R in a Nutshell, 2nd Edition

Principal Components Analysis

Another technique for analyzing data is principal components analysis. Principal components analysis breaks a set of (possibly correlated) variables into a set of uncorrelated variables.

In R, principal components analysis is available through the function prcomp in the stats package:

## S3 method for class 'formula':
prcomp(formula, data = NULL, subset, na.action, ...)

## Default S3 method:
prcomp(x, retx = TRUE, center = TRUE, scale. = FALSE,
       tol = NULL, ...)

Here is a description of the arguments to prcomp.

Argument	Description	Default
formula	In the formula method, specifies formula with no response variable, indicating columns of a data frame to use in the analysis.
data	An optional data frame containing the data specified in formula.
subset	An optional vector specifying observations to include in the analysis.
na.action	A function specifying how to deal with NA values.
x	In the default method, specifies a numeric or complex matrix of data for the analysis.
retx	A logical value specifying whether rotated variables should be returned.	TRUE
center	A logical value specifying whether values should be zero centered.	TRUE
scale	A logical value specifying whether values should be scaled to have unit variance.	TRUE
tol	A numeric value specifying a tolerance value below which components should be omitted.	NULL
...	Additional arguments passed to other methods.

As an example, let’s try principal components analysis on a matrix of team batting statistics. Let’s start by loading the ...