What exactly constitutes a "level" in mixed models? In most texts I have read levels seem to be synonym with random variables (student ID, classroom, school, etc). But can predictors also be levels? For example, if I'm interested in math scores, family income, and IQ, can I say these are levels nested within students?
As an example consider this data set:
df = data.frame(ID=rep(c("ID1","ID2","ID3","ID4","ID5","ID6"),each=4), scores=floor(runif(24, min=0, max=100)), age=rep(c(14,17,14,16,18,12),each=4), test=rep(c(1,2),times=12), day=rep(c("day1","day2"),each=2,times=6),school=rep(c("A","B"),each=12))
I'd read it as
school as the upper level (level 1), then pupil
ID nested within schools (level 2), then
day nested within pupil ID? (level 3), then
test nested within day (level 4). Is that correct? What about
age, can that be considered a separate level as well?