How is the log likelihood scaled for glmer objects when using the Gauss-Hermite approximation for the integral?
Here are two fits:  one using the Laplace approx. (default value for nAGQ) and the other uses a 2-pt adaptive Gauss-Hermite approx. (nAGQ=2).  The log-likelihoods are too different to be attributed to the evaluation of the integral alone.


1.  > lme.bin=glmer(y~zb+zw+xw+(1+xw|cl.lme),family="binomial"); logLik(lme.bin)
'log Lik.' -237.8779 (df=7)

2.  > lmeGH.bin=glmer(y~zb+zw+xw+(1+xw|cl.lme),family="binomial", nAGQ=2); logLik(lmeGH.bin)
'log Lik.' -179.703 (df=7)


For comparison purposes, the all fixed effects glm model fit is:
> sim.glm=glm(cbind(y,n-y)~xw+zb+zw,family=binomial()); logLik(sim.glm)
'log Lik.' -308.2794 (df=4)

A nonparametric mixing distribution fit yields a log-likelihood of:  [1] -231.5072





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