princomp
Principal Components Analysis
princomp
performs a principal components analysis on the given
numeric data matrix and returns the results as an object of class
princomp
.
- Keywords
- multivariate
Usage
princomp(x, ...)
"princomp"(formula, data = NULL, subset, na.action, ...)
"princomp"(x, cor = FALSE, scores = TRUE, covmat = NULL, subset = rep_len(TRUE, nrow(as.matrix(x))), ...)
"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 formulaformula
. By default the variables are taken fromenvironment(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 thena.action
setting ofoptions
, and isna.fail
if that is unset. The factory-fresh default isna.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
(andcov.mve
orcov.mcd
from package \href{https://CRAN.R-project.org/package=#1}{\pkg{#1}}MASSMASS). If supplied, this is used rather than the covariance matrix ofx
. - ...
- arguments passed to or from other methods. If
x
is a formula one might specifycor
orscores
. - 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 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
.
Value
- 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"
: seeloadings
for itsprint
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 ifx
was supplied, and ifcovmat
was also supplied if it was a covariance list. For the formula method,napredict()
is applied to handle the treatment of values omitted by thena.action
. - call
- the matched call.
- na.action
- If relevant.
princomp
returns a list with class "princomp"
containing the following components:
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.
See Also
summary.princomp
, screeplot
,
biplot.princomp
,
prcomp
, cor
, cov
,
eigen
.
Examples
library(stats)
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 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)))