qbpca {bpca} R Documentation

## 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.

bpca

### Examples

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

## 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!)')