[R-sig-ME] nAGQ

[John Poe]

Hello all,

I'm getting ready to teach multilevel modeling and am putting together some
simulations to show relative accuracy of PIRLS, Laplace, and various
numbers of quadrature points in lme4 when true random effects distributions
aren't normal. Every bit of intuition I have says that nAGQ=100 should do
better than nAGQ=11 which should be better than Laplace. Every stats
article I've ever read on the subject also agrees with that intuition.
There was some debate over if it actually matters that some solutions are
more accurate but no debate that they are or are not actually more
accurate. But that's not what's showing up.

When I fit the models and predict Empirical Bayes means I look at
histograms and they look as close to identical as possible. When I use KL
Divergence and Gateaux derivatives to test for differences in the
distributions both show very low scores meaning the distributions are very
very similar.

Furthermore, when I tried a multimodal distribution they all did a bad job
of approximation of the true random effect. The exact same bad job.

I feel like I'm taking crazy pills. The only thing I can think that makes
any sense is lme4 is overriding my choices for approximation of the random
effects in the models themselves or the calculation of the EB means is
being done the same way regardless of the model.

Any ideas?

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