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_len(TRUE, nrow(as.matrix(x))), fix_sign = TRUE, ...)

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

Arguments

`formula`	a formula with no response variable, referring only to numeric variables.
`data`	an optional data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`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`.
`x`	a numeric 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. (The correlation matrix can only be used if there are no constant variables.)
`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` (and `cov.mve` or `cov.mcd` from package MASS). If supplied, this is used rather than the covariance matrix of `x`.
`fix_sign`	Should the signs of the loadings and scores be chosen so that the first element of each loading is non-negative?
`...`	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`	An optional data frame or matrix in which to look for variables with which to predict. If omitted, the scores are used. If the original fit used a formula or a data frame or a matrix with column names, `newdata` must contain columns with the same names. Otherwise it must contain the same number of columns, to be used in the same order.

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 was 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 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. For the formula method, `napredict()` is applied to handle the treatment of values omitted by the `na.action`.
`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: fix_sign = TRUE alleviates that.

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

require(graphics)

## The variances of the variables in the
## USArrests data vary by orders of magnitude, so scaling is appropriate
(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
## The signs of the columns of the loadings are arbitrary
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[1:5, ]

## (Simple) Robust PCA:
## Classical:
(pc.cl  <- princomp(stackloss))
## Robust:
(pc.rob <- princomp(stackloss, covmat = MASS::cov.rob(stackloss)))

[Package stats version 4.4.0 Index]