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List:       r-sig-mixed-models
Subject:    Re: [R-sig-ME] P-values from interaction terms using lme4
From:       Douglas Bates <bates () stat ! wisc ! edu>
Date:       2017-08-09 14:59:32
Message-ID: CAO7JsnTzwD53PiU0Bqfos55bSx_yBUyRk0W+4ieip7T3K8vEgg () mail ! gmail ! com
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On Wed, Aug 9, 2017 at 9:54 AM Phillip Alday <phillip.alday@mpi.nl> wrote:

> On 08/09/2017 04:46 PM, Douglas Bates wrote:
>


> > Technically it is true that the number of parameters does not depend on
> > the number of random effects, only on the number of unique values in the
> > covariance matrices for the random effects.  However, I think that leads
> > to an undercount of the effective number of parameters when, say,
> > performing a likelihood ratio test of models that differ in their random
> > effects specification.
>
> This is related to the more general issue of degrees of freedom in mixed
> models, right?
>

Yes.

But in terms of estimation (especially as implemented in
> lme4/MixedModels.jl), increasing the levels of a random effect will
> generally provide better estimates, right?
>

Yes.  Or, to put it the other way, it is unrealistic to expect to obtain
precise estimates of variance components unless there is(are) a large
number of levels in the grouping factor(s) for the random effects.

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