On 11/29/2012 05:41 PM, Steve Brewer wrote:
> [...]
>
> Incidentally, I was initially very skeptical of the sumF approach until I
> started comparing sumF results to perMANOVA results (using PC-Ord) on
> several different datasets of mine and got strikingly similar results
> between the two techniques. It seems to go against what a lot of
> statisticians are saying about the unique value of multivariate stats. I
> don't have a satisfactory explanation for why it seems to work with my
> data.
I think this is similar to the approach of David Warton:

" The problem of testing for an effect of a difference in mean
abundance between a set of multivariate samples (Fig. 4c) can
be addressed using the simple approach of fitting separate
models to each taxon, then summing the test statistics, and
using resampling to assess the significance of this multivariate
test statistic (Warton 2011). This 'sum-of-LR' statistic is analogous
to the 'sum-of-F' approach based on analysis of variance
(Edgington & Onghena 2007), which was previously shown to
have better power properties than distance-based analyses
(Warton & Hudson 2004). The key advantage however of the
sum-of-LR approach is that we can correctly model the mean--
variance relationship, leading to better power properties than
sum-of-F statistics when sampling is unbalanced (Warton
2008b). The effectiveness of the approach is demonstrated in
Fig. 4c, where compared with PERMANOVA, power of the
sum-of-LR statistic was usually much higher and tended to
vary much less as a function of the variance of the effect taxon.
See Warton (2011) for further simulations demonstrating
power advantages. "

- cited from:
Warton, David I., Stephen T. Wright, and Yi Wang. "Distance-based 
Multivariate Analyses Confound Location and Dispersion Effects." 
/Methods in Ecology and Evolution/ (2011).

Have a look at the mvabund-package, implementing their methods:
Wang, Yi, Ulrike Naumann, Stephen T. Wright, and David I. Warton. 
"Mvabund- an R Package for Model-based Analysis of Multivariate 
Abundance Data." /Methods in Ecology and Evolution/ (February 2012). 
doi:10.1111/j.2041-210X.2012.00190.x.

Eduard

>
> Steve
>
>
> 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 11/29/12 9:43 AM, "Jari Oksanen" <jari.oksanen@oulu.fi> wrote:
>
>> Steve,
>>
>> This is R, so it is not about whether this can be done, but how this can
>> be done. Unfortunately, doing exactly this requires some fluency in R.
>> Doing something similar is very simple.
>>
>> The description of your problem sounds very much like the description of
>> permutation test in redundancy analysis (RDA). The difference is that in
>> RDA you sum up nominators and denominators before getting the ratio, but
>> in your model you sum up the ratios. So in RDA test you have (num_1 +
>> num_2 + ... + num_p)/(den_1 + den_2 + ... + den_p), and in your
>> description you have num_1/den_1 + num_2/den_2 + ... + num_p/den_p. The
>> former test in canned for instance in the vegan package, but the latter
>> you must develop yourself (and the former method of summing variances
>> instead of their ratios feels sounder). It would not be too many lines of
>> code to fit your code, though. Please note that RDA works by fitting
>> linear models for each species independently so that you can get all
>> needed statistics from a fitted RDA in the vegan package (function rda).
>> The following function extracts F-values by species from a fitted
>> vegan:::rda() result object:
>>
>> spF <-
>> function (object)
>> {
>>    inherits(object, "rda") || stop("needs an rda() result object")
>>    df1 <- object$CCA$qrank
>>    df2 <- nrow(object$CA$Xbar) - df1 - 1
>>    num <- colSums(predict(object, type="working", model="CCA")^2)
>>    den <- colSums(predict(object, type="working", model="CA")^2)
>>    (num/df1)/(den/df2)
>> }
>>
>> HTH, Jari Oksanen
>> ________________________________________
>> From: r-sig-ecology-bounces@r-project.org
>> [r-sig-ecology-bounces@r-project.org] on behalf of Steve Brewer
>> [jbrewer@olemiss.edu]
>> Sent: 29 November 2012 16:42
>> To: r-sig-ecology@r-project.org
>> Subject: [R-sig-eco] summing F stats and permutation
>>
>> Dear Colleagues,
>>
>> I'm wondering if anyone in this group has developed code for doing a sumF
>> test for examining community responses in an experiment. For those not
>> familiar, sumF is a simple univariate alternative to MANOVA and perMANOVA,
>> wherein univariate ANOVAs and their associated F statistics are calculated
>> for each species' abundance and then the F statistic for each effect is
>> summed over all species. The significance of the resulting summed F
>> statistic is then evaluated using random permutation. The summed F
>> statistic
>> is interpreted as an overall community response to the treatments, whereas
>> the F statistic for each species provides a measure of the contribution
>> that
>> species makes to treatment differences.
>>
>> I could envision a variety of ways in which this could be done in R, but
>> I'm
>> not adept enough in R to figure out how to do it myself. One possibility
>> might involve using permute or shuffle to get the randomized data
>> matrices,
>> but it is not clear to me how one could simultaneously calculate the
>> Anovas
>> for all species and sum the resulting F statistics for each random
>> permutation. There is no reason why traditional F statistics would have to
>> be used. Pseudo-F statistics based on distances for each species'
>> abundance
>> could be calculated instead and then summed across species.
>>
>> PLEASE NOTE THAT I AM ALREADY AWARE OF THE OBJECTIONS TO THIS APPROACH TO
>> COMMUNITY ANALYSIS. Nevertheless, I am interested in pursuing this using
>> R,
>> if possible.
>>
>> Any suggestions are welcomed.
>>
>> Thanks,
>>
>> Steve
>> 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
>>
>>
>>
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