princomp {stats}  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(TRUE, nrow(as.matrix(x))), ...) ## 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
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 “factoryfresh”
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 . 
... 
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.

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 SPLUS 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 NAhandling is applied to
the scores (if requested): see napredict
.
princomp
only handles socalled Rmode 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 Qmode 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
"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 nonnull 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. 
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.
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, SpringerVerlag.
summary.princomp
, screeplot
,
biplot.princomp
,
prcomp
, cor
, cov
,
eigen
.
## 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 plot(pc.cr) # shows a screeplot. biplot(pc.cr) ## Formula interface princomp(~ ., data = USArrests, cor = TRUE) # NAhandling USArrests[1, 2] < NA pc.cr < princomp(~ Murder + Assault + UrbanPop, data = USArrests, na.action=na.exclude, cor = TRUE) pc.cr$scores