[R-sig-ME] lmer question

[Douglas Bates]

I would recommend sending inquiries like this to the
R-SIG-Mixed-Models at R-project.org mailing list, which I have taken the
liberty of cc:'ing on this reply.  I am not always able to give a
rapid response to questions about mixed models in R.

On Wed, Mar 31, 2010 at 12:09 PM, Vivek Ayer <vivek.ayer at gmail.com> wrote:
> Hi Doug,
>
> I'm quite interested in your lmer function in the lme4 package and had
> a question on how it worked vs. lm().
>
> This is the command I run in R to get the desired mixed effect result:
>
> fitlmmixed <- lmer(MeasuredPathLoss ~ (1 | SiteLabel) + LogDist + Diffraction)
>
> Here's what I'd run to get the purley fixed effect result:
>
> fitlmfixed <- lm(MeasuredPathLoss ~ -1 + factor(SiteLabel) + LogDist +
> Diffraction)
>
> lm and lmer have interesting applications in the field of radio
> propagation and I just wanted to know how the parameters are treated.
>
> When I run summary on the former, it says the degrees of freedom are
> just LogDist, Diffraction, (1 | SiteLabel), the group intercept and
> sigma = 5. When I run summary on the latter, it says the degrees of
> freedom are LogDist, Diffraction, Sigma, and one deg of freedom for
> each factor. So clearly, in all cases, a pure fixed effects model will
> have more degrees of freedom than a mixed effects model and thus a
> better a logLik, but now by much. However, the advantage of fixed
> effects goes away when your group has many factors.
>
> So with those parameters I have above, the mixed model will always
> have 5 degs of freedom, while the fixed model can have no limit.
>
> Of course, this means the fixed effects model will allocate much more
> memory to the point where a machine may run out of memory, but this
> doesn't occur in lmer(). Why is that? Also, lmer is run fairly
> quickly, while producing very close results to lm's fixed effect. In
> lmer, is there really deg of freedom for each random effect, but all
> those degrees are bunched up into one effect, greatly reducing the
> number of parameters?
>
> Thanks,
> Vivek Ayer
>