[R] Degree of freedom in the linear mixed effect model using lme function in R

[Kingsford Jones]

Hi Sidzabda,

Adjusting df for non-sphericity is generally not discussed in modern
mixed effects modeling because likelihood-based estimators are far
more flexible in structuring covariance matrices than the classical
method of moments estimators based on expected mean squares.  However,
there are still many unanswered questions and controversies relating
to the appropriate df to use for testing.  Some issues are discussed
here:

https://stat.ethz.ch/pipermail/r-help/2006-May/094765.html

That said, the good news is (and I'll try to be a little cautious
since it's a messy issue) when models are carefully developed, there
are tests available in nlme that are generally well received by
reviewers for applied journals.  I don't know enough about your data
to recommend specific models and tests, but I can recommend that you
look into the correlation structures available in nlme.  Essentially
these allow you to model the autocorrelation through the error
covariance matrices so you are left with (reasonably) independent
pieces of information for testing and building confidence intervals.
A possibility for your data would be to add the argument
correlation=corAR1(form=~Year) to a gls (no random effects) or lme
(mixed effects) call.  Chapter 5 of Pinheiro and Bates 2000 will give
you insight into how the correlation arguments work, while sections
2.3 and 2.4 will help you understand some of the issues concerning
inferences.

If you have further questions I recommend the r-sig-mixed-models list.

hoping it helps,

Kingsford Jones



On Fri, Jul 10, 2009 at 9:27 AM, Djibril
Dayamba<Djibril.Dayamba at ess.slu.se> wrote:
> Hello,
> I would appreciate if somebody could help me clear my mind about the below issues.
> I have a factorial experiment to study the effects of Grazing and Fire on Forest biomass production. The experimental unit (to which the treatment combinations are applied) are PLOTs. The measures were made repeatedly for 13 years.
> I am planning to use the linear mixed effect model function lme in R for this. I know that in software like SPSS, using Repeated Measure analysis of variance for studies like mine, sometimes (case of non-sphericity), one needs to adjust for the degree of freedom (DF) used to test the significance of the "within subject factor" (Time i.e., Year in my case).
> My question is:
> How does this work with lme in R? Isn't it enough for me to specify in my model, Year в plotID as a random factor to account for the temporal autocorrelation? Or what else should I do to ensure that I have correct results from the summary function applied to my model (correct t- and p-values)? Thanks in advance.
>
> With regards,
>
> Sidzabda Djibril Dayamba,
> Swedish University of Agricultural Sciences
> Faculty of Forest SCience
> Southern Swedish Forest Research Centre
> Tropical Silviculture and Seed Laboratory
> PO Box 101
> SE - 230 53 Alnarp,
> Sweden
> Tel: +46 76 83 515 70 (Mobile)
>        +46 40 41 53 95 (Office)
>
>
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>
>
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