R help - Sep 2011 - F and Wald chi-square tests in mixed-effects models

I have a doubt about the calculation of tests for fixed effects in
mixed-effects models.

I have read that, except in well-balanced designs, the F statistic that
is usually calculated for ANOVA tables may be far from being distributed
as an exact F distribution, and that's the reason why the anova method
on "mer" objects (calculated by lmer) do not calculate the denominator
df nor a p-value. --- See for instance Douglas Bates' long post on this
topic, in:
https://stat.ethz.ch/pipermail/r-help/2006-May/094765.html

However, Anova does calculate p-values from Wald chi-square tests for
fixed terms from "mer" objects (as well as from "lme"
objects, from
lme). I suppose that the key to understand the logic for this is in Fox
& Weisberg's commentary in "An R Companion to Applied
Regression" (2nd
edition, p. 272), where they say: "Likelihood ratio tests and F tests
require fitting more than one model to the data, while Wald tests do
not."

Unfortunately, that's too brief a commentary for me to understand why
and how the Wald test can overcome the deficiencies of F-tests in
mixed-effects models. The online appendix of "An R Companion..." about
mixed-effects models does not comment on hypothesis tests either.

I would appreciate if someone can give some clues or references to read
about this issue.

Thanks,
Helios

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Helios de Rosario <helios.derosario <at> ibv.upv.es> writes:
> 
> I have a doubt about the calculation of tests for fixed effects in
> mixed-effects models.
> 
> I have read that, except in well-balanced designs, the F statistic that
> is usually calculated for ANOVA tables may be far from being distributed
> as an exact F distribution, and that's the reason why the anova method
> on "mer" objects (calculated by lmer) do not calculate the
denominator
> df nor a p-value. --- See for instance Douglas Bates' long post on this
> topic, in:
> https://stat.ethz.ch/pipermail/r-help/2006-May/094765.html
> 
> However, Anova does calculate p-values from Wald chi-square tests for
> fixed terms from "mer" objects (as well as from "lme"
objects, from
> lme). I suppose that the key to understand the logic for this is in Fox
> & Weisberg's commentary in "An R Companion to Applied
Regression" (2nd
> edition, p. 272), where they say: "Likelihood ratio tests and F tests
> require fitting more than one model to the data, while Wald tests do
> not."
> 
> Unfortunately, that's too brief a commentary for me to understand why
> and how the Wald test can overcome the deficiencies of F-tests in
> mixed-effects models. The online appendix of "An R Companion..."
about
> mixed-effects models does not comment on hypothesis tests either.
> 
> I would appreciate if someone can give some clues or references to read
> about this issue.
  Can you please repost this to the r-sig-mixed-models list?  I think this
is an important point and may get lost in the noise here.  I would guess
that the answer is "you can do this, but that doesn't mean you
should."

I'm
  replying
    via
      gmane --
         it 
           complains 
              if the 
                quoted material
                    is too large
                       a fraction of my
                         post.
                           Sorry.
        
   Ben Bolker