[R-sig-ME] standard errors of mixed-effect model coefficients

[Douglas Bates]

Thank you for permitting me to copy the mailing list on my reply, Julia.

On Fri, Sep 30, 2011 at 2:33 PM, Julia Liu <liujulia7 at gmail.com> wrote:
> Dear Prof. Bates,

> I am sorry if I am being intrusive sending you email asking questions.
> However, I have a question about R function lmer(). How to retrieve standard
> errors (s.e.) of coefficients from a lmer object? By coefficients, I mean
> the final coefficients = fixed+random. I know se.fixef() and se.ranef()
> return s.e. for fixed and random coefficients, respectively. Is there a
> function that return the combined? If not, (this is a more statistic
> question then), how to calculate the s.e. for the fixed+random?

I don't know a good answer for that question.  The typical way that
one extracts standard errors of coefficients, or in the case of an
lmer model, the fixed-effects, is

coef(summary(fittedModel))[, "Std. Error"]

The way that I view a mixed-effects model the random effects are
unobserved random variables, not parameters, so standard errors are
not defined.  You can extract conditional standard deviations for
these objects, which is what is done in creating the "caterpillar
plots" (dotplot(ranef(fittedModel, postVar=TRUE)))

I would be uncomfortable mixing these two concepts.  Of course, if you
are willing to adopt a Bayesian point of view then the fixed effects
and the random effects are all parameters and you can evaluate the
standard deviation of the marginal posterior densities, probably by
MCMC.