hi steve,

Am 08.03.2012 20:07 schrieb "Steve Brewer" <jbrewer@olemiss.edu>:
>
> Kay,
>
> Seems like a clever and reasonable approach, but I have a couple of
> comments/questions.
>
> First, it seems that with this approach, you cannot evaluate the sediment
> x hydrology, the sediment x depth or the sediment x hydrology x depth
> interactions. I'm not sure if Arnaud is interested in these interactions,
> but one generally is in most split-plots.

you're right, when it comes to interactions things get complicated.
however, for your design with partly crossed factors i'm rather clueless.

to test 3-way interactions will not be sensible in any case. generally,
these seldomly give reasonable results and with your samplesize you wont
get far, i guess.

> Second, I tried your approach with my own data (which is just a split
> plot). Perhaps I did it wrong, but the resulting anova seems wrong to me.
> The residual df are too high, I think because the analysis is not taking
> the strata variation and its df (in Arnaud's case, the site effect) out of
> the error term.

bear in mind that you have the same errors because in a PERMANOVA the model
stays the same, only the permutation is restricted.

> Here's a suggestion. First, simplify Arnaud's design to a split plot
> (removing the depth effect. In the species file, this will entail summing
> abundances across depths for each site x hydrology combination.
>
> Use a design predictor file as originally described by Arnaud (except
> without the depth factor); I.e., site1, site2, ... site9, three sediment
> types - sed1, sed2, sed3, and two hydrology types - dry, wet.
>
> To analyze the split-plot effects, I would suggest the following
>
> Adonis(community ~ sediment*hydrology + site, strata = site)
>
> You should get an anova table that will give you the sediment main effect,
> the hydrology main effect, the sediment*hydrology interaction, the site
> effect (probably not of interest), and residual error. ***Note that the
> sediment main effect is garbage here because it is tested with the
> residual error term, which is not the correct error term and must be
> disregarded; Your approach to getting it seems reasonable to me.*** The
> hydrology effect and the hydrology*treatment interaction should be
> correct, however, because both are tested with the residual (I.e.,
> split-plot) error term.
>
> For the split-split plot effects, you need to make a term equivalent to
> the site x hydrology term (as described by Arnaud). That will be the
> strata effect for the split-split plot (but not for the split-plot
> effects). In this case, you'll use a species dataset in which the
> abundances are not summed across depths for each site x hydro combination.
> This is identical to the original species data file. In this case, I
> suggest the following analysis:
>
> Adonis(community ~ sediment*hydrology*depth + site_hydro, strata =
> site_hydro).
>
> Here, you disregard all results except those of depth and its interactions
> with sediment and/or hydrology.
>
> Another possible way to test the sediment main effect would be to create a
> new species data file in which abundances are summed across all
> hydrologies and depths for each site. The adonis statement is then simply:
>
> Adonis(community ~ sediment)
>
> I'd appreciate any feedback.
>
> Thanks,
> Steve
>
best wishes,
kay
>
> J. Stephen Brewer
> Professor
> Department of Biology
> PO Box 1848
>  University of Mississippi
> University, Mississippi 38677-1848
>  Brewer web page - http://home.olemiss.edu/~jbrewer/
> FAX - 662-915-5144
> Phone - 662-915-1077
>
>
>
>
> On 3/5/12 4:45 AM, "Kay Cichini" <kay.cichini@gmail.com> wrote:
>
> >Hi Arnaud and list-members,
> >
> >what about the following:
> >
> >library(vegan)
> >
> >Sediment<-as.factor(rep(c("Sed1","Sed2","Sed3"),each=36))
>
>Site<-as.factor(rep(c("Site1","Site2","Site3","Site4","Site5","Site6","Sit
> >e7","Site8","Site9"),each=12))
> >Hydrology<-as.factor(rep(rep(c("Dry","Wet"),each=6),9))
> >Depth<-as.factor(rep(rep(c("D1","D2"),each=3),18))
> >
> >nobs = length(Site)
> >
> ># depth and hydrology are nested within sites:
> >table(Site, Depth)
> >table(Site, Hydrology)
> >
> ># so the following call is ok as it restricts permutation on sites -
> ># that is, levels of depth and hydrology are shuffled only within and not
> ># across sites:
> >set.seed(123)
> >community <- matrix(rnorm(nobs * 3, 10, 1), nobs, 3)
> >adonis(community ~ Hydrology * Depth, perm = 999, strata = Site)
> >
> ># sediment is different:
> >table(Site, Sediment)
> >
> ># to allow for this structure you would need to shuffle sites as
> ># a whole. the below restriction will randomly assign levels of sediment
> ># to the sites - like this:
> >ctrl = permControl(strata = Site, permute.strata = TRUE)
> >table(Site, perm.Sediment = Sediment[permuted.index2(nobs, control =
> >ctrl)])
> >
> >### to test sediment you'd need a customized code:
> >(fit <- adonis(community ~ Sediment, permutations = 1))
> >
> >### number of perms
> >B <- 999
> >
> >### setting up frame which will be populated by
> >### random r2 values:
> >pop <- rep(NA, B + 1)
> >
> >### the first entry will be the true r2:
> >pop[1] <- fit$aov.tab[1, 5]
> >
> >for(i in 2:(B+1)){
> >     idx <- permuted.index2(nobs, control = ctrl)
> >     fit.rand <- adonis(community ~ Sediment[idx], permutations = 1)
> >     pop[i] <- fit.rand$aov.tab[1,5]
> >}
> >
> >### get the p-value (H0: Sediment has no effect on location of
> >communities):
> >print(pval <- sum(pop >= pop[1]) / (B + 1))
> >
> >### make a histogram to see random R2-values and the true one:
> >hist(pop, xlab = "Population R2")
> >abline(v = pop[1], col = 2, lty = 3)
> >
> >What do you think?
> >Kay
> >
> >
> >2012/3/4 Arnaud Foulquier <arnaud.foulquier@gmail.com>
> >
> >> I have run the two analysis. The only differences are the p-values that
> >> appear in the anova tables. Other values (Df, SumsOfSqs, MeanSqs,
> >>F.Model)
> >> are not modified because they are calculated on the "original" (not
> >> permuted) data.
> >>
> >> The p-value is calculated by comparing the value of F obtained with the
> >> original data to the distribution obtained by permutations. If i
> >>understand
> >> well, the strata argument is used to constrain the permutations of the
> >> original data within the groups specified in the strata argument. The
> >> distribution of the F-statistic that is generated by permutations is
not
> >> the
> >> same according to whether the strata argument is specified or not. This
> >>is
> >> why the p-values are modified when the strata argument is specified.
> >>
> >> However, I'm not sure that strata=Site_Hydro correctly specify the
> >>nested
> >> structure of my data.
> >>
> >>
> >>
> >>
> >>
> >> --
> >> View this message in context:
> >>
> >>
http://r-sig-ecology.471788.n2.nabble.com/split-split-plot-design-and-ado
> >>nis-tp7332029p7342690.html
> >> Sent from the r-sig-ecology mailing list archive at Nabble.com.
> >>
> >> _______________________________________________
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> >>
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