R: Biplot for Principal Components

biplot.princomp {mva} | R Documentation

## Biplot for Principal Components

### Description

Produces a biplot (in the strict sense) from the output of `princomp`.

### Usage

    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

    data(USArrests)
    biplot(princomp(USArrests))

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