[R-sig-ME] lme approximation method for dfs

[Phillip Alday]

Hi,

On 23/5/20 9:11 am, Salahadin Lotfi wrote:
> Dear all,
> I have a very simple question but, have been having a hard time to figure
> it out.
> I am using a mixed model with random intercept and slope using lme function
> with an unstructured covariance matrix. I know lmer uses Satterthwaite's
> approximation method to approximate dfs of fixed effects,

This is not accurate. lme4 by default doesn't even try to figure out the
df and doesn't report p-values. The lmerTest package adds in options to
use Satterthwaite or Kenward-Roger approximations for p-values, but
depending on who you ask around here, the sentiment for those
approximations ranges from "of course" to "hmrpf, why would you bother?"
to "the heretics must be purged!". 

The GLMM FAQ (https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html)
has some info on each of these, but I'll copy and paste something
relevant that I wrote on a different mailing list:

Treating the t-values as z-values is as reasonable as using the
t-distribution with some estimated degrees of freedom for studies with
20-30 subjects and 10s of observations per condition per subject for two
reasons. One is that a t-distribution with dozens of degrees of freedom
is essentially a normal distribution, and so even if you could figure
out what the "right" number of degrees of freedom were, it wouldn't be
far off from the number you get from the normal distribution. The other
reason is that none of these asymptotic results are guaranteed to be
particularly great for anything other than very well behaved linear
mixed models, which is why things like parametric bootstrap are the gold
standard for figuring out coverage intervals. And for large models,
bootstrapping is about as fast as KR (because KR as implemented in
pbkrmodcomp, which lmerTest depends on, computes the inverse of a large
n x matrix).

> but I am not sure
> what is the preferred method that lme uses. Is it Wald or Likelihood ratio?

Wald and likelihood ratio are not degrees of freedom estimates. The
likelihood-ratio tests do have a df, which corresponds to the difference
in the number of free parameters between the models, but this not the
relevant df. (It's numerator degrees of freedom in the ANOVA framework,
while what you need are the denominator degrees of freedom.) The Wald
tests are just the things you see in the table of the fixed effects,
i.e. the tests corresponding to the t- or z-values (or more generally
the ANOVA-style tests / tests of linear hypotheses you then construct
from the fixed effects).


> I don't think lme offers such an option to specify an approximation method
> for dfs of fixed effects. Does it?

The dfs in nlme are computed using the "inner-outer" rule which doesn't
work well for many types of designs common in cognitive neuroscience.
More information on this is in the GLMM FAQ, search for "Df
alternatives" on that page.


Hope that helps!

Phillip


>
> I appreciate any response in advance.
> Sala
>
>
> *************
> Salahadin (Sala) Lotfi
>
> PhD Candidate of Cognitive Neuroscience
>
> University of Wisconsin-Milwaukee
>
> Anxiety Disorders Laboratory
>
> President, Association of Clinical and Cognitive Neuroscience, UWM
>
> 	[[alternative HTML version deleted]]
>
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