lmer question

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