# [R-sig-eco] equation 9 Peres-Neto et al. 2006

Etienne Laliberte etiennelaliberte at gmail.com
Fri Apr 8 01:47:45 CEST 2011

```Dear Ivan,
In such situations, it's probably best to contact the corresponding author
first.
Etienne

-----Original Message-----
From: r-sig-ecology-bounces at r-project.org
[mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of Ivan Jimenez
Sent: Friday, 8 April 2011 4:19 AM
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] equation 9 Peres-Neto et al. 2006

Dear r-sig-eco members,

I am applying the bootstrap procedure to test differences between
fractions from RDA variation partitioning, following the interesting a
very useful paper by Peres-Neto et al. (2006, Variation partitioning of
species data matrices: estimation and comparison of fractions. Ecology
87: 2614-2625). I don't have (and don't use) Matlab, so I am
implementing the test in R, which would seem straightforward to do given
the functions available in package vegan. Nonetheless, I would like
confirmation that there is a typo in equation 9 (page 2621) of the
Peres-Neto et al. paper. The Matlab code in supplement 2 of the paper
(file "TestingFractionDiffRDA.m", deposited here:
http://www.esapubs.org/archive/ecol/E087/158/suppl-2.htm) would seem
right, but it would seem not to match equation 9 in the paper. In
particular, equation 9, in page in 2621, is written this way:

Yhat_xboot = X Bx (I-P) Y_xboot

Yhat_wboot = W Bw (I-P) Y_wboot

Where (following the notation of the paper):

Bx = ( (X'X)^-1) X' (I-P) Y

Bw = ( (W'W)^-1) W' (I-P) Y

I suspect equation 9 should be:

Yhat_xboot = X ( (X'X)^-1) X' (I-P) Y_xboot

Yhat_wboot = W ( (W'W)^-1) W' (I-P) Y_wboot

I would appreciate it if someone has the time to look at this and either
confirm or correct my observation.

Best regards,

Ivan Jimenez

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