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.htmlHowever, 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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