Package 'bpca'

Title: Biplot of Multivariate Data Based on Principal Components Analysis
Description: Implements biplot (2d and 3d) of multivariate data based on principal components analysis and diagnostic tools of the quality of the reduction.
Authors: José C. Faria [aut, cre], Ivan B. Allaman [aut], Clarice G. B. Demétrio [aut]
Maintainer: José C. Faria <[email protected]>
License: GPL (>= 2)
Version: 1.3-7
Built: 2025-02-15 04:40:01 UTC
Source: https://github.com/jcfaria/bpca

Help Index

Biplot of Multivariate Data Based on Principal Components Analysis

Description

Implements biplot (2d and 3d) and diagnostic tools of the quality of the reduction.

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.

Examples

##
## Grouping objects with different symbols and colors - 2d and 3d
##

dev.new(w=6, h=6)
oask <- devAskNewPage(dev.interactive(orNone=TRUE))

## Not run: 
# 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)

## End(Not run)

##
## 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')

plot(bpca(ontario),
     type='co',
     obj.labels=obj.lab)

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')

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

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

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

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

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

## Not run: 
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)

Biplot of Multivariate Data Based on Principal Components Analysis

Description

Computes biplot reduction on data.frame, matrix or prcomp objects and returns a bpca object.

Usage

bpca(x, ...)
  ## Default S3 method:
bpca(x,
     d=1:2,
     center=2,
     scale=TRUE,
     method=c('hj', 'sqrt', 'jk', 'gh'),
     iec=FALSE,
     var.rb=FALSE,
     var.rd=FALSE,
     limit=10, ...)
  ## S3 method for class 'prcomp'
bpca(x,
     d=1:2, ...)

Arguments

x

A data.frame, matrix or prcomp object.
d

A vector giving the first and last eigenvalue to be considered by the biplot reduction. It can be d=1:3 or d=c(1,3) for 3d biplot. The default is d=1:2.
center

Numeric. The type of centering to be performed:
‘⁠0⁠’ - no centering
‘⁠1⁠’ - global-centered = sweep(x, 1, mean(x))
‘⁠2⁠’ - column-centered = sweep(x, 2, apply(x, 2, mean))
‘⁠3⁠’ - double-centered = sweep(sweep(x, 1, apply(x, 1, mean)), 2, apply(x, 2, mean)) + mean(x)
The default is 2.
scale

Logical. A value indicating whether the variables should be scaled to have unit variance before the analysis takes place:
FALSE - no scale;
TRUE - scale.
method

A vector of character strings that indicates the method of factorization:
‘⁠hj⁠’ - ‘⁠HJ⁠’ (‘⁠simetric⁠’, Galindo Villardón (1986));
‘⁠sqrt⁠’ - ‘⁠SQRT⁠’ (‘⁠squared root - simetric⁠’, Gabriel (1971));
‘⁠jk⁠’ - ‘⁠JK⁠’ (‘⁠row metric preserving⁠’, Gabriel (1971));
‘⁠gh⁠’ - ‘⁠GH⁠’ (‘⁠column metric preserving⁠’, Gabriel (1971)).
iec

Logical. If TRUE the matrix of eigenvalues, coordinates od objects and variables will be inverted. The default is FALSE.
var.rb

A logical value. If TRUE, all correlation coefficients for all variables (under the biplot projection) will be computed.
var.rd

A logical value. If TRUE, the diagnostic of the representation of variables projected by the biplot will be computed. If var.rd is TRUE the var.rb parameter must be also TRUE.
limit

A vector giving the percentual limit to define poor representation of variables.
...

Additional parameters. It is necessary to be S3 method.

Details

The biplot is a multivariate method for graphing row and column elements using a single plot (Gabriel, 1971).

The biplot of a matrix

nYp_{n}Y_{p}

projects on the same plot: rows (associated with n objects) and columns (associated with p variables), markers from data that forms a two-way table (data.frame or matrix object). The markers are computed from the singular value decomposition, svd(Y), and subsequent factorization.

The bi refers to the kind of information contained in a data set disposed in a two-way table. If the data are a tri-dimensional array the method will be called triplot (not still contemplated in the bpca package).

The basic idea behind the biplot method was to add the information about the variables to the principal component graph (Johnson & Wichern, 1988).

Considering the results of

svd(nYp)svd(_{n}Y_{p})

  • d: A vector containing the singular values of Y, of length min(n, p);

  • u: A matrix whose columns contain the left singular vectors of Y, present if ‘⁠nu > 0⁠’. Dimension ‘⁠c(n, nu)⁠’;

  • v: A matrix whose columns contain the right singular vectors of Y, present if ‘⁠nv > 0⁠’. Dimension c(p, nv).

and also,

s2=diag(d)s^2 = diag(d)

n=n_objects(Y)n = n\_objects(Y)

it is possible an approximation of Y:

nYp≈Ym=g.h′_{n}Y_{p} \approx Y_{m} = g.h'

in various ways. The methods of factorization computed by the bpca function are:

  • HJ - simetric, Galindo Villardón (1986):

    g=u∗s2g = u*s^2

    h=s2∗v′h = s^2*v'

  • SQRT - squared root simetric, Gabriel (1971):

    g=u∗s2g = u*\sqrt{s^2}

    h=s2∗v′h = \sqrt{s^2}*v'

  • JK - row metric preserving, Gabriel (1971):

    g=u∗s2g = u*s^2

    h=v′h = v'

  • GH - column metric preserving, Gabriel (1971):

    g=n−1∗ug = \sqrt{n-1}*u

    h=1n−1∗s2∗v′h = \frac{1}{\sqrt{n-1}}*s^2*v'

Considering

nYp≈Ym_{n}Y_{p} \approx Y_{m}

it is possible to deduce that if the rank (r) of the matrix

nYp_{n}Y_{p}

is bigger than ‘m’, the biplot representation of Y will be an approximation, and accurate only in the case of

r=mr = m

.

Due to the need of different methods of factorization, if ‘⁠x⁠’ is a prcomp object, the method bpca.prcomp will go back from the prcomp function. In other words, it will regenerates, or computes, the inverse of the svd decomposition of the given data

nYp_{n}Y_{p}

After this, it will make a call to the method bpca.default with the adequate parameters.

The biplot is used with many multivariate methods to display relationships between objects, variables and the interrelationship between objects and variables (as prevalence, importance). There are many variations of biplots (see the references).

Value

The function bpca returns an object of class bpca.2d or bpca.3d. Both are list objects with the slots:

call

The call used.
eigenvalues

A vector of the eigenvalues.
eigenvectors

A vector of the eigenvectors.
numer

A vector of the number of eigenvalues considered in the reduction.
importance

A matrix with the general and partial variation explained by the reduction.
coord

A list with the coordinates of the two components: objects and variables.
var.rb

A matrix of all correlation coefficients for all variables under the biplot projection.
var.rd

A matrix of the diagnostic of the poor projection of variable correlations by the biplot reduction.

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)

# Exploring the object 'bp' created by the function 'bpca'
class(bp)
names(bp)
str(bp)

summary(bp)
bp$call
bp$eigenval
bp$eigenvec
bp$numb
bp$import
bp$coord
bp$coord$obj
bp$coord$var
bp$var.rb
bp$var.rd

## Not run: 
##
## Example 2
## Computing and plotting a bpca object with 'scatterplot3d' package - 3d
##

bp <- bpca(gabriel1971,
           d=2:4)

plot(bp,
     var.factor=3,
     xlim=c(-2,2),
     ylim=c(-2,2),
     zlim=c(-2,2))

# Exploring the object 'bp' created by the function 'bpca'
class(bp)
names(bp)
str(bp)

summary(bp)
bp$call
bp$eigenval
bp$eigenvec
bp$numb
bp$import
bp$coord
bp$coord$obj
bp$coord$var
bp$var.rb
bp$var.rd

##
## 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!

##
## 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)

## End(Not run)

devAskNewPage(oask)

Data Tools for Multivariate

Description

Calculates vector variable lengths, angles between vector variables and variable correlations from ‘data.frame’ or ‘matrix’ objects

Usage

dt.tools(x,
           center=2,
           scale=TRUE)

Arguments

x

A data.frame or matrix object.
center

Numeric. The type of centering to be performed:
‘⁠0⁠’ - no centering;
‘⁠1⁠’ - global-centered = sweep(x, 1, mean(x));
‘⁠2⁠’ - column-centered = sweep(x, 2, apply(x, 2, mean));
‘⁠3⁠’ - double-centered = sweep(sweep(x, 1, apply(x, 1, mean)), 2, apply(x, 2, mean)) + mean(x).
The default is 2.
scale

Logical. A value indicating whether the variables should be scaled to have unit variance before the analysis takes place:
FALSE - no scale;
TRUE - scale.

Details

This function computes: vector variable lengths, angles between vector variables and variable correlations from data.frame or matrix objects.

If the data are centered (center=2), the correlations are the same as those obtained by the cor function.

Value

An list with the components:

length

A vector of the lengths.
angle

A matrix of the angles.
r

A matrix of the observed correlations.

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

##
## Computes: vector variable lengths, angles between vector variables and
## variable correlations from data.frame or matrix objects (n x p)
## n = rows (objects)
## p = columns (variables)
##

dt <- dt.tools(iris,
               2)  # No numeric columns are removed in dt.tools 

# Exploring the object 'bp' created by the function 'var.tools'
class(dt)
names(dt)
str(dt)

dt$length
dt$angle
dt$r
dt

# Checking the determinations
(iris.tools <- round(dt.tools(iris,
                              center=2)$r,
                     5))

(iris.obsv  <- round(cor(iris[-5]),
                     5))

all(iris.tools == iris.obsv)

Percentages of households having various facilities and appliances in East Jerusalem Arab areas, by quarters of the town

Description

Percentages of households having various facilities and appliances in East Jerusalem Arab areas, by quarters of the town. The average percentages in each quarter indicate the standard of living of that area and the average percentage of each facility or appliance its over-all prevalence.

Usage

data(gabriel1971)

Format

The format is: ⁠ num [1:8, 1:9] 98.2 78.8 14.4 86.2 32.9 73 4.6 29.2 97.2 81 ... - attr(*, "dimnames")=List of 2 ..$ : chr [1:8] "toilet" "kitchen" "bath" "eletricity" ... ..$ : chr [1:9] "CRISTIAN" "ARMENIAN" "JEWISH" "MOSLEM" ... ⁠

References

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

Examples

##
## A simple example
##
data(gabriel1971)
bp <- bpca(gabriel1971)

dev.new(w=6, h=6)
plot(bp,
     var.factor=2)

# Exploring the object 'bp' created by the function 'bpca'
class(bp)
names(bp)
str(bp)

summary(bp)
bp$call
bp$eigenval
bp$eigenvec
bp$numb
bp$import
bp$coord
bp$coord$obj
bp$coord$var
bp$var.rb
bp$var.rd

A didactic matrix of genotypes (rows) and environments (columns)

Description

A didatic matrix of genotypes (rows) and environments (columns) proposed by Weikai Yan and Manjit S. Kang in GGE biplot analysis: a graphical tool for breeders, geneticists, and agronomists.

Usage

data(gge2003)

Format

The format is: ⁠ num [1:4, 1:3] 20 6 -10 8 -9 12 -6 -12 6 -15 ... - attr(*, "dimnames")=List of 2 ..$ : chr [1:4] "G1" "G2" "G3" "G4" ..$ : chr [1:3] "E1" "E2" "E3" ⁠

References

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

Examples

##
## Example from YAN, W & KANG, M.S. GGE biplot analysis : a graphical tool
## for breeders, geneticists, and agronomists
##

data(gge2003)
bp <- bpca(t(gge2003), var.rb=TRUE)

as.dist(bp$var.rb)

dev.new(w=8, h=4)
op = par(no.readonly=TRUE)
par(mfrow=c(1,2))

plot(bpca(gge2003, var.pos=2),
     main='Columns as variables \n (var.pos=2)',
     var.col=1,
     obj.col=c(2:4, 2), obj.cex=.8)

plot(bpca(gge2003, var.pos=1),
     main='Rows as variables \n (var.pos=1)',
     var.col=1,
     obj.col=2:4, obj.cex=.8)

par(op)

Films shown at five festivals in Brazil from 2007 to 2011

Description

A data.frame containing the films shown at five festivals in Brazil from 2007 to 2011.

Usage

data(marina)

Format

The format is: ⁠ 'data.frame': 25 obs. of 6 variables: year: int 2011 2011 2011 2011 2011 2010 2010 2010 2010 2010 ... regE: Factor w/ 5 levels "CO","N","NE",..: 1 5 4 3 2 1 5 4 3 2 ... F : int 84 55 63 44 25 40 54 37 49 27 ... D : int 26 13 19 16 7 9 14 11 19 6 ... MD : int 22 9 13 14 5 6 11 10 13 3 ... WD : int 4 4 6 2 2 3 3 1 6 3 ... # # Description # year: Year in which the film was shown regE: Region where the film was shown F : Total number of films D : Number of documentaries MD : Documentary directed by men WD : Documentary directed by woman ⁠

Examples

data(marina)

marina

Ontario winter wheat (1993)

Description

The sample data are yields from the 1993 Ontario winter wheat (Triticum aestivum L.) performance trials, in which 18 cultivars were tested at nine locations (Yan and Kang 2003)

Usage

data(ontario)

Format

A data frame with 18 observations on the following 10 variables.

Source

Yan W, Kang MS (2003). GGE Biplot Analysis: A Graphical Tool for Breeders, Geneticists, and Agronomists. CRC Press, Boca Raton, FL, USA.

Examples

data(ontario)

# 2d
plot(bpca(ontario,
          d=1:2))

# 3d
plot(bpca(ontario,
          d=1:3),
     rgl.use=TRUE)

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<360180 < 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)

Print Method for xtable.bpca Objects

Description

Returns (and prints) a summary list for xtable.bpca objects.

Usage

## S3 method for class 'xtable.bpca'
print(x, 
      hline.after = getOption("xtable.hline.after", NULL), 
      include.colnames = getOption("xtable.include.colnames", FALSE), 
      add.to.row = getOption("xtable.add.to.row", NULL), 
      sanitize.text.function = getOption("xtable.sanitize.text.function", NULL),
      sanitize.rownames.function = getOption("xtable.sanitize.rownames.function", 
                                             sanitize.text.function), 
      sanitize.colnames.function = getOption("xtable.sanitize.rownames.function", 
                                             sanitize.text.function),...)

Arguments

x

A given object of the class xtable or xtable.bpca.
hline.after

When type="latex", a vector of numbers between -1 and nrow(x), inclusive, indicating the rows after which a horizontal line should appear. Default value is NULL which means draw a line before and after the columns names, draw a line before variables and at the end of the table.
include.colnames

If TRUE the columns names are printed. Default value is FALSE which means a column more elaborate was done.
add.to.row

A list of two components. The first component (which should be called 'pos') is a list that contains the position of rows on which extra commands should be added at the end. The second component (which should be called 'command') is a character vector of the same length as the first component, which contains the command that should be added at the end of the specified rows. Default value is NULL.
sanitize.text.function

All non-numeric entries (except row and column names) are sanitized in an attempt to remove characters which have special meaning for the output format. If sanitize.text.function is not NULL, it should be a function taking a character vector and returning one, and will be used for the sanitization instead of the default internal function. Default value is NULL.
sanitize.rownames.function

Like the sanitize.text.function, but applicable to row names. The default uses the sanitize.text.function.
sanitize.colnames.function

Like the sanitize.text.function, but applicable to column names. The default uses the sanitize.text.function.
...

Other arguments of the print.xtable function (see xtable package).

Author(s)

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

See Also

xtable.bpca; xtable

Examples

## Example 1: Principal labels in portuguese
library(xtable)

bp2 <- bpca(gabriel1971)  
tbl <- xtable(bp2)
rownames(tbl) <- gsub('Eigenvectors','Autovetores',rownames(tbl))
rownames(tbl) <- c(rownames(tbl)[1:9],'Autovalores','Variância retida','Variância acumulada')
dimnames(tbl)[[2]] <- c('CP 1','CP 2')

print(tbl)

## Example 2: With bold in the column  
tbl1 <- xtable(bp2)
bold <- function(x){
  paste('\textbf{',
        x, 
        '}')
}

print(tbl1,
      sanitize.colnames.function = bold)

# Example 3: With italic in the rows
tbl2 <- xtable(bp2)
italic <- function(x){
  paste('& \textit{',
        x, 
        '}')
} # It is necessary the character "&" to adapt the number of column of the table!

print(tbl2,
      sanitize.rownames.function = italic)

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)

Summary Method for bpca Objects

Description

Returns (and prints) a summary list for bpca (bpca.2d and bpca.3d) objects.

Usage

## S3 method for class 'bpca'
summary(object,
        presentation=FALSE, ...)

Arguments

object

A given object of the class bpca, (bpca.2d or bpca.3d).
presentation

Logic. If TRUE the summary of the class bpca, (bpca.2d, bpca.3d is showed well formated in the screen, else, return a list. The default is FALSE.
...

Potential further arguments (require by generic).

Author(s)

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

See Also

bpca, xtable.bpca

Examples

##
## Example 1
## bpca - 2d
##
# bpca
bp <- bpca(gabriel1971)
summary(bp)
summary(bp,
        presentation=TRUE)

##
## Example 2
## bpca - 3d
##
bp <- bpca(gabriel1971,
           d=1:3)

# bpca
sm <- summary(bp)
str(sm)
sm
summary(bp,
        presentation=TRUE)

Projected Correlations by bpca

Description

Computes the matrix of graphical correlations represented by biplot for a matrix of variable coordinates.

Usage

var.rbf(x)

Arguments

x

A given object of the classes ‘⁠bpca.2d⁠’ and ‘⁠bpca.3d⁠’.

Value

A matrix of graphical correlations represented by biplot.

Note

This function is mainly for internal use in the bpca package, and may not remain available (unless we see a good reason).

Author(s)

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

See Also

bpca

Examples

##
## Particular use
##

bp1 <- bpca(gabriel1971)
bp1$var.rb # NA

# Computes the correlations of all variables under the biplot projection
(res <- var.rbf(bp1$coord$var)) 

##
## Common use
##

bp2 <- bpca(gabriel1971,
            var.rb=TRUE)

bp2$var.rb

Diagnostic of Projected Correlations

Description

Computes the diagnostic of poor graphical correlations projected by biplot according to an arbitrary ‘⁠limit⁠’.

Usage

var.rdf(x,
          var.rb,
          limit)

Arguments

x

A given object of the classe data.frame or matrix.
var.rb

A given object of the class matrix with the projected correlations by biplot.
limit

A vector giving the percentual limit to define poor representation of variables.

Value

A data.frame of poor graphical correlations projected by biplot.

Note

This function is mainly for internal use in the bpca package, and may not remain available (unless we see a good reason).

Author(s)

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

See Also

bpca.

Examples

##
## Example 1
## Diagnostic of gabriel1971 dataset representation
##

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

bp1 <- bpca(gabriel1971,
            meth='hj',
            var.rb=TRUE)

(res <- var.rdf(gabriel1971,
                bp1$var.rb,
                lim=3))
class(res)

##
## Example 2
## Diagnostic of gabriel1971 dataset representation with var.rd parameter
##

bp2 <- bpca(gabriel1971,
            meth='hj',
            var.rb=TRUE,
            var.rd=TRUE,
            limit=3)

plot(bp2,
     var.factor=2)

bp2$var.rd

bp2$eigenvectors

# Graphical visualization of the importance of the variables not contemplated
# in the reduction
plot(bpca(gabriel1971,
          meth='hj',
          d=3:4),
     main='hj',
     xlim=c(-1,1),
     ylim=c(-1,1))

# Interpretation:
# RUR followed by CRISTIAN contains information dimensions that
# wasn't contemplated by the biplot reduction (PC3).
# Between all, RUR followed by CRISTIAN, variables are the most poor represented
# by a 2d biplot.

## Not run: 
##
## Example 3
## Diagnostic of iris dataset representation with var.rd parameter
##

bp3 <- bpca(iris[-5],
            var.rb=TRUE,
            var.rd=TRUE,
            limit=3)

plot(bp3,
     obj.col=c('red', 'green3', 'blue')[unclass(iris$Species)],
     var.factor=.3)

bp3$var.rd
bp3$eigenvectors

# Graphical diagnostic
plot(bpca(iris[-5],
          d=3:4),
     obj.col=c('red', 'green3', 'blue')[unclass(iris$Species)],
     obj.names=FALSE,
     var.factor=.6,
     xlim=c(-2,3),
     ylim=c(-1,1))

# Interpretation:
# Sepal.length followed by Petal.Width contains information in dimensions
# (PC3 - the PC3 is, essentially, a contrast among both) that wasn't fully
# contemplated by the biplot reduction (PC1 and PC2) .
# Therefore, between all variables, they have the most poor representation by a
# 2d biplot.

bp4 <- bpca(iris[-5],
            d=1:3,
            var.rb=TRUE,
            var.rd=TRUE,
            limit=2)

plot(bp4,
     obj.names=FALSE,
     obj.pch=c('+', '-', '*')[unclass(iris$Species)],
     obj.col=c('red', 'green3', 'blue')[unclass(iris$Species)],
     obj.cex=1,
     xlim=c(-5,5),
     ylim=c(-5,5),
     zlim=c(-5,5),
     var.factor=.5)

bp4$var.rd
bp4$eigenvectors

round(bp3$var.rb, 2)

round(cor(iris[-5]), 2)

# Good representation of all variables with a 3d biplot!

## End(Not run)

devAskNewPage(oask)

LaTeX table of the Biplot.

Description

This function returns a LaTeX table of the bpca objects.

Usage

## S3 method for class 'bpca'
xtable(x,
       caption = NULL,
       label = NULL,
       align = NULL,
       digits = NULL,
       display = NULL,
       auto = FALSE, ...)

Arguments

x

A object of the class bpca objects.
caption

Character vector of length 1 or 2 containing the table's caption or title. If length is 2, the second item is the "short caption" used when LaTeX generates a "List of Tables". Set to NULL to suppress the caption. Default value is NULL.
label

Character vector of length 1 containing the LaTeX ‘⁠\label⁠’ or HTML anchor. Set to NULL to suppress the label. Default value is NULL.
align

Character vector of length equal to the number of columns of the resulting table, indicating the alignment of the corresponding columns. Also, "|" may be used to produce vertical lines between columns in LaTeX tables, but these are effectively ignored when considering the required length of the supplied vector. If a character vector of length one is supplied, it is split as strsplit(align, "")[[1]] before processing. Since the row names are printed in the first column, the length of align is one greater than ncol(x) if x is a data.frame. Use "l", "r", and "c" to denote left, right, and center alignment, respectively. for a LaTeX column of the specified width. For HTML output the "p" alignment is interpreted as "l", ignoring the width request. Default depends on the class of x.
digits

Numeric vector of length equal to one (in which case it will be replicated as necessary) or to the number of columns of the resulting table or matrix of the same size as the resulting table, indicating the number of digits to display in the corresponding columns. Since the row names are printed in the first column, the length of the vector digits or the number of columns of the matrix digits is one greater than ncol(x) if x is a data.frame. Default depends on the class of x. If values of digits are negative, the corresponding values of x are displayed in scientific format with abs(digits) digits.
display

Character vector of length equal to the number of columns of the resulting table, indicating the format for the corresponding columns. Since the row names are printed in the first column, the length of display is one greater than ncol(x) if x is a data.frame. These values are passed to the formatC function. Use "d" (for integers), "f", "e", "E", "g", "G", "fg" (for reals), or "s" (for strings). "f" gives numbers in the usual xxx.xxx format; "e" and "E" give n.ddde+nn or n.dddE+nn (scientific format); "g" and "G" put x[i] into scientific format only if it saves space to do so. "fg" uses fixed format as "f", but digits as number of significant digits. Note that this can lead to quite long result strings. Default depends on the class of x.
auto

Logical, indicating whether to apply automatic format when no value is passed to align, digits, or display. This autoformat (based on xalign, xdigits, and xdisplay) can be useful to quickly format a typical matrix or data.frame. Default value is FALSE.
...

Additional arguments. (Currently ignored.)

Details

This function extracts tabular information from x and returns an object of class "xtable.bpca", "xtable" or "data.frame".

It is necessary to declare the latex packages: ‘⁠multirow⁠’ in the preamble of the Rnoweb file to make available all the resources of the function xtable.bpca.

Value

An object of the class xtable.bpca.

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, xtable

Examples

## Example 1: The simplest possible 
library(xtable)

bp <- bpca(iris[-5],
           d=1:3)

xtable(bp)

## Example 2: With caption and label 
bp2 <- bpca(gabriel1971) 

xtable(bp2,
       caption='Biplot gabriel1971',
       label='example_2')