Let's take the Pixel dataset as example.
Grouped Data: pixel ~ day | Dog/Side
Dog Side day pixel
1 1 R 0 1045.8
2 1 R 1 1044.5
3 1 R 2 1042.9
pixel is the response. Dog with 10 levels. Side with 2 levels. day with 9 levels.
I want to fit a model where the covariance matrix is the direct(kronecker) product between the 10x10 identity Dog matrix, 2x2 identity Side matrix, a the 9x9 AR1 day matrix.
So should it be something like
lme(pixel~1,corr=corAR1(form~1|Dog/Side),weights=varIdent(form=~1|Dog*Side),data=Pixel)
But here I have got a nesting structure between Dog and Side in the corr term. Although this is correct for this dataset, I want it to be cross Dog:Side in general. Furthermore, I am not sure the different components corr and weights will be combined together using direct product internal of lme.
p.s. I understand this dataset is not balanced, so not all 10x2x9=180 combinations are present. But I still need the direct product structure in general, perhaps suitably adjusted for the missing levels.
