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?


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



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