Mathematical definition of random slope models


New Member
Good morning everyone! I have implemented the following lme model in r:
lme_mod<-lme(Value ~ Time+Treatment+Time*Treatment, random = ~ 1+Time| person_ID, method="ML", data=C)
*Time is repeated 3 times for each patient (time=1,2,3)

I am analyzing the following residuals: resid(lme_mod)

Could you write to me the mathematical definition of this model and in particular the mathematical expression/formula of the
to better explain these residuals
? Which kind of residuals are them?

Thank you very much