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

[Ross Boylan]

On Thu, Sep 26, 2013 at 04:23:47PM +0000, Ben Bolker wrote:
> 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 ...


If the limit is hard-coded to 25, it will be hard to discover if using
>25 matters.  That seems to me an argument for not hard coding it.  I
suppose if the results had not stabilized by 25 that would be an
indication.

OTOH, 25 is a lot of quadrature points.

One problem I've encountered with high number of quadrature
points--not in lmer, but I think it's a general issue--is that as the
number of quadrature points goes up the extreme x values go up, and
numerical problems are more likely.  Usually one can compensate by
coding the likelihood defensively.

Ross Boylan