[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.
<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
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