biplot.princomp            package:stats            R Documentation

Biplot for Principal Components

Description:

     Produces a biplot (in the strict sense) from the output of
     'princomp' or 'prcomp'

Usage:

     ## S3 method for class 'prcomp':
     biplot(x, choices = 1:2, scale = 1, pc.biplot = FALSE, ...)

     ## S3 method for class 'princomp':
     biplot(x, choices = 1:2, scale = 1, pc.biplot = FALSE, ...)

Arguments:

       x: an object of class '"princomp"'.

 choices: length 2 vector specifying the components to plot. Only the
          default is a biplot in the strict sense. 

   scale: The variables are scaled by 'lambda ^ scale' and the
          observations are scaled by 'lambda ^ (1-scale)' where
          'lambda' are the singular values as computed by 'princomp'.
          Normally '0 <= scale <= 1', and a warning  will be issued if
          the specified 'scale' is outside this range. 

pc.biplot: If true, use what Gabriel (1971) refers to as a "principal
          component biplot", with 'lambda = 1' and observations scaled
          up by sqrt(n) and variables scaled down by sqrt(n).  Then
          inner products between variables approximate covariances and
          distances between observations approximate Mahalanobis
          distance. 

     ...: optional arguments to be passed to 'biplot.default'.

Details:

     This is a method for the generic function 'biplot'.  There is
     considerable confusion over the precise definitions: those of the
     original paper, Gabriel (1971), are followed here.  Gabriel and
     Odoroff (1990) use the same definitions, but their plots actually
     correspond to 'pc.biplot = TRUE'.

Side Effects:

     a plot is produced on the current graphics device.

References:

     Gabriel, K. R. (1971). The biplot graphical display of matrices
     with applications to principal component analysis. _Biometrika_,
     *58*, 453-467.

     Gabriel, K. R. and Odoroff, C. L. (1990). Biplots in biomedical
     research. _Statistics in Medicine_, *9*, 469-485.

See Also:

     'biplot', 'princomp'.

Examples:

     require(graphics)
     biplot(princomp(USArrests))

