2 correlated random effects with quadrature?

Ross Boylan <ross at ...> writes:

Is there a way to fit generalized linear mixed model with 2 correlated
random effects in R, using quadrature?  At the moment, I'm only
concerned with binary outcomes.

When I try glmer from lme4 with the quadrature argument I get
Error: AGQ only defined for a single scalar random-effects term

Yes, I know 2 dimensional quadrature is slow.

Ross Boylaln

I don't know offhand of an R package that will do this.  I'm pretty
sure AS-REML uses PQL (not even Laplace approximation): AD Model Builder can 
only do GHQ for nested/grouped models (i.e. not crossed) with a single
random effect per block.  As far as I know you're simply out of luck:
both GHQ and the ability to handle crossed random effects are fairly
rare among GLMM platforms, and the combination seems even rarer.
I presume you've (1) compared Laplace approximation to GHQ with simpler
examples and (2) compared Laplace approximation to 'truth' in simulations
and found it wanting in one or both cases?  One alternativepossibility 
for improving the quality of the approximation would be to use importance
sampling in AD Model Builder ...