In particular I am interested in knowing the assumptions about level-1 and level-2 residuals and what are their expected theoretical distributions.
The usual assumptions are that the random effects are distributed multivariate normal. This assumption makes some of the maths behind fitting the model tractable.
Depending on what use the model is to be put, then we might also like the conditional distribution of the response to be normally distributed - and for that we would like the level-1 (unit level) residuals to be normally distributed.