[R-sig-ME] nAGQ > 1 in lme4::glmer gives unexpected likelihood

[Rolf Turner]

On 26/04/20 6:51 pm, D. Rizopoulos wrote:

> I would say that you can compare a linear model with a linear mixed 
> model using a likelihood ratio test. Under maximum likelihood you 
> integrate the random effects out. Hence, you are testing whether some 
> variance components are zero, i.e., the linear model is nested within 
> the linear mixed model. The technical problem is that the distribution 
> of the statistic will not be the classic chi-squared distribution 
> because for the variance parameters the null hypothesis lies on the 
> boundary of the corresponding parameter space.

<SNIP>

OK.  So the problem is that the null value is on the boundary of the
parameter space (whence the asymptotics for the distribution of the 
likelihood ratio statistic don't work) and *NOT* that the "normalising 
constants" (or underlying measures) are different.  I have a clear and 
distinct (and presumably erroneous!!!) recollection of having read that 
the problem was the latter, perhaps *in addition* to the former.

Can the wise denizens of this list confirm to me the problem is *only* 
the former?

Be that as it may, is not still true that in general log likelihood is 
well-defined only up to an additive constant?

cheers,

Rolf

-- 
Honorary Research Fellow
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276