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)

Arguments

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'

Value

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

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 $s_{5} = \frac{2 a}{2 a + b + c}$
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 $s_{8} = \frac{a d}{\sqrt{(a + b) (a + c) (d + b) (d + c)}}$
9 = Phi of Pearson: S14 coefficient of Gower & Legendre $s_{9} = \frac{a d - b c}{\sqrt{(a + b) (a + c) (b + d) (d + c)}}$
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

Run this code

# NOT RUN {
data(aviurba)
for (i in 1:10) {
    d <- dist.binary(aviurba$fau, method = i)
    cat(attr(d, "method"), is.euclid(d), "\n")}
# }

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