[R-sig-ME] p values for balanced experimental designs in lme.

[Ben Bolker]

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On 10-12-13 05:18 PM, Taylor, Jason wrote:
> I am looking for some confirmation on the use of F statistics and P
> values in the anova(model) output for lme, specifically for balanced
> experimental designs.
> 
> Briefly, I will explain my experiment.
> 
> I have twelve experimental units that have each been assigned to one
> of three nutrient treatments. Within each experimental unit I have
> excluded grazers from half of the unit (Split plot). I sampled each
> unit on day 14 and day 28 of the experiment (Repeated measurement).
> 
> There are no missing data points so my data is balanced.
> 
> I am interested in the effects of Nutrients, Grazing and how they
> change with date.
> 
> I am using random effects in a mixed model to account for the
> grouping structure of the data.
> 
> lme (Response~Nut*Graz*Date,random=~1|Stream/Graz) or
> 
> lmer(Response~Nut*Graz*Date+(1|Stream)+(1|Stream:Graz))
> 
> So my question returns to the much asked F tests/P value debate.   I
> have read Pinheiro and Bates, Zuur et al., all the posts including D.
> Bates statement, the wiki, the Trends in Ecology and Evolution paper
> (Dr. Bolker).  If I understand everything I have read this is my
> conclusion:
> 
> Since my data is balanced, the null distribution of the computed
> ratio of sums of squares approaches an F distribution and F tests and
> associated P values should be reliable from anova(model) outputs for
> lme.  This appears to be correct in that I get similar (but not
> exactly the same) F values when I run lme, lmer or aov with
> Error(Stream/Graz).   Thus, I should be able to report a traditional
> anova table with DF, F and p values in my manuscript (which is what
> journals want in my field for simple experiments).
> 
> Are my conclusions correct?

  I think so.

  I'm not quite sure why you used 1|Stream/Graz in one case and
1|Stream:Graz in another -- I think they need not be exactly equivalent
(Stream/Graz is equivalent to Graz+Graz:Stream, I think, although I
always get the syntax backward), although in this case they may indeed
be equivalent.

> 
> One response to my question who suggested I send it along to the list
> serve is listed below.
> 
> 
>> I believe this isn't an issue for normally distributed data in the
>> case of balanced designs, or isn't much of an issue with normal
>> data and >reasonably large sample sizes. In those cases you can use
>> lme() which does report P values and which calculates DF as
>> indicated in P&B's book.
> 
>> But keep in mind that for unbalanced data you'll be getting
>> P-values from type I SS.
> 
> 
> 
>> To get type III SS you'd need to change the contrasts before
>> fitting your model with lme():
> 
>> options(list(contrasts=c(ordered="contr.treatment",unordered="contr.poly")))
>
>> 
> 
> 
>> And then:
> 
>> anova(model, type="m")
> 
> 
> 
>> BTW, an important reason to post to the list is so that others can
>> benefit from your questions. You may find it easier to get answers
>> posting to R->sig-eco for ecologically-oriented questions or
>> R-sig-ME for mixed-effect model-oriented questions ...
> 
> 
> 
> Best regards,
> 
> Jason
> 
> 
> 
> [[alternative HTML version deleted]]
> 
> _______________________________________________ 
> R-sig-mixed-models at r-project.org mailing list 
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

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