prcomp {mva}R Documentation

Principal Components Analysis

Description

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

Usage

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

Arguments

x a numeric or complex 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. (Components are omitted if their standard deviations are less than or equal to tol times the standard deviation of the first component.) With the default null setting, no components are omitted. Other settings for tol could be tol = 0 or tol = sqrt(.Machine$double.eps), which would omit essentially constant components.

Details

The calculation is done by a singular value decomposition of the (centered and scaled) 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.

If the input has more variables than units then La.svd is used, and the results may differ in sign from versions prior to 1.7.0.

Value

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

sdev the standard deviations of the principal components (i.e., the square roots of the eigenvalues of the covariance/correlation 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 columns 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.

Note

The signs of the columns of the rotation matrix are arbitrary, and so may differ between different programs for PCA, and even between different builds of R.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

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

Venables, W. N. and B. D. Ripley (1997, 9) Modern Applied Statistics with S-PLUS, Springer-Verlag.

See Also

princomp, cor, cov, svd, eigen.

Examples

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

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