[R-sig-ME] nAGQ

[John Poe]

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 using 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 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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