[R-sig-ME] nAGQ = 0

[Poe, John]

I'm pretty sure that nAGQ=0 is generating conditional modes of group values
for the random effects without subsequently using a laplace approximation.
This is really not something that you want to do unless it's a last resort.
It's kind of like estimating a linear probability model with a random
intercept and using the values for that in the cloglog model. My
understanding is that it's not even an option in most other software.
Someone please correct me if I'm wrong here because what I've found on it
has been kind of vague and I'm making some assumptions.

My guess is that the random intercepts/slopes are going to be too small and
their distributions could be distorted if you're not actually approximating
the integral with something like quadrature or mcmc. That's the case with
PQL and MQL according to simulation evidence at least and even though this
isn't the same as PQL I'd expect a similar problem at first blush.

As to if this is a real practical problem or a theory  problem there's been
kind of a disagreement on that within the stats literature. Some people
argue, in binary outcome models, that biased random intercepts can bias
everything else and others have argued this fear is overblown. This might
well have been settled by actual statisticians by now, I'm not sure.  It's
gotten enough attention in the literature that people certainly worried
about it a lot.

Below are two articles on the topic with simulations but I've seen the
fixed effects results (and LR tests) change based on the random effects
approximation technique in my work so I'm always a bit paranoid about it.
Model misspecification and having oddly shaped random intercepts (as with
count models) can seem to make this problem worse.

You can try using the BRMS package if you aren't comfortable switching to
something totally unfamiliar. It's a wrapper for Stan designed to use lme4
syntax and a lot of good default settings. It's pretty easy to use if you
know lme4 syntax and can read up on mcmc diagnostics.

Litière, S., et al. (2008). "The impact of a misspecified random‐effects
distribution on the estimation and the performance of inferential
procedures in generalized linear mixed models." Stat Med 27(16): 3125-3144.

McCulloch, C. E. and J. M. Neuhaus (2011). "Misspecifying the shape of a
random effects distribution: why getting it wrong may not matter."
Statistical Science: 388-402.


On Sep 3, 2017 5:49 PM, "Rolf Turner" <r.turner at auckland.ac.nz> wrote:

> On 04/09/17 03:48, Jonathan Judge wrote:
>
>> Rolf:
>>
>> I have not studied this extensively with smaller datasets, but with
>> larger datasets --- five-figure and especially six-figure n --- I have
>> found that it often makes no difference.
>>
>
> When uncertain, I have used a likelihood ratio test to see if the
>> differences are likely to be material.
>>
>
> My overall suggestion would be that if the dataset is small enough
>> for  this choice to matter, it is probably also small enough to solve the
>> model through MCMC, in which case I would recommending using that,
>> because the incorporated uncertainty often gives you better parameter
>> estimates than any increased level of quadrature.
>>
>
>
> Thanks Jonathan.
>
> (a) How small is "small"?  I have 3 figure n's. I am currently mucking
> about with two data sets.  One has 952 observations (with 22 treatment
> groups, 3 random effect reps per group).  The other has 142 observations
> (with 6 treatment groups and again 3 reps per group).  Would you call the
> latter data set small?
>
> (b) I've never had the courage to try the MCMC approaches to mixed models;
> have just used lme4.  I guess it's time that I bit the bullet.
> Psigh.  This is going to take me a while.  As an old dog I *can* learn new
> tricks, but I learn them *slowly*. :-)
>
> (c) In respect of the likelihood ratio test that you suggest --- sorry to
> be a thicko, but I don't get it.  It seems to me that one is fitting the
> *same model* in both instances, so the "degrees of freedom" for such a test
> would be zero.  What am I missing?
>
> Thanks again.
>
> cheers,
>
> Rolf
>
> --
> Technical Editor ANZJS
> Department of Statistics
> University of Auckland
> Phone: +64-9-373-7599 ext. 88276
>
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