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@fs.fed.us
> To: S.Ellison@LGCGroup.com; iaingallagher@btopenworld.com; r-sig-mixed-models@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@r-project.org [mailto:r-sig-mixed-models-bounces@r-project.org] On Behalf Of S Ellison
> Sent: Friday, January 24, 2014 5:40 AM
> To: Iain Gallagher; r-sig-mixed-models@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
> >
> >       [[alternative HTML version deleted]]
> 
> 
> 
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