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

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 nonnegative? 
... 
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, 
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 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
.
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

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. 
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, SpringerVerlag.
See Also
summary.princomp
, screeplot
,
biplot.princomp
,
prcomp
, cor
, cov
,
eigen
.
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)
## NAhandling
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)))