| Version: | 1.7.7 |
| Date: | 2020-06-18 |
| Title: | Calibration of Scatterplot and Biplot Axes |
| Author: | Jan Graffelman <jan.graffelman@upc.edu> |
| Maintainer: | Jan Graffelman <jan.graffelman@upc.edu> |
| Depends: | R (≥ 3.5.0), MASS |
| Description: | Package for drawing calibrated scales with tick marks on (non-orthogonal) variable vectors in scatterplots and biplots. Also provides some functions for biplot creation and for multivariate analysis such as principal coordinate analysis. |
| License: | GPL-2 |
| NeedsCompilation: | no |
| Packaged: | 2020-06-18 19:36:22 UTC; jangr |
| Repository: | CRAN |
| Date/Publication: | 2020-06-19 05:40:14 UTC |
Function for Principal Coordinate Analysis
Description
Function PrinCoor implements Principal Coordinate Analysis, also known as classical metric multidimensional scaling or
classical scaling. In comparison with other software, it offers refined statistics for goodness-of-fit at the level of individual observations and pairs of observartions.
Usage
PrinCoor(Dis, eps = 1e-10)
Arguments
Dis |
A distance matrix or dissimilarity matrix |
eps |
A tolerance criterion for deciding if eigenvalues are zero or not |
Details
Calculations are based on the spectral decomposition of the scalar product matrix B, derived from the distance matrix.
Value
X |
The coordinates of the the solution |
la |
The eigenvalues of the solution |
B |
The scalar product matrix |
standard.decom |
Standard overall goodness-of-fit table using all eigenvalues |
positive.decom |
Overall goodness-of-fit table using only positive eigenvalues |
absolute.decom |
Overall goodness-of-fit table using absolute values of eigenvalues |
squared.decom |
Overall goodness-of-fit table using squared eigenvalues |
RowStats |
Detailed goodness-of-fit statistics for each row |
PairStats |
Detailed goodness-of-fit statistics for each pair |
Author(s)
Jan Graffelman jan.graffelman@upc.edu
References
Graffelman, J. (2019) Goodness-of-fit filtering in classical metric multidimensional scaling with large datasets. <doi: 10.1101/708339>
Graffelman, J. and van Eeuwijk, F.A. (2005) Calibration of multivariate scatter plots for exploratory analysis of relations within and between sets of variables in genomic research Biometrical Journal, 47(6) pp. 863-879.
See Also
Examples
data(spaindist)
results <- PrinCoor(as.matrix(spaindist))
General function for making biplots
Description
Function bplot creates biplots on the basis matrices of row
and column markers.
Usage
bplot(Fr,G,rowlab=rownames(Fr),collab=rownames(G),qlt=rep(1,nrow(Fr)),
refaxis=TRUE,ahead=T,xl=NULL,yl=NULL,frame=F,qltlim=0,rowch=19,
colch=19,qltvar=NULL,rowcolor="red",colcolor="blue",rowmark=TRUE,
colmark=TRUE,rowarrow=FALSE,colarrow=TRUE,markrowlab=TRUE,
markcollab=TRUE,xlab="",ylab="",cex.rowlab=1,cex.rowdot=0.75,
cex.collab=1,cex.coldot=0.75,cex.axis=0.75,lwd=1,arrowangle=10,...)Arguments
Fr |
matrix with coordinates of the row markers. |
G |
matrix with coordinates of the column markers. |
rowlab |
vector with labels for the rows. |
collab |
vector with labels for the columns. |
qlt |
goodness of fit of the rows. |
refaxis |
draw coordinate system |
ahead |
put a head on the vectors |
xl |
limits for the x-axis. |
yl |
limits for the y-axis. |
frame |
draw a box around the plot |
qltlim |
draw only the vectors with a goodness of fit larger than |
rowch |
character used for the row markers. |
colch |
character used for the column markers. |
qltvar |
vector with the goodness of fit of each variable. |
rowcolor |
colour used for the row markers. |
colcolor |
colour used for the column markers. |
rowmark |
show row markers ( |
colmark |
show column markers ( |
rowarrow |
draw vectors from the origin to the row markers ( |
colarrow |
draw vectors from the origin to the column markers ( |
markrowlab |
depict row marker labels ( |
markcollab |
depict column marker labels ( |
xlab |
a label for the x-axis. |
ylab |
a label for the y-axis. |
cex.rowlab |
expansion factor for the row labels. |
cex.rowdot |
expansion factor for the row markers. |
cex.collab |
expansion factor for the column labels. |
cex.coldot |
expansion factor for the column markers. |
cex.axis |
expansion factor for the axis. |
lwd |
line width for biplot vectors. |
arrowangle |
angle for the edges of the arrowhead. |
... |
extra arguments for plot. |
Value
None. The function produces a graphic.
Author(s)
Jan Graffelman (jan.graffelman@upc.edu)
Examples
set.seed(123)
X <- matrix(runif(40),byrow=TRUE,ncol=4)
colnames(X) <- paste("X",1:ncol(X),sep="")
out.pca <- princomp(X,cor=TRUE)
Fp <- out.pca$scores
Gs <- as.matrix(unclass(out.pca$loadings))
bplot(Fp,Gs,colch=NA)
Calibration of Biplot and Scatterplot Axis
Description
Routine for the calibration of any axis (variable vector) in a biplot or a scatterplot
Usage
calibrate(g,y,tm,Fr,tmlab=tm,tl=0.05,dt=TRUE,dp=FALSE,
lm=TRUE,verb=TRUE,axislab="",reverse=FALSE,
alpha=NULL,labpos=1,weights=diag(rep(1,length(y))),
axiscol="blue",cex.axislab=0.75,graphics=TRUE,where=3,
laboffset=c(0,0),m=matrix(c(0,0),nrow=1),markerpos=3,
showlabel=TRUE,lwd=1,shiftvec=c(0,0),shiftdir="none",shiftfactor=1.05)
Arguments
g |
the vector to be calibrated (2 x 1). |
y |
the data vector corresponding to |
tm |
the vector of tick marks, appropiately centred and/or scaled. |
Fr |
the coordinates of the rows markers in the biplot. |
tmlab |
a list or vector of tick mark labels. |
tl |
the tick length. By default, the tick markers have length 0.05. |
dt |
draw ticks. By default, ticks markers are drawn. Set dt=F in order to compute calibration results without actually drawing the calibrated scale. |
dp |
drop perpendiculars. With dp=T perpendicular lines will be drawn from the row markers specified by Fr onto the calibrated axis. This is a graphical aid to read off the values in the corresponding scale. |
lm |
label markers. By default, all tick marks are labelled. Setting lm=F turns off the labelling of the tick marks. This allows for creating tick marks without labels. It is particularly useful for creating finer scales of tickmarks without labels. |
verb |
verbose parameter (F=be quiet, T=show results). |
axislab |
a label for the calibrated axis. |
reverse |
puts the tick marks and tick mark labels on the other side of the axis. |
alpha |
a value for the calibration factor. This parameter should only be specified if a calibration is required that is different from the one that is optimal for data recovery. |
labpos |
position of the label for the calibrated axis (1,2,3 or 4). |
laboffset |
offset vector for the axis label. If specified, shifts the label by the specified amounts with respect to the current position. |
weights |
a matrix of weights (optional). |
axiscol |
color of the calibrated axis. |
cex.axislab |
character expansion factor for axis label and tick mark labels. |
graphics |
do graphics or not (F=no graphical output, T=draws calibrated scale). |
where |
label placement (1=beginning,2=middle,3=end). |
m |
vector of means. |
markerpos |
position specifier for the tick mark labels (1,2,3 or 4). |
showlabel |
show axis label in graph (T) or not (F). |
lwd |
line with for the calibrated axis |
shiftvec |
a shift vector for the calibrated axis ((0,0) by default) |
shiftdir |
indicates in which direction the axis should be
shifted ("left","right" or "none"). This direction is w.r.t. vector |
shiftfactor |
scalar by which the shift vector is stretched (or
shrunken). By default, the length of the shift vector is stretched
by 5 percent ( |
Details
This program calibrates variable vectors in biplots and scatterplots, by drawing tick marks along a given the vector and labelling the tick marks with specified values. The optimal calibration is found by (generalized) least squares. Non-optimal calibrations are possible by specifying a calibration factor (alpha).
Value
Returns a list with calibration results
useralpha |
calibration factor specified by the user |
optalpha |
optimal calibration factor |
lengthoneunit |
length in the plot of one unit in the scale of the calibrated variable |
gof |
goodness of fit (as in regression) |
gos |
goodness of scale |
M |
coordinates of the tick markers |
ang |
angle in degrees of the biplot axis with the positive x-axis |
shiftvec |
the supplied or computed shift vector |
yt |
fitted values for the variable according to the calibration |
e |
errors according to the calibration |
Fpr |
coordinates of the projections of the row markers onto the calibrated axis |
Mn |
coordinates of the tick marker end points |
Author(s)
Jan Graffelman jan.graffelman@upc.edu
References
Gower, J.C. and Hand, D.J., (1996) Biplots. Chapman & Hall, London
Graffelman, J. and van Eeuwijk, F.A. (2005) Calibration of multivariate scatter plots for exploratory analysis of relations within and between sets of variables in genomic research Biometrical Journal, 47(6) pp. 863-879.
Graffelman, J. (2006) A guide to biplot calibration.
See Also
Examples
x <- rnorm(20,1)
y <- rnorm(20,1)
x <- x - mean(x)
y <- y - mean(y)
z <- x + y
b <- c(1,1)
plot(x,y,asp=1,pch=19)
tm<-seq(-2,2,by=0.5)
Calibrate.z <- calibrate(b,z,tm,cbind(x,y),axislab="Z",graphics=TRUE)
Delivery of Dutch Calves
Description
This data set gives a cross classification of 7275 calves born in the late nineties according to type of production and type of delivery.
Usage
data(calves)Format
A data frame containing a contingency table of 7275 observations.
Source
Holland Genetics. http://www.hg.nl
References
Graffelman, J. (2005) A guide to scatterplot and biplot calibration.
Canonical correlation analysis
Description
canocor performs canonical correlation analysis on the
basis of the standardized variables and stores extensive output
in a list object.
Usage
canocor(X, Y)
Arguments
X |
a matrix containing the X variables |
Y |
a matrix containing the Y variables |
Details
canocor computes the solution by a singular value
decomposition of the transformed between set correlation matrix.
Value
Returns a list with the following results
ccor |
the canonical correlations |
A |
canonical weights of the x variables |
B |
canonical weights of the y variables |
U |
canonical x variates |
V |
canonical y variates |
Fs |
biplot markers for x variables (standard coordinates) |
Gs |
biplot markers for y variables (standard coordinates) |
Fp |
biplot markers for x variables (principal coordinates) |
Gp |
biplot markers for y variables (principal coordinates) |
fitRxy |
goodness of fit of the between-set correlation matrix |
fitXs |
adequacy coefficients of x variables |
fitXp |
redundancy coefficients of x variables |
fitYs |
adequacy coefficients of y variables |
fitYp |
redundancy coefficients of y variables |
Author(s)
Jan Graffelman jan.graffelman@upc.edu
References
Hotelling, H. (1935) The most predictable criterion. Journal of Educational Psychology (26) pp. 139-142.
Hotelling, H. (1936) Relations between two sets of variates. Biometrika (28) pp. 321-377.
Johnson, R. A. and Wichern, D. W. (2002) Applied Multivariate Statistical Analysis. New Jersey: Prentice Hall.
See Also
Examples
set.seed(123)
X <- matrix(runif(75),ncol=3)
Y <- matrix(runif(75),ncol=3)
cca.results <- canocor(X,Y)
Draw a circle
Description
circle draws a circle in an existing plot.
Usage
circle(radius,origin)
Arguments
radius |
the radius of the circle |
origin |
the origin of the circle |
Value
NULL
Author(s)
Jan Graffelman jan.graffelman@upc.edu
Examples
set.seed(123)
X <- matrix(rnorm(20),ncol=2)
plot(X[,1],X[,2])
circle(1,c(0,0))
Connect two sets of points by lines
Description
dlines connects two sets of points by lines in
a rowwise manner.
Usage
dlines(SetA, SetB, lin = "dotted")
Arguments
SetA |
matrix with the first set of points |
SetB |
matrix with teh second set of points |
lin |
linestyle for the connecting lines |
Value
NULL
Author(s)
Jan Graffelman (jan.graffelman@upc.edu)
See Also
Examples
X <- matrix(runif(20),ncol=2)
Y <- matrix(runif(20),ncol=2)
plot(rbind(X,Y))
text(X[,1],X[,2],paste("X",1:10,sep=""))
text(Y[,1],Y[,2],paste("Y",1:10,sep=""))
dlines(X,Y)
Size measurements of archeological goblets
Description
This data set gives 6 different size measurements of 25 goblets
Usage
data(goblets)Format
A data frame containing 25 observations.
Source
Manly, 1989
References
Manly, B. F. J. (1989) Multivariate statistical methods: a primer. London: Chapman and Hall, London
Dimensions of heads of first and second sons for 25 families
Description
Variables X1 and X2 are the head length and head breadth of the first son and Y1 and Y2 are the same variables for the second son.
Usage
data(heads)Format
A data frame containing 25 observations.
Source
Mardia, 1979, p. 121
References
Frets, G. P. (1921) Heredity of head form in man, Genetica 3, pp. 193-384.
Mardia, K. V. and Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. Academic Press London.
Anderson, T. W. (1984) An Introduction to Multivariate Statistical Analysis. New York: John Wiley, Second edition.
Linnerud's exercise and body measurements
Description
The data set consist of 3 exercise variables (Tractions a la barre fixe, Flexions, Sauts) and 3 body measurements (Poids, Tour de talle, Pouls) of 20 individuals.
Usage
data(linnerud)Format
A data frame containing 20 observations.
Source
Tenenhaus, 1998, table 1, page 15
References
Tenenhaus, M. (1998) La Regression PLS. Paris: Editions Technip.
Generates a matrix of ones
Description
ones generates a matrix of ones.
Usage
ones(n, p = n)
Arguments
n |
number of rows |
p |
number of columns |
Details
if only n is specified, the resulting matrix will be square.
Value
a matrix filled with ones.
Author(s)
Jan Graffelman (jan.graffelman@upc.edu)
See Also
Examples
Id <- ones(3)
print(Id)
Origin
Description
Draws coordinate axes in a plot.
Usage
origin(m=c(0,0), ...)Arguments
m |
the coordinates of the means (2 x 1). |
... |
other arguments passed on to the |
Author(s)
Jan Graffelman (jan.graffelman@upc.edu)
See Also
Examples
X <- matrix(runif(40),ncol=2)
plot(X[,1],X[,2])
origin(m=c(mean(X[,1]),mean(X[,2])))
Convert radians to degrees.
Description
rad2degree converts radians to degrees.
Usage
rad2degree(x)
Arguments
x |
an angle in radians |
Value
the angle with the positive x-axis in degrees.
Author(s)
Jan Graffelman (jan.graffelman@upc.edu)
Examples
x <- pi/2
a <- rad2degree(x)
cat("angle is",a,"degrees\n")
Redundancy analysis
Description
rda performs redundancy analysis and stores extensive output
in a list object.
Usage
rda(X, Y, scaling = 1)
Arguments
X |
a matrix of x variables |
Y |
a matrix of y variables |
scaling |
scaling used for x and y variables. 0: x and y only centered. 1: x and y standardized |
Details
Results are computed by doing a principal component analyis of the fitted values of the regression of y on x.
Plotting the first two columns of Gxs and Gyp, or of Gxp and Gys provides a biplots of the matrix of regression coefficients.
Plotting the first two columns of Fs and Gp or of Fp and Gs provides a biplot of the matrix of fitted values.
Value
Returns a list with the following results
Yh |
fitted values of the regression of y on x |
B |
regression coefficients of the regresson of y on x |
decom |
variance decomposition/goodness of fit of the fitted values AND of the regression coefficients |
Fs |
biplot markers of the rows of Yh (standard coordinates) |
Fp |
biplot markers of the rows of Yh (principal coordinates) |
Gys |
biplot markers for the y variables (standard coordinates) |
Gyp |
biplot markers for the y variables (principal coordinates) |
Gxs |
biplot markers for the x variables (standard coordinates) |
Gxp |
biplot markers for the x variables (principal coordinates) |
Author(s)
Jan Graffelman (jan.graffelman@upc.edu)
References
Van den Wollenberg, A.L. (1977) Redundancy Analysis, an alternative for canonical correlation analysis. Psychometrika 42(2): pp. 207-219.
Ter Braak, C. J. F. and Looman, C. W. N. (1994) Biplots in Reduced-Rank Regression. Biometrical Journal 36(8): pp. 983-1003.
See Also
Examples
X <- matrix(rnorm(75),ncol=3)
Y <- matrix(rnorm(75),ncol=3)
rda.results <- rda(X,Y)
Compute a shift vector for a calibrated axis.
Description
shiftvector computes two shift vectors perpendicular to the
supplied biplot or scatterplot axis g. The vector norm is
computed from the two most extreme data points.
Usage
shiftvector(g, X, x = c(1, 0), verbose = FALSE)
Arguments
g |
a biplot or scatterplot axis |
X |
a n by 2 matrix of scatterplot or biplot coordinates |
x |
reference axis, (1,0) by default |
verbose |
print information or not |
Details
shiftvector locates the tow most extreme datapoints in the
direction perpendicular to axis g.
Value
dr |
the right (w.r.t. the direction of |
dl |
the left (w.r.t. the direction of |
Author(s)
Jan Graffelman (jan.graffelman@upc.edu)
References
Graffelman, J. and van Eeuwijk, F.A. (2005) Calibration of multivariate scatter plots for exploratory analysis of relations within and between sets of variables in genomic research Biometrical Journal, 47(6) pp. 863-879.
Graffelman, J. (2006) A guide to biplot calibration.
See Also
Examples
X <- matrix(rnorm(100),ncol=2)
Xs <- scale(X)
g <- c(1,1)
plot(Xs[,1],Xs[,2],asp=1,pch=19)
textxy(Xs[,1],Xs[,2],1:nrow(X))
arrows(0,0,g[1],g[2])
text(g[1],g[2],"g",pos=1)
out <- shiftvector(g,X,verbose=TRUE)
dr <- out$dr
dl <- out$dl
arrows(0,0,dl[1],dl[2])
text(dl[1],dl[2],"dl",pos=1)
arrows(0,0,dr[1],dr[2])
text(dr[1],dr[2],"dr",pos=1)
Road distances between Spanish cities
Description
Road distances in kilometers between 47 Spanish cities
Usage
data(spaindist)Format
A data frame containing 47 observations.
References
Graffelman, J. (2019) Goodness-of-fit filtering in classical metric multidimensional scaling with large datasets. <doi: 10.1101/708339>
Frequencies of nesting storks in Denmark
Description
Danish data from 1953-1977 giving the frequency of nesting storks, the human birth rate and the per capita electricity consumption.
Usage
data(storks)Format
A data frame containing 25 observations.
Source
Gabriel and Odoroff, Table 1.
References
Gabriel, K. R. and Odoroff, C. L. (1990) Biplots in biomedical research. Statistics in Medicine 9(5): pp. 469-485.
Nice placement of labels in a plot
Description
Function textxy calls function text in order to add text
to points in a graph. textxy chooses a different position
for the text depending on the quadrant. This tends to
produces better readable plots, with labels fanning away from the origin.
Usage
textxy(X, Y, labs, m = c(0, 0), cex = 0.5, offset = 0.8, ...)
Arguments
X |
x coordinates of a set of points |
Y |
y coordinates of a set of points |
labs |
labels to be placed next to the points |
m |
coordinates of the origin of the plot (default (0,0)) |
cex |
character expansion factor |
offset |
controls the distance between the label and the point. A value of 0 will plot labels on top of the point. Larger values give larger separation between point and label. The default value is 0.8 |
... |
additiona arguments for function |
Value
NULL
Author(s)
Jan Graffelman (jan.graffelman@upc.edu)
References
Graffelman, J. (2006) A guide to biplot calibration.
See Also
Examples
x <- rnorm(50)
y <- rnorm(50)
plot(x,y,asp=1)
textxy(x,y,1:50,m=c(mean(x),mean(y)))