[R-sig-ME] nAGQ

[Ben Bolker]

Can you give a few more details of your simulations? E.g. response
distribution, mean of the response, cluster size?

On Sat, Jul 6, 2024, 9:52 PM John Poe <jdpoe223 using gmail.com> wrote:

> 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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