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

[Helios de Rosario]

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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