| princomp | R Documentation |
princomp performs a principal components analysis on the given
numeric data matrix and returns the results as an object of class
princomp.
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, ...)
formula |
a formula with no response variable, referring only to numeric variables. |
data |
an optional data frame (or similar: see
|
subset |
an optional vector used to select rows (observations) of the
data matrix |
na.action |
a function which indicates what should happen
when the data contain |
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
|
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 |
object |
Object of class inheriting from |
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, |
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 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.
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
|
center |
the means that were subtracted. |
scale |
the scalings applied to each variable. |
n.obs |
the number of observations. |
scores |
if |
call |
the matched call. |
na.action |
If relevant. |
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.
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.
summary.princomp, screeplot,
biplot.princomp,
prcomp, cor, cov,
eigen.
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)))
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