An example of a linear regression model with nested random effects (2 levels) is:
ui + uij + eijs,
where ui and uij are the random effects.
In the current example the models is a logistic regression with 4 levels of nesting, i.e.
the random effects part looks like:
ui + uij + uijk + uijkl
To effiently implement this model in ADMB-RE one must make use of the SEPARABLE_FUNCTION keyword.
In this particular example i=1,...,100, j=1,2, k=1,2 and l=1,2.
So by calling the SEPARABLE_FUNCTION for each value of i, one in effect breaks up the computation
into 100 smaller computations, which helps ADMB-RE avoid dealing with large matrices (800x800 in this case).
It takes about 1-2 minutes to fit the model.