[R] F and Wald chi-square tests in mixed-effects models

Ben Bolker bbolker at gmail.com
Thu Sep 29 23:04:06 CEST 2011

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."

      gmane --
              if the 
                quoted material
                    is too large
                       a fraction of my
   Ben Bolker

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