singh: Importance of Variables According to the Singh (1981) Criterion

Description

A function to calculate the Singh (1981) criterion for importance of variables based on the squared generalized Mahalanobis distance. $$S_{.j} = \sum_{i=1}^{n-1} \sum_{i'>i}^{n} (x_{ij} - x_{i'j}) * (\bold{x}_i - \bold{x}_{i'})' * \bold{\Sigma}_{j}^{-1}$$

Usage

## S3 method for class 'default':
singh(data, cov, inverted = FALSE)
## S3 method for class 'singh':
plot(x, ...)

Arguments

data

a data frame or matrix of data (n x p).

cov

a variance-covariance matrix (p x p).

inverted

logical. If FALSE (default), cov is supposed to be a variance-covariance matrix.

an object of class "singh".

...

further graphical arguments.

Value

singh returns a matrix containing the Singh statistic, the importance proportion and the cummulative proprtion of each variable (column) in data.

References

Singh, D. (1981) The relative importance of characters affecting genetic divergence. Indian Journal Genetics & Plant Breeding, 41:237-245.

Examples

Run this code

# Manly (2004, p.65-66)
x1 <- c(131.37, 132.37, 134.47, 135.50, 136.17)
x2 <- c(133.60, 132.70, 133.80, 132.30, 130.33)
x3 <- c(99.17, 99.07, 96.03, 94.53, 93.50)
x4 <- c(50.53, 50.23, 50.57, 51.97, 51.37)
x <- cbind(x1, x2, x3, x4)
Cov <- matrix(c(21.112,0.038,0.078,2.01, 0.038,23.486,5.2,2.844,
	0.078,5.2,24.18,1.134, 2.01,2.844,1.134,10.154), 4, 4)
(s <- singh(x, Cov))
plot(s)

# End (not run)