ade4 (version 1.7-19)

dist.binary: Computation of Distance Matrices for Binary Data

Description

computes for binary data some distance matrice.

Usage

dist.binary(df, method = NULL, diag = FALSE, upper = FALSE)

Value

returns a distance matrix of class dist between the rows of the data frame

Arguments

df

a matrix or a data frame with positive or null numeric values. Used with as.matrix(1 * (df > 0))

method

an integer between 1 and 10 . If NULL the choice is made with a console message. See details

diag

a logical value indicating whether the diagonal of the distance matrix should be printed by `print.dist'

upper

a logical value indicating whether the upper triangle of the distance matrix should be printed by `print.dist'

Author

Daniel Chessel
Stéphane Dray

Details

Let be the contingency table of binary data such as \(n_{11} = a\), \(n_{10} = b\), \(n_{01} = c\) and \(n_{00} = d\). All these distances are of type \(d=\sqrt{1-s}\) with s a similarity coefficient.

1 = Jaccard index (1901)

S3 coefficient of Gower & Legendre \(s_1 = \frac{a}{a+b+c}\)

2 = Simple matching coefficient of Sokal & Michener (1958)

S4 coefficient of Gower & Legendre \(s_2 =\frac{a+d}{a+b+c+d}\)

3 = Sokal & Sneath(1963)

S5 coefficient of Gower & Legendre \(s_3 =\frac{a}{a+2(b+c)}\)

4 = Rogers & Tanimoto (1960)

S6 coefficient of Gower & Legendre \(s_4 =\frac{a+d}{(a+2(b+c)+d)}\)

5 = Dice (1945) or Sorensen (1948)

S7 coefficient of Gower & Legendre \(s_5 =\frac{2a}{2a+b+c}\)

6 = Hamann coefficient

S9 index of Gower & Legendre (1986) \(s_6 =\frac{a-(b+c)+d}{a+b+c+d}\)

7 = Ochiai (1957)

S12 coefficient of Gower & Legendre \(s_7 =\frac{a}{\sqrt{(a+b)(a+c)}}\)

8 = Sokal & Sneath (1963)

S13 coefficient of Gower & Legendre \(s_8 =\frac{ad}{\sqrt{(a+b)(a+c)(d+b)(d+c)}}\)

9 = Phi of Pearson

S14 coefficient of Gower & Legendre \(s_9 =\frac{ad-bc}{\sqrt{(a+b)(a+c)(b+d)(d+c)}}\)

10 = S2 coefficient of Gower & Legendre

\(s_1 = \frac{a}{a+b+c+d}\)

References

Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5--48.

Examples

data(aviurba)
for (i in 1:10) {
    d <- dist.binary(aviurba$fau, method = i)
    cat(attr(d, "method"), is.euclid(d), "\n")}