R: Principal Components Analysis

prcomp {mva}

R Documentation

Principal Components Analysis

Description

Performs a principal components analysis on the given data matrix and returns the results as a prcomp object.

Usage

prcomp(x, retx = TRUE, center = TRUE, scale. = FALSE, tol = NULL)

Arguments

x

a matrix (or data frame) which provides the data for the principal components analysis.

retx

a logical value indicating whether the rotated variables should be returned.

center

a logical value indicating whether the variables should be shifted to be zero centered. Alternately, a vector of length equal the number of columns of x can be supplied. The value is passed to scale.

scale

a logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place. The default is FALSE for consistency with S, but in general scaling is advisable. Alternately, a vector of length equal the number of columns of x can be supplied. The value is passed to scale.

tol

a value indicating the magnitude below which components should be omitted. With the default null setting, no components are omitted. Other settings for tol could be tol = 0 or tol = sqrt(.Machine$double.eps).

Details

The calculation is done with svd on the data matrix, not by using eigen on the covariance matrix. This is generally the preferred method for numerical accuracy. The print method for the these objects prints the results in a nice format and the plot method produces a scree plot.

Value

prcomp returns an list with class "prcomp" containing the following components:

sdev

the standard deviation of the principal components (i.e., the eigenvalues of the cov matrix, though the calculation is actually done with the singular values of the data matrix).

rotation

the matrix of variable loadings (i.e., a matrix whose olumns contain the eigenvectors). The function princomp returns this in the element loadings.

x

if retx is true the value of the rotated data (the data multiplied by the rotation matrix) is returned.

References

Mardia, K. V., J. T. Kent, J and M. Bibby (1979), Multivariate Analysis, London: Academic Press.

Venables, W. N. and B. D. Ripley (1997), Modern Applied Statistics with S-Plus, Springer-Verlag.

Examples

## the variances of the variables in the
## USArrests data vary by orders of magnitude
data(USArrests)
prcomp(USArrests)
prcomp(USArrests, scale = TRUE)
plot(prcomp(USArrests))
summary(prcomp(USArrests))