An example of a model with two crossed random effects is:
ui + vj + e,
where u and v are the random effects.
Crossed random effects causes problems in many software packages, particularly when there are many levels of crossings.
In ADMB-RE there is no limit to the number of crossed levels you can have (but there is of course an upper
limit to total number of random effects element you can put in).
The current model is a logistic regression with 5 crossed random effects (with 10 levels within each):
u1i1 + u2i2 + u2i2 + u3i3 + u4i4 +
There are about 5,000 observations (0's or 1's) for randomly selected combinations of i1,...,i5.
It takes about 4 minutes to fit the model.