[R-sig-ME] Fixed effects in lmer()

[Duncan Jackson]

Hi everyone.
I have some questions about lmer() and I'm wondering if you might be able
to help me out.
I’ve run a mixed-model in lmer() including multiple random effects and a
fixed effect.  I’ve noticed that if I run a comparison simple regression
model with no random effects but the same fixed effect, I get precisely the
same unstandardised beta coefficient for my fixed effect in the simple
regression as I get if I run the mixed model.
Am I correct in thinking, therefore, that the beta coefficients generated
in the mixed model in lmer() do not control for the random effects in the
model?  Would it make a difference in this respect if participants in my
dataset were nested in a random effect?  Also, how does one summarise
an overall R square value for the impact of a set of fixed effects in a
mixed model with lmer()?
On another note, I was wondering if there were any more recent suggestions
about how to handle random effects in REML-based models using lmer() that
are fenced at zero.  Is it possible that alternative optimizers might
assist in this respect?  One issue I find when comparing lmer() with
Bayesian estimators is that the difficulties in this respect often appear
to arise with very small effects (i.e., those that approach near-zero
variance estimates).
Looking forward to hearing your thoughts.
Kind regards,
Duncan

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