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

Rolf Turner r@turner @end|ng |rom @uck|@nd@@c@nz
Sun Apr 26 11:06:04 CEST 2020

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.


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?



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Department of Statistics
University of Auckland
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