qbpca {bpca}

Quality of the Representation of Variables by Biplot

Description

This function returns an object of the class qbpca. It is a simple measure of the quality of biplot representation of the variables. The observed (in the data) and projected (under biplot reduction) correlations are computed.

Usage

  qbpca(x,
        bpca)

Arguments

x

A data.frame or matrix object.

bpca

A object of the class bpca.

Details

This function binds the vectors of observed (from the matrix or data.frame) and projected (under biplot reduction) correlations for all variables.

Value

An object of class qbpca and data.frame with two columns:

obs

A vector of the observed correlations for all variables.

var.rb

A vector of the projected correlations for all variables determined under biplot reduction).

Author(s)

Faria, J. C.
Allaman, I. B.
Demétrio C. G. B.

References

Johnson, R. A. and Wichern, D. W. (1988) Applied multivariate statistical analysis. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 6 ed.

See Also

bpca

Examples

##
## Example 1
## Example of 'var.rb=TRUE' parameter as a measure of the quality of the biplot - 2d
##

oask <- devAskNewPage(dev.interactive(orNone=TRUE))

## Differences between methods of factorization
# SQRT
bp1 <- bpca(gabriel1971,
            meth='sqrt',
            var.rb=TRUE)

qbp1 <- qbpca(gabriel1971,
              bp1)

plot(qbp1,
     main='sqrt - 2d \n (poor)')


# JK
bp2 <- bpca(gabriel1971,
            meth='jk',
            var.rb=TRUE)

qbp2 <- qbpca(gabriel1971,
              bp2)

plot(qbp2,
     main='jk - 2d \n (very poor)')


# GH
bp3 <- bpca(gabriel1971,
            meth='gh',
            var.rb=TRUE)

qbp3 <- qbpca(gabriel1971,
              bp3)

plot(qbp3,
     main='gh - 2d \n (good)')


# HJ
bp4 <- bpca(gabriel1971,
            meth='hj',
            var.rb=TRUE)

qbp4 <- qbpca(gabriel1971,
             bp4)

plot(qbp4,
     main='hj - 2d \n (good)')

##
## Example 2
## Example of 'var.rb=TRUE' parameter as a measure of the quality of the biplot - 3d
##

## Differences between methods of factorization
# SQRT
bp1 <- bpca(gabriel1971,
            meth='sqrt',
            d=1:3,
            var.rb=TRUE)

qbp1 <- qbpca(gabriel1971,
              bp1)

plot(qbp1,
     main='sqrt - 3d \n (poor)')


# JK
bp2 <- bpca(gabriel1971,
            meth='jk',
            d=1:3,
            var.rb=TRUE)

qbp2 <- qbpca(gabriel1971,
             bp2)

plot(qbp2,
     main='jk - 3d \n (very poor)')


# GH
bp3 <- bpca(gabriel1971,
            meth='gh',
            d=1:3,
            var.rb=TRUE)

qbp3 <- qbpca(gabriel1971,
              bp3)

plot(qbp3,
     main='gh - 3d \n (whow!)')


# HJ
bp4 <- bpca(gabriel1971,
            meth='hj',
            d=1:3,
            var.rb=TRUE)

qbp4 <- qbpca(gabriel1971,
              bp4)

plot(qbp4,
     main='hj - 3d \n (whow!)')

devAskNewPage(oask)