[R] different DF in package nlme and lme4

[Frank E Harrell Jr]

Douglas Bates wrote:
> Christoph Buser wrote:
> 
>> Hi all
>>
>> I tried to reproduce an example with lme and used the Orthodont
>> dataset.
>>
>> library(nlme)
>> fm2a.1 <- lme(distance ~ age + Sex, data = Orthodont, random = ~ 1 | 
>> Subject)
>> anova(fm2a.1)
...

>> Regards,
>> Christoph Buser
>>
> 
> No.  The calculation of denominator degrees of freedom in lme4 is bogus 
> and I believe this is documented.  Note that for all practical purposes 
> there is very little difference between 25 and 100 denominator degrees 
> of freedom.
> 
> lme4 is under development (and has been for a seemingly interminable 
> period of time).  Getting the denominator degrees of freedom calculation 
> "right" is way down the list of priorities.
> 
> Many people express dismay about the calculation of denominator degrees 
> of freedom in all versions of lme4.  IIRC Frank Harrell characterizes 
> this as one of the foremost deficiencies in R relative to SAS.  I don't 
> agree that this is a glaring deficiency.  In fact I believe that there 
> is no "correct" answer.  The F statistics in a mixed model do not have 
> an F distribution under the null hypothesis.  It's all an approximation, 
> which is why I don't stay up nights worrying about the exact details of 
> the approximation.

Doug - the main concern is accurate P-values; I don't really care which 
approximations are best, just that the ones used are at least as good as 
those in SAS.  Without being an expert, I have come to believe that at 
the moment SAS is better than R in 2 areas: accurate P-values from mixed 
models and handling massive databases.  On the former point I could 
easily be swayed by some type I error simulations.

> 
> My plan for lme4 is that one slot in the summary object for an lme model 
> will be an incidence table of terms in the fixed effects versus grouping 
> factors for the random effects.  This table will indicate whether a 
> given term varies within groups defined by the grouping factor.  Anyone 
> who wants to implement their personal favorite calculation of 
> denominator degrees of freedom based on this table will be welcome to do 
> so.

I will be interested also to see timings of lme4 (using S4) vs nlme 
(using S3) for the same model.

Cheers,

Frank

> 
> I personally think that tests on the fixed-effects terms will be better 
> implemented using the restricted likelihood-ratio tests defined by 
> Reinsel and Ahn rather than the Wald tests and the whole issue of 
> denominator degrees of freedom may be moot.
> 
> My apologies if I seem to be peeved.  I am not upset by your question - 
> it is an entirely reasonable question.  It is just that I have discussed 
> the issue of denominator degrees of freedom too many times.
> 
> To me a more important objective of lme4 is to be able to handle random 
> effects associated with crossed or partially crossed grouping factors. I 
> believe that in those cases the calculation of denominator degrees of 
> freedom will be very complicated and even more of an approximation than 
> in the case of nested grouping factors.  This is why I would rather 
> finesse the whole issue by using the Reinsel and Ahn approach.
>