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 formula
princomp(formula, data = NULL, subset, na.action, …)
# S3 method for default
princomp(x, cor = FALSE, scores = TRUE, covmat = NULL,
subset = rep_len(TRUE, nrow(as.matrix(x))), fix_sign = TRUE, …)
# S3 method for princomp
predict(object, newdata, …)
a formula with no response variable, referring only to numeric variables.
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).
an optional vector used to select rows (observations) of the
data matrix x.
a numeric matrix or data frame which provides the data for the principal components analysis.
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.)
a logical value indicating whether the score on each principal component should be calculated.
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 of class inheriting from "princomp".
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.
princomp returns a list with class "princomp"
containing the following components:
the standard deviations of the principal components.
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.
the means that were subtracted.
the scalings applied to each variable.
the number of observations.
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.
the matched call.
If relevant.
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.
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.
# NOT RUN {
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)
# }
# NOT RUN {
pc.cr$scores[1:5, ]
# }
# NOT RUN {
## (Simple) Robust PCA:
## Classical:
(pc.cl <- princomp(stackloss))
# }
# NOT RUN {
## Robust:
(pc.rob <- princomp(stackloss, covmat = MASS::cov.rob(stackloss)))
# }