degrees of freedom in mixed model

Meh... My feeling is that the amount of controversy on this point is 
rather more limited than S Ellison lets on. Of course Bates is 
(famously, at this point) deeply skeptical about the approximate 
degrees of freedom approaches, but I get the impression that few of 
the rest of us who have spent some time thinking about the matter have 
any sort of strong feelings about it. The Satterthwaite method 
(implemented in lmerTest) is widely used, well understood, and 
basically seems to work quite well for controlling error rates in most 
cases, based on simulations. I think if you are wanting to scrutinize 
your model and the tests of the coefficients therein, there are far 
bigger fish to fry than worrying about the issue of approximate DFs 
vs. bootstrapping vs. MCMC vs. ... Jake

From: jbaldwin at fs.fed.us To: S.Ellison at LGCGroup.com; 
iaingallagher at btopenworld.com; r-sig-mixed-models at r-project.org
Date: Fri, 24 Jan 2014 15:40:32 +0000 Subject: Re: [R-sig-ME] degrees 
of freedom in mixed model

S Ellison:  Despite you being a chemist, I think you're at least 
mostly correct.  But from the construction of my statement, it's 
obvious that I am a statistician and I'm allowed, by law, to be wrong 
5% of the time.  And if I claim to be a Frequentist, I don't even 
have to identify which of my particular statements are incorrect.

Jim

Jim Baldwin Station Statistician Pacific Southwest Research Station 
USDA Forest Service

-----Original Message----- From:
r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of S 
Ellison Sent: Friday, January 24, 2014 5:40 AM To: Iain Gallagher; 
r-sig-mixed-models at r-project.org Subject: Re: [R-sig-ME] degrees of 
freedom in mixed model

library(lme4) model1 <- lmer(value~group + (1|animal), data=bip)
summary(model1)

.......

so I'd then have:

qf(0.95,3,5) or qf(0.95,3,4)

for my critical F value?

Any advice (incuding whether the appraoch is right) would be useful.

It's the wrong approach.

You are using lmer, which uses maximum likelihood estimation, not 
classical sums of squares. The degrees of freedom don't mean the same 
thing, and the distribution of REML estimates of variance isn't 
necessarily chi-squared. So F is interpretable in the same way as it 
would be in classical anova.

If you want p-values from an lmer model, you could get hold of the 
lmerTest package. Other recommended approaches include variants on 
MCMC. There is a great deal of controversy on this point, though; try 
Googling "p-values from lmer" with particular attention to anything 
by Douglas Bates (the package author). You _should_ find enough to 
make you worry that the method used by lmerTest (which as I 
understand it implements a method used by SAS) comes with quite 
strong theoretical objections. I am quite sure the lmerTest authors 
know that perfectly well and offer lmerTest as a package for those 
who want to find out or for those whose management insist on a 
SAS-compatible answer. But if I read correctly, that doesn't make it 
the right thing to do

[Caveat - I'm a chemist. I could be wrong about this]

Best

iain

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