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

[Jari Oksanen]

Steve,

The code gives you a vector of F-values calculated separately for each species. Taking sum of those vectors gives you the sum of all F-values.

For the ordinary F-values (sum numerators and denominators and get their ratio) you can use anova or pemutest functions in vegan.

Cheers, Jari
On 29 Nov 2012, at 18:41, Steve Brewer wrote:

> 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
>> 
>> 
>> 
>>       [[alternative HTML version deleted]]
>> 
>> _______________________________________________
>> R-sig-ecology mailing list
>> R-sig-ecology at r-project.org
>> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
> 
>