Dear R-help,

We are conducting a distance-based redundancy analysis using capscale and
then testing for statistical significance for six terms in the model for the
constrained ordination using anova.cca in the vegan package. The
significance test is sequential, i.e., testing for significance of a term
only after accounting for all preceding terms. Could someone please provide
us with either the actual formula for the pseudo-F statistic or a reference
that provides this formula?

We ask because we are doing the exact same analysis in another program
(using distLM in PRIMER 6 v 6.1.13 and PERMANOVA+ v 1.0.3 from PRIMER-E),
but we are getting very different pseudo-F ratios despite specifying the
exact same order of model terms, using the same Bray-Curtis distance measure
(distance matrices produced by the two programs are the same), and using the
same sequential test for significance. Below is a table displaying the order
of the model terms and the pseudo-F values computed by R and by PRIMER (we
also ran the same analysis in CANOCO which showed the same results in
pseudo-F values as PRIMER). We have not been able to figure out why we get
very different pseudo-F values, leading us to believe that R calculates
pseudo-F values differently than PRIMER for the sequential tests.
Furthermore, constrained ordination outputs, i.e., eigenvalues, proportion
of variability explained by each constrained axes, etc. appear to be
identical between the two programs.  Below we provide (1) the table showing
the different pseudo-F values; (2) the formula used by PRIMER to calculate
pseudo-F values that we think is the same being used in R, but need
confirmation; and (3) the R code used for this analysis.  

(1) Table


Model

Social Variables

PRIMER pseudo-F

R pseudo-F


SEQUENTIAL TESTS

GroupSize

1.1904

1.5528


 

Board

1.5079

1.8872


 

MtgStyle

1.1326

1.4007


 

DmStyle

1.0971

1.3437


 

DifView

1.4892

1.7299


 

VolAuton

2.2923

2.2925

 

(2) pseudo-F formula

We know that PRIMER uses the following formula to calculate the pseudo-F for
a sequential test of significance (equation 4.3, Anderson, Gorley, and
Clarke 2008, Chapter 4. Pg. 129, and based on pseudo-F equation in Legendre
and Anderson (1999), Ecological Monographs vol. 69):

 

F= (SSFull - SSReduced)/(qFull-qReduced)

        (SSTotal-SSFull)/(N - qFull - 1)

 (3) R code

## creating Bray-Curtis of Biodiversity data

H.BC <- vegdist(H.Full [,14:211], "bray")

 

## Distance based redundancy analysis (dbRDA)

m1<-capscale(H.BC ~ GroupSize + Board + MtgStyle + DmStyle + DifView +
VolAuton, SScomp [,14:19], distance = "euclidean", add = TRUE)

### NOTE: pseudo-F values are the same with or without correcting for
negative eigenvalues (although they are different from other programs).

 

## Sequential test for terms

anova.cca(m1, by="terms", perm.max=1000, permu=500) 

 

Thank you very much for any help or insights that anyone can provide,

Kristen

 

Kristen A. Ross, PhD

Post Doctoral Researcher 

University of Illinois at Chicago

kristenrossUIC@gmail.com

          and

Research Associate

Green Mountain College

One Brennan Circle

Poultney, VT 05764

 


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