[R-sig-eco] summing F stats and permutation

[Steve Brewer]

Jari,

Thanks. This is helpful. I knew that RDA obtained predicted abundances for
each species, but I didn't know that function rda could be used to
calculate F statistics for each predictor for each species. That does seem
like a promising way to approach the problem. So the code you've sent me
is showing how to extract and sums the numerator and denominator SS and
then calculate the ratio from those sums and the dfs? Or is it showing how
to obtain Fs for each species and then summing them?

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.

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 at 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 at r-project.org
>[r-sig-ecology-bounces at r-project.org] on behalf of Steve Brewer
>[jbrewer at olemiss.edu]
>Sent: 29 November 2012 16:42
>To: r-sig-ecology at 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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>
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