r mixed model unstructured and ar1 covariance matrices

Question

My goal is to specify two different covariance matrices for two different random intercepts.

Briefly, this is my dataset.

Outcome is continuous (school test scores)

13 Schools in my study. Random students selected for testing. All students who were selected were tested. Students nested within Schools.

I am interested in estimating the random intercept for each School and each Student.

So this is my model.

lme( y ~ SchoolName + Age + Sex, random = ~1 | SchoolName/StudentID, data= df)

I am interested in

• Schools following unstructured covariance matrix
• Students , ar1.

I have another variable time, which is a discreate variable that takes values either 10,11,12,13 . So I specified the model like this

`lme( y ~ SchoolName + Age + Sex, 
     random = ~1 | SchoolName/StudentID, 
     correlation = corAR1(form = ~1 | time/StudentID,
 data= df)`

I am seeing an error, "Incompatible formulas in random and correlation", How to resolve this error. Please help.

Answer 1

Sointu is right. But it seems that it is possible to use something like this, where I use an example of my own:

HAR <- lme(read ~ 1+occf, data=da, random= ~1|school, 
           correlation=corAR1(form = ~ occasion |school/id),
           weights = varIdent(form = ~1|occasion))

This way you get a random intercept across schools, and a heterogeneous AR1 structure across time points (occasion) within student id.

But you say you'd like an unstructured covariance matrix across schools. The above would give a compound symmetry structure. I cannot easily understand why you would like an unstructured pattern for schools. Suppose you have maximally 20 students in a school. Then the unstructured pattern would try to estimate 1/22021=210 (co)variances. That would be very hard to estimate. Also, there is no logical order for the students in a school, they are exchangeable I guess, and thus the compound symmetry structure seems more plausible.