R: Principal Components Analysis

princomp {stats}

R Documentation

Principal Components Analysis

Description

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

Usage

princomp(x, ...)

## S3 method for class 'formula':
princomp(formula, data = NULL, subset, na.action, ...)

## Default S3 method:
princomp(x, cor = FALSE, scores = TRUE, covmat = NULL,
         subset = rep(TRUE, nrow(as.matrix(x))), ...)

## S3 method for class 'princomp':
predict(object, newdata, ...)

Arguments

`formula`	a formula with no response variable.
`data`	an optional data frame containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`x`	a numeric matrix or data frame which provides the data for the principal components analysis.
`subset`	an optional vector used to select rows (observations) of the data matrix `x`.
`na.action`	a function which indicates what should happen when the data contain `NA`s. The default is set by the `na.action` setting of `options`, and is `na.fail` if that is unset. The “factory-fresh” default is `na.omit`.
`cor`	a logical value indicating whether the calculation should use the correlation matrix or the covariance matrix.
`scores`	a logical value indicating whether the score on each principal component should be calculated.
`covmat`	a covariance matrix, or a covariance list as returned by `cov.wt`, `cov.mve` or `cov.mcd`. If supplied, this is used rather than the covariance matrix of `x`.
`...`	arguments passed to or from other methods. If `x` is a formula one might specify `cor` or `scores`.
`object`	Object of class inheriting from `"princomp"`
`newdata`	Data frame in which to predict

Details

princomp is a generic function with "formula" and "default" methods.

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. A preferred method of calculation is to use svd on x, as is done in prcomp.

Note that the default calculation uses divisor N for the covariance matrix.

The print method for the these objects prints the results in a nice format and the plot method produces a scree plot (screeplot). There is also a biplot method.

If x is a formula then the standard NA-handling is applied to the scores (if requested): see napredict.

princomp only handles so-called R-mode PCA, that is feature extraction of variables. If a data matrix is supplied (possibly via a formula) it is required that there are at least as many units as variables. For Q-mode PCA use prcomp.

Value

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

`sdev`	the standard deviations of the principal components.
`loadings`	the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors). This is of class `"loadings"`: see `loadings` for its `print` method.
`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. These are non-null only if `x` was supplied, and if `covmat` was also supplied if it was a covariance list.
`call`	the matched call.
`na.action`	If relevant.

Note

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

References

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

Venables, W. N. and B. D. Ripley (2002). Modern Applied Statistics with S, Springer-Verlag.

Examples

## The variances of the variables in the
## USArrests data vary by orders of magnitude, so scaling is appropriate
data(USArrests)
(pc.cr <- princomp(USArrests))  # inappropriate
princomp(USArrests, cor = TRUE) # =^= prcomp(USArrests, scale=TRUE)
## Similar, but different:
## The standard deviations differ by a factor of sqrt(49/50)

summary(pc.cr <- princomp(USArrests, cor = TRUE))
loadings(pc.cr)  ## note that blank entries are small but not zero
plot(pc.cr) # shows a screeplot.
biplot(pc.cr)

## Formula interface
princomp(~ ., data = USArrests, cor = TRUE)
# NA-handling
USArrests[1, 2] <- NA
pc.cr <- princomp(~ Murder + Assault + UrbanPop,
                  data = USArrests, na.action=na.exclude, cor = TRUE)
pc.cr$scores

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