[R-sig-ME] lme vs. lmer

[Douglas Bates]

On Tue, Sep 29, 2009 at 3:58 PM, Peter Dalgaard
<p.dalgaard at biostat.ku.dk> wrote:
> Ben Bolker wrote:
>>
>> Douglas Bates wrote:
>>>
>>> On Tue, Sep 29, 2009 at 1:02 PM, Ben Bolker <bolker at ufl.edu> wrote:
>>>
>>>> Christopher David Desjardins wrote:
>>>>>
>>>>> I've started working through Pinheiro & Bates, 2000 and noticed the use
>>>>> of lme from the nlme package. I am curious if lmer from lme4 has
>>>>> superseded lme or if lme still holds its own? The reason I ask is that
>>>>> I
>>>>> have taken a few classes where we've solely used lmer and just read
>>>>> about lme today. If both functions are on equal footing, can the
>>>>> p-values from lme be trusted?
>>>>> Thanks!
>>>>> Chris
>>>>
>>>>  You should read the extended discussion of p-values, degrees of
>>>> freedom, etc. that is on the R wiki (I think) and referenced from the R
>>>> FAQ.  At least in my opinion, (n)lme is still fine (and indeed necessary
>>>> at this stage for fitting heteroscedastic and correlated models).  The
>>>> df/p-value estimates, however, are "use at your own risk" -- you'll have
>>>> to read the literature and decide for yourself.
>>>>  I still think there's room for someone to implement (at least)
>>>> Satterthwaite and (possibly) Kenward-Roger corrections, at least for the
>>>> sake of comparison, but I'm not volunteering.
>>>
>>> You may need to define them first.  Many of the formulas in the mixed
>>> models literature assume a hierarchical structure in the random
>>> effects - certainly we used such a formula for calculating the
>>> denominator degrees of freedom in the nlme package. But lme4 allows
>>> for fully or partially crossed random effects so you can't think in
>>> terms of "levels" of random effects.
>>>
>>> Referring to the "Satterthwaite and Kenward-Roger corrections" gives
>>> the impression that these are well-known formulas and implementing
>>> them would be a simple matter of writing a few lines of code.  I don't
>>> think it is.  I would be very pleased to incorporate such code if it
>>> could be written but, as I said, I don't even know if such things are
>>> defined in the general case, let alone easy to calculate.
>>>
>>> I am not trying to be argumentative (although of late I seem to have
>>> succeeded in being that).  I'm just saying that I don't think this is
>>> trivial. (It I wanted to be argumentative I would say that it is
>>> difficult and, for the most part, irrelevant. :-)
>>
>>  Fair enough. Actually, I'm not sure I meant implementing them in lmer
>> -- even implementing them in nlme would be useful (and perhaps more
>> straightforward, if not trivial). I also wouldn't impose the requirement
>> that they have to be feasible for huge data sets -- I'm just curious if
>> they can be implemented within lme in a relatively straightforward/
>> boneheaded way.
>>   But again, this is very far down my to-do list (and at the edge
>> of my abilities) and completely off yours, so unless someone else bites
>> it won't happen.
>
> I don't think (n)lme is all that easy either; you still need to sort out the
> connection between its multilevel formulation and the projection matrices in
> the K-R paper. In both nlme and lme4, an implementation is almost certainly
> possible, although probably complicated and perhaps at the expense of all
> computational efficiency.
>
> One main problem is that even when they can be calculated, the corrections
> rely on a normal distribution assumption which is more than likely wrong in
> practice. This isn't any different from ordinary t-tests: once you get into
> the single-digit df regime, you really don't know what you are doing, and if
> there are more than 30 df, the normal approximation works well enough
> without the correction.
>
> Accordingly, I tend to see low df more as a warning flag than as something
> that gives accurate p values, and I sometimes wonder whether there is a way
> to raise such a flag more expediently.

I agree, wholeheartedly.

My general advice to those who are required to produce a p-value for a
particular fixed-effects term in a mixed-effects model is to use a
likelihood ratio test.  Fit the model including that term using
maximum likelihood (i.e. REML = FALSE), fit it again without the term
and compare the results using anova.

The likelihood ratio statistic will be compared to a chi-squared
distribution to get a p-value and this process is somewhat suspect
when the degrees of freedom would be small.  However, so many other
things could be going wrong when you are fitting complex models to few
observations that this may be the least of your worries.

I appreciate that for Ben and others in fields like ecology the need
to incorporate many different possible terms in models for
comparatively small data sets may be inevitable.  But it is also
inevitable that the precision of the information one can extract from
such small data sets is low.  Reducing such analysis to a set of
p-values for various terms and treating these p-values as if they were
precisely determined is an oversimplification, even when journal
editors insist on such an oversimplification.