R: Principal Components Analysis

princomp {mva}

R Documentation

Principal Components Analysis

Description

princomp performs a principal components analysis on the given data matrix and returns the results as a princomp object.

loadings extracts the loadings.

screeplot plots the variances against the number of the principal component. This is also the plot method.

Usage

princomp(x, cor = FALSE, scores = TRUE,
         subset = rep(TRUE, nrow(as.matrix(x))))
loadings(x)
plot(x, npcs = min(10, length(x$sdev)),
          type = c("barplot", "lines"), ...) 
screeplot(x, npcs = min(10, length(x$sdev)),
          type = c("barplot", "lines"), ...) 

print(x,...)  summary(object)  predict(object,...)

Arguments

x

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

cor

a logical value indicating whether the calculation should use the correlation matrix or the covariance matrix.

score

a logical value indicating whether the score on each principal component should be calculated.

subset

a vector used to select rows (observations) of the data matrix x.

x, object

an object of class "princomp", as from princomp().

npcs

the number of principal components to be plotted.

type

the type of plot.

...

graphics parameters.

Details

The calculation is done using eigen on the correlation or covariance matrix, as determined by cor. This is done for compatibility with the S-PLUS result (even though alternate forms for x—e.g., a covariance matrix—are not supported as they are in S-PLUS). A preferred method of calculation is to use svd on x, as is done in prcomp.

Note that the scaling of results is affected by the setting of cor. If cor is TRUE then the divisor in the calculation of the sdev is N-1, otherwise it is N. This has the effect that the result is slightly different depending on whether scaling is done first on the data and cor set to FALSE, or done automatically in princomp with cor = TRUE.

The print method for the these objects prints the results in a nice format and the plot method produces a scree plot.

Value

princomp returns a list with class "princomp" containing the following components:

sdev

the standard deviations of the principal components (i.e., the square roots of the eigenvalues, rescaled by (N-1)/N)

loadings

the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors).

center

the means that were subtracted.

scale

the scalings applied to each variable.

n.obs

the number of observations.

scores

if scores = TRUE, the scores of the supplied data on the principal components.

call

the matched call.

References

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.

Examples

## the variances of the variables in the
## USArrests data vary by orders of magnitude
data(USArrests)
(pc.cr <- princomp(USArrests))
princomp(USArrests, cor = TRUE)
princomp(scale(USArrests, scale = TRUE, center = TRUE), cor = FALSE)

summary(pc.cr <- princomp(USArrests))
loadings(pc.cr)
plot(pc.cr) # does a screeplot.
biplot(pc.cr)