nAGQ

In lme4 the agq stuff is only for GLMMs, ie for glmer not lmer. I'm not
sure of the theory in your case ...

On Sun, Jul 7, 2024, 3:50 PM John Poe <jdpoe223 at gmail.com> wrote:

Sure,

I wrote several different random effects distributions based mostly on
mixtures of normals. The main idea was that I was trying to break anything
that would assume normality of the random effects when trying to
approximate them.

One of the worst cases I could come up with was a random effect
distribution that had two modes surrounding the mean, one mode was for a
normal distribution and one was for a weibull with a long tail. So both
asymmetrical and multimodal.

All of the simulations had 5000 groups with 500 observations per group
and a binary outcome. I wanted to avoid shrinkage problems or distortions
from too few groups.

I used lme4 to fit the models and extract random effects estimates.


On Sun, Jul 7, 2024, 2:29?PM Ben Bolker <bbolker at gmail.com> wrote:

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 at 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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