cailliez {ade4} | R Documentation

## Transformation to make Euclidean a distance matrix

### Description

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

### Usage

    cailliez(distmat, print = FALSE)

### Arguments

`distmat` | an object of class `dist`
`print` | if TRUE, prints the eigenvalues of the matrix

### Value

an object of class `dist` containing a Euclidean distance matrix.

### Author(s)

Daniel Chessel chessel@biomserv.univ-lyon1.fr

### 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

    library(mva)
    data(capitales)
    d0 <- as.dist(capitales$df)
    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

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