cailliez: Transformation to make Euclidean a distance matrix

In ade4: Analysis of Ecological Data : Exploratory and Euclidean Methods in Environmental Sciences

Description

This function computes the smallest positive constant that makes Euclidean a distance matrix and applies it.

Usage

cailliez(distmat, print = FALSE, tol = 1e-07, cor.zero = TRUE)

Arguments

distmat	an object of class dist
print	if TRUE, prints the eigenvalues of the matrix
tol	a tolerance threshold for zero
cor.zero	if TRUE, zero distances are not modified

Value

an object of class dist containing a Euclidean distance matrix.

Author(s)

Daniel Chessel
Stéphane Dray [e-mail]

References

Cailliez, F. (1983) The analytical solution of the additive constant problem. Psychometrika, 48, 305–310.

Legendre, P. and Anderson, M.J. (1999) Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs, 69, 1–24.

Legendre, P., and Legendre, L. (1998) Numerical ecology, 2nd English edition edition. Elsevier Science BV, Amsterdam.

From the DistPCoa program of P. Legendre et M.J. Anderson
http://www.fas.umontreal.ca/BIOL/Casgrain/en/labo/distpcoa.html

Examples

data(capitales)
d0 <- capitales$dist
is.euclid(d0) # FALSE
d1 <- cailliez(d0, TRUE)
# Cailliez constant = 2429.87867 
is.euclid(d1) # TRUE
plot(d0, d1)
abline(lm(unclass(d1)~unclass(d0)))
print(coefficients(lm(unclass(d1)~unclass(d0))), dig = 8) # d1 = d + Cte
is.euclid(d0 + 2428) # FALSE
is.euclid(d0 + 2430) # TRUE the smallest constant

Example output

[1] FALSE
Cailliez constant = 2429.87867 
[1] TRUE
(Intercept) unclass(d0) 
  2429.8787      1.0000 
[1] FALSE
[1] TRUE

ade4 documentation built on May 2, 2019, 5:50 p.m.