[R-sig-ME] Maximum nAGQ=25?

[Ben Bolker]

Rafael Sauter <rafael.sauter at ...> writes:

> 
> Dear R-sig-ME,
> 
> since the beginning of this year the new lme4-version is available on
> CRAN which has some major changes compared to older versions.
> I am still running the old lme4-version ‘0.999999.2’.
> 
> Now I am surprised by one of the changes in the current new version
> '1.0-4': 
> the GH-approximation allows only for a maximum of 25 quadrature points
> (nAGQ=25) whereas in the old version I did not encounter any such
> restrictions for the number of quadrature points.
> As I did not find any discussion about this change in the new
> lme4-version let me allow to ask:
> 
> 1) Why is 25 a reasonable upper bound for nAGQ? What were the reasons to
> implement this upper bound? Is the increasing complexity as mentioned in
> the details of '?glmer' the the main reason for this?
> 
> 2) Is this somehow related to the fact that at the moment in the new
> lme4 version nAGQ>1 is only available for models with a single, scalar
> random-effects term (as discussed here
> https://stat.ethz.ch/pipermail/r-sig-mixed-models/2013q3/020573.html and
> will this maximum of nAGQ=25 stay that way in the future also when
> non-scalar random effects will be implemented again?
> 
> I'd be glad for any hints and explanations about this issue.
> Thanks,
> 

   I will only speak for myself: other lme4-authors (especially Doug
Bates) may chime in on this one.  I believe there isn't a rigorous
argument for why >25 quadrature points is too many: ?glmer says
" A model with a single, scalar random-effects term could
reasonably use up to 25 quadrature points per scalar integral."
For example, Figure 1 of Breslow "Whither PQL?" (2003) shows 
trace plots of non-adaptive and adaptive GHQ (glmer uses adaptive
GHQ) for one example -- the plots level off well before 20,
which is the maximum shown in the plot.  I think we would certainly
be willing to reconsider this limit if you can show that there is
some sensible case where it matters ...

  This is unrelated to the issue of non-scalar random effects, which
as I might have previously stated on this list (or not) is really
a matter of finding time & energy to implement it within the new
framework (patches welcome).

  Ben Bolker