The value of q is the total number of random effects and the value of
n is the number of observations. I included that check because it did
not make sense to me to try to fit more random effects than you have
observations.
I guess I could be persuaded that it would make sense
in some circumstances because the random effects are determined by a
penalized least squares optimization.
What is the nature of the model that would require it to have more
random effects than observations?
Commonly, genetic models fit 2 or more random effects per individual, with
different prespecified covariance matrices (A, D, A*A, A*D...)