lme approximation method for dfs

Wow! Such a thorough answer, Phillip. Thanks very much.
I misspoken when I said the lmer would generate p values for fixed effects (yes it is indeed lmerTest package which does it).
Just to make sure I understand it correctly:
lme uses ML/REML to approximate beta weights of fixed effects,
it uses Wald to approximate t/z values (fixed effects), and
it uses "inner-outer" rule to get denominator of df (ddf) which is apparently the least optimal method to estimate ddf among other methods (etc., Satterthwaite's). Lastly, is this "inner-outer" rule the same as "containment method"?

Maarten,
First of all thank you for the nice pointer. The emmeans is elegant. But, I could not get it to work. Could you point out what I am missing in the emmeans function?
  Here is my code:
## Group and Time are categorical IVs with three levels.
lme_fit<- lme(DV~  factor (Group) * factor(TIME), random = ~ TIME | SubjectID, # factor(Group) * factor(TIME)
                  correlation = corSymm (form = ~ 1 | SubjectID),
                  weights = varIdent (form = ~ 1 | TIME),
                  data = my_data,
                  method= "REML",
                  na.action = "na.omit")
emmeans::emmeans(lme.fit, mode= "appx-satterthwaite", adjustSigma = TRUE) ## NOT working


I appreciate for taking time and replying.
Sala

*************
Salahadin (Sala) Lotfi

PhD Candidate of Cognitive Neuroscience

University of Wisconsin-Milwaukee

Anxiety Disorders Laboratory

President, Association of Clinical and Cognitive Neuroscience, UWM


On Sat, May 23, 2020 at 5:01 PM Maarten Jung <Maarten.Jung at mailbox.tu-dresden.de> wrote:

Dear Sala,

As Phillip Alday explained, there is no implementation of the Satterthwaite approximation in the nlme package. If you want to stick with this package, the only way I know to get something similar (for lme objects) is to use functions of the emmeans package with the argument "mode" set to "appx-satterthwaite" (see [1]).

[1] https://cran.r-project.org/web/packages/emmeans/vignettes/models.html#K

Best,
Maarten


On Sat, 23 May 2020, 17:07 Phillip Alday <phillip.alday at mpi.nl> wrote:

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

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