plot {bpca}

Biplot of Multivariate Data Based on Principal Components Analysis

Description

These are methods for objects of class bpca.2d, bpca.3d and qbpca.

Usage

  ## S3 method for class 'bpca.2d'
plot(x,
     type=c('bp', 'eo', 'ev', 'co', 'cv', 'ww', 'dv', 'ms', 'ro', 'rv'),
     c.color='darkgray',
     c.lwd=1,
     c.number=5,
     c.radio=1,
     obj.id=1:2,
     var.id=1,
     base.color='red3',
     base.lty='dotted',
     proj.color='gray',
     proj.lty='dotted',
     a.color='blue',
     a.lty='solid',
     a.lwd=2,
     a.length=.1,
     ref.lines=TRUE,
     ref.color='navy',
     ref.lty='dotted',
     var.factor=1,
     var.color='red3',
     var.lty='solid',
     var.pch=20,
     var.pos=4,
     var.cex=.6,
     var.offset=.2,
     obj.factor=1,
     obj.color='black',
     obj.pch=20,
     obj.pos=4,
     obj.cex=.6,
     obj.offset=.2,
     obj.names=TRUE,
     obj.labels,
     obj.identify=FALSE,
     xlim,
     ylim,
     xlab,
     ylab, ...)

  ## S3 method for class 'bpca.3d'
plot(x,
     rgl.use=FALSE,
     ref.lines=TRUE,
     ref.color='navy',
     ref.lty=ifelse(rgl.use, NA, 'dotted'),
     clear3d=ifelse(rgl.use, TRUE, NULL),
     simple.axes=ifelse(rgl.use, TRUE, NULL),
     aspect=ifelse(rgl.use, c(1, 1, 1), NULL),
     var.factor=1,
     var.color='red3',
     var.lty=ifelse(rgl.use, NA, 'solid'),
     var.pch=ifelse(rgl.use, NULL, 20),
     var.pos=ifelse(rgl.use, 0, 4),
     var.cex=ifelse(rgl.use, .8, .6),
     var.offset=ifelse(rgl.use, NULL, .2),
     obj.color='black',
     obj.pch=ifelse(rgl.use, NULL, 20),
     obj.pos=ifelse(rgl.use, 0, 4),
     obj.cex=ifelse(rgl.use, .8, .6),
     obj.offset=ifelse(rgl.use, NULL, .2),
     obj.names=TRUE,
     obj.labels,
     obj.identify=FALSE,
     box=FALSE,
     angle=ifelse(rgl.use, NULL, 40),
     xlim,
     ylim,
     zlim,
     xlab,
     ylab,
     zlab, ...)

  ## S3 method for class 'qbpca'
plot(x,
     xlab='Index',
     ylab='r',
     pch=c(1,8),
     col=c(4,2), ...)

Arguments

x

A bpca.2d, bpca.3d or qbpca object.

type

Type of biplot:
‘⁠bp⁠’ - conventional biplot;
‘⁠eo⁠’ - evaluate an object;
‘⁠ev⁠’ - evaluate a variable;
‘⁠co⁠’ - compare two objects;
‘⁠cv⁠’ - compare (relationship among) variables;
‘⁠ww⁠’ - which won where/what;
‘⁠dv⁠’ - discrimitiveness vs. representativeness;
‘⁠ms⁠’ - mean vs. stability;
‘⁠ro⁠’ - rank objects with ref. to an “ideal” variable;
‘⁠rv⁠’ - rank variables with ref. to an “ideal” object.

c.color

The color of circles.

c.lwd

The lwd of circles.

c.number

The number of circles.

c.radio

The radio of circles.

obj.id

An object(s) number(s) or name(s). It is used with reprojctions to identify the object(s) when the type option is ‘⁠'eo'⁠’ or ‘⁠'co'⁠’. The default is ‘⁠1⁠’ for ‘⁠'eo'⁠’ and 1:2 for ‘⁠'co'⁠’.

var.id

A variable number or name. It is used with reprojections to identify the variable when the ‘⁠type⁠’ option is 'ev'.

base.color

The color for the base lines. It is used only with reprojections.

base.lty

The ‘⁠lty⁠’ for the base lines. It is used only with reprojections.

proj.color

The color for the projections lines. It is used only with reprojections.

proj.lty

The ‘⁠lty⁠’ for the projections lines. It is used only with reprojections.

a.color

The color for the arrow. It is used only with reprojections.

a.lty

The ‘⁠lty⁠’ for the arrow. It is used only with reprojections.

a.lwd

The ‘⁠lwd⁠’ for the arrow. It is used only with reprojections.

a.length

The ‘⁠length⁠’ for the arrow. It is used only with reprojections.

rgl.use

A logical value. If TRUE the 3d scatter will be done with the rgl environment, in another way the scatterplot3d will be used.

ref.lines

A logical value. If TRUE, the reference lines will be added to the biplot.

ref.color

Line color for reference lines.

ref.lty

Line type of the reference lines.

clear3d

A logical value. It clears (or not) a 3d biplot before making a new one. Used only if rgl.use=TRUE.

simple.axes

A logical value to draw simple axes. Used only if rgl.use=TRUE.

aspect

A vector of the apparent ratios of the ‘⁠x⁠’, ‘⁠y⁠’, and ‘⁠z⁠’ axes of the bounding box. Used only if rgl.use=TRUE.

var.factor

Factor of expansion/reduction of length lines of the variables.

var.color

A vector of colors for the variables representation.

var.lty

Line type for the variables. Used only if rgl.use=FALSE.

var.pch

A vector of plotting symbols or characters for the variables. If too short, the values are recycled. Used only if rgl.use=FALSE.

var.pos

Position of labels for the variables.

var.cex

Character expansion for the variables.

var.offset

The distance (in character widths) which separates the label from identified points of variables. Negative values are allowed. Used only if rgl.use=FALSE.

obj.factor

Factor of expansion/reduction of length lines of the objects.

obj.color

A vector of colors for the objects representation.

obj.pch

A vector of plotting symbols or characters for objects. If too short, the values are recycled. Used only if rgl.use=FALSE.

obj.pos

Position of labels for objects.

obj.cex

Character expansion for objects.

obj.offset

The distance (in character widths) which separates the label from identified points of objects. Negative values are allowed. Used only if rgl.use=FALSE.

obj.names

A logical value to represent objects as spheres or points.

obj.identify

A logical value. If TRUE, it is possible, in interative way, to identify the objects with the mouse.

obj.labels

A vector of labels for objects.

box

A logical value to whether to draw a box. Used only if ‘⁠rgl.use=TRUE⁠’.

angle

Angle between ‘⁠x⁠’ and ‘⁠y⁠’ axis (Attention: result depends on scaling). For 180 < angle < 360 the returned functions xyz.convert and points3d will not work properly. Used only if rgl.use=FALSE.

pch

A vector of plotting symbols or characters.

col

A vector of colors.

xlab

A label for the ‘⁠x⁠’ axis.

ylab

A label for the ‘⁠y⁠’ axis.

zlab

A label for the ‘⁠z⁠’ axis (bpca.3d only).

xlim

The ‘⁠x⁠’ limits of the plot.

ylim

The ‘⁠y⁠’ limits of the plot.

zlim

The ‘⁠z⁠’ limits of the plot (bpca.3d only).

...

Other graphical parameters may also be passed as arguments to these functions.

Details

A biplot aims to represent both the observations and variables of a matrix of multivariate data on the same plot.

The methods plot.bpca.2d draw a 2d biplot (PC1 and PC2 on axis ‘⁠x⁠’ and ‘⁠y⁠’, respectively). It uses the traditional graphics system.

The methods plot.bpca.3d draw a 3d biplot (PC1, PC2 and PC3 on axis ‘⁠x⁠’, ‘⁠y⁠’ and ‘⁠z⁠’, respectively) in two ways:

1. static: It uses the package scatterplot3d based on traditional graphic system. Use the parameter ‘⁠rgl.use=FALSE⁠’ for it. It is the default.

2. dinamic: It uses the package rgl a 3D real-time rendering device driver system for R. Use the parameter ‘⁠rgl.use=TRUE⁠’ for it.

The method qb.pca draws a scatterplot of the correlations observed (in the data) and projected (under the biplot) related to the variables. It uses the traditional graphics system. qb.pca is a simple (and graphical) measure of the quality of the biplot reduction associated to the variables.

Author(s)

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

References

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

Galindo Vilardón, M. P. (1986) Una alternativa de representación simultánea: HJ-Biplot. Qüestiió, 10(1):13-23, 1986.

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

Gower, J.C. and Hand, D. J. (1996) Biplots. Chapman & Hall.

Yan, B. W. and Kang, M. S. (2003) GGE biplot analysis: a graphical tool for breeders, geneticists, and agronomists. CRC Press, New York, 288p.

See Also

biplot.prcomp

Examples

##
## Example 1
## Computing and ploting a bpca object with 'graphics' package - 2d
##

bp <- bpca(gabriel1971)

dev.new(w=6, h=6)
oask <- devAskNewPage(dev.interactive(orNone=TRUE))
plot(bp,
     var.factor=2)

# Additional graphical parameters (nonsense)
plot(bpca(gabriel1971,
          meth='sqrt'),
     main='gabriel1971 - sqrt',
     sub='The graphical parameters are working fine!',
     var.factor=2,
     var.cex=.6,
     var.col=rainbow(9),
     var.pch='v',
     obj.pch='o',
     obj.cex=.5,
     obj.col=rainbow(8),
     obj.pos=1,
     obj.offset=.5)

##
## Example 2
## Computing and plotting a bpca object with 'scatterplot3d' package - 3d
##

bp <- bpca(gabriel1971,
           d=1:3)

plot(bp,
     var.factor=3)

# Additional graphical parameters (nonsense)
plot(bpca(gabriel1971,
          d=1:3,
          meth='jk'),
     main='gabriel1971 - jk',
     sub='The graphical parameters are working fine!',
     var.factor=6,
     var.pch='+',
     var.cex=.6,
     var.col='green4',
     obj.pch='*',
     obj.cex=.8,
     obj.col=1:8,
     ref.lty='solid',
     ref.col='red',
     angle=70)

##
## Example 3
## Computing and plotting a bpca object with 'rgl' package - 3d
##

plot(bpca(gabriel1971,
          d=1:3),
     rgl.use=TRUE,
     var.factor=2)

# Suggestion: Interact with the graphic with the mouse
# left button: press, maintain and movement it to interactive rotation;
# right button: press, maintain and movement it to interactive zoom.
# Enjoy it!

## Not run: 
##
## Example 4
## Grouping objects with different symbols and colors - 2d and 3d
##

# 2d
plot(bpca(iris[-5]),
     var.factor=.3,
     var.cex=.7,
     obj.names=FALSE,
     obj.cex=1.5,
     obj.col=c('red', 'green3', 'blue')[unclass(iris$Species)],
     obj.pch=c('+', '*', '-')[unclass(iris$Species)])

# 3d static
plot(bpca(iris[-5],
          d=1:3),
     var.factor=.2,
     var.color=c('blue', 'red'),
     var.cex=1,
     obj.names=FALSE,
     obj.cex=1,
     obj.col=c('red', 'green3', 'blue')[unclass(iris$Species)],
     obj.pch=c('+', '*', '-')[unclass(iris$Species)])

# 3d dynamic
plot(bpca(iris[-5],
          method='hj',
          d=1:3),
     rgl.use=TRUE,
     var.col='brown',
     var.factor=.3,
     var.cex=1.2,
     obj.names=FALSE,
     obj.cex=.8,
     obj.col=c('red', 'green3', 'orange')[unclass(iris$Species)],
     simple.axes=FALSE, box=TRUE)

##
## Example 5
## Computing and plotting a bpca object with 'obj.identify=TRUE' parameter - 2d
##

bp <- bpca(gabriel1971)

# Normal labels
if(interactive())
plot(bp,
     obj.names=FALSE,
     obj.identify=TRUE)

# Alternative labels
if(interactive())
plot(bp,
     obj.names=FALSE,
     obj.labels=c('toi', 'kit', 'bat', 'ele', 'wat', 'rad', 'tv', 'ref'),
     obj.identify=TRUE)

##
## Example 6
## Computing and plotting a bpca object with 'obj.identify=TRUE' parameter - 3d
##

bp <- bpca(gabriel1971,
           d=1:3)

# Normal labels
if(interactive())
plot(bp,
     obj.names=FALSE,
     obj.identify=TRUE)

# Alternative labels
if(interactive())
plot(bp,
     obj.names=FALSE,
     obj.labels=c('toi', 'kit', 'bat', 'ele', 'wat', 'rad', 'tv', 'ref'),
     obj.identify=TRUE)

##
## New options plotting
##
plot(bpca(ontario))

# Labels for all objects
(obj.lab <- paste('g',
                  1:18,
                  sep=''))

# Giving obj.labels
plot(bpca(ontario),
    obj.labels=obj.lab) 

# Evaluate an object (1 is the default)
plot(bpca(ontario),
     type='eo',
     obj.cex=1)

plot(bpca(ontario),
     type='eo',
     obj.id=7,
     obj.cex=1)

# Giving obj.labels
plot(bpca(ontario),
     type='eo',
     obj.labels=obj.lab,
     obj.id=7,
     obj.cex=1)

# The same as above
plot(bpca(ontario),
     type='eo',
     obj.labels=obj.lab,
     obj.id='g7',
     obj.cex=1)

# Evaluate a variable (1 is the default)
plot(bpca(ontario),
     type='ev',
     var.pos=2,
     var.cex=1)

plot(bpca(ontario),
     type='ev',
     var.id='E7',
     obj.labels=obj.lab,
     var.pos=1,
     var.cex=1)

# A complete plot
cl <- 1:3
plot(bpca(iris[-5]),
     type='ev',
     var.id=1,
     var.fac=.3,
     obj.names=FALSE,
     obj.col=cl[unclass(iris$Species)])
legend('topleft',
       legend=levels(iris$Species),
       text.col=cl,
       pch=19,
       col=cl,
       cex=.9,
       box.lty=0)   

# Compare two objects (1 and 2 are the default)
plot(bpca(ontario), 
     type='co',
     c.radio=.4,
     c.color='blue',
     c.lwd=2)

plot(bpca(ontario),
     type='co',
     obj.labels=obj.lab,
     c.radio=.5,
     c.color='blue',
     c.lwd=2)

plot(bpca(ontario),
     type='co',
     obj.labels=obj.lab,
     obj.id=13:14)

plot(bpca(ontario),
     type='co',
     obj.labels=obj.lab,
     obj.id=c('g7', 
              'g13'))

# Compare two variables
plot(bpca(ontario),
     type='cv',
     c.number=3,
     c.radio=1.5)

# Which won where/what
plot(bpca(ontario),
     type='ww')

# Discrimitiveness vs. representativeness
plot(bpca(ontario),
     type='dv')

plot(bpca(ontario),
     type='dv',
     c.number=4,
     c.radio=1)

# Means vs. stability
plot(bpca(ontario),
     type='ms')

plot(bpca(ontario),
     type='ms',
     c.number=3)

# Rank objects with ref. to the ideal variable 
plot(bpca(ontario),
     type='ro')

plot(bpca(ontario),
     type='ro',
     c.number=6,
     c.radio=.5)

# Rank variables with ref. to the ideal object
plot(bpca(ontario),
     type='rv')

plot(bpca(ontario),
     type='rv',
     c.number=6,
     c.radio=.5)

plot(bpca(iris[-5]),
     type='eo',
     obj.id=42,
     obj.cex=1)

plot(bpca(iris[-5]),
     type='ev',
     var.id='Sepal.Width')

plot(bpca(iris[-5]),
     type='ev',
     var.id='Sepal.Width',
     var.factor=.3)

## End(Not run)

devAskNewPage(oask)