Information Technology Reference
In-Depth Information
From (7.48) the column chi-squared distances are generated by the columns of
(
Nq
)
−
1
/
2
(
X
,
N
11
−
X
)(
C
,
Np
I
−
C
)
−
1
.
(7.51)
Now the columns of (
Nq
)
−
1
/
2
XC
−
1
give the coordinates of the positive assessments while
the columns of (
Nq
)
−
1
/
2
(
N
11
-X
)(
Np
I
-
C
)
−
1
give the coordinates of the negative
assessments. Writing
x
k
for the
k
th column of
X
, we see that the coordinates of the
k
th attribute in its positive form are given by
u
k
=
x
k
/
c
k
and in its negative form by
v
k
=
(
N
1
−
x
k
)/(
Np
−
c
k
)
. It follows that any point on the line joining these two points
has the form
x
k
c
k
+
(
1
−
λ)
N
1
−
x
k
Np
−
c
k
.
λ
Setting
Np
, this becomes 1/
p
, showing that all attributes share this point, which,
of course, is the mean. The points representing the positive and negative forms of an
attribute are at the extremities of a line through the mean which divides its two ends in
the ratio
c
k
:
Np
−
c
k
.
λ
=
c
k
/
7.5 Functions for constructing CA biplots
7.5.1 Function
cabipl
Our main function for constructing the one-, two- and three-dimensional CA biplots
described in Sections 7.2 - 7.4 is the function
cabipl
, which we now describe in
detail. The reader is encouraged to study and experiment with its arguments. As is
the case with our other main functions such as
PCAbipl
,
CVAbipl
and
biadbipl
,
several functions are called by
cabipl
for drawing the biplot, adding features to
it and changing its appearance that are generally not directly called by the user.
In addition to these functions, there are several closely related functions that users
may like to call in order to add enhancements to an existing biplot or to obtain
information associated with an existing biplot. These functions are briefly introduced in
Sections 7.5.2 - 7.5.5.
Usage
cabipl
uses the same calling conventions as
PCAbipl
and shares the following argu-
ments with it:
alpha.3d
constant
line.length
predictions.3d
aspect.3d
dim.biplot
markers
predictions.sample
ax
exp.factor
markers.size
reflect
ax.col.3d
e.vects
n.int
rotate.degrees
ax.name.col
factor.x
offset
side.label
ax.name.size
factor.y
offset.m
size.ax.3d
cex.3d
font.3d
ort.lty
size.points.3d
col.plane.3d
ID.labs
pos
Title
col.text.3d
ID.3d
pos.m
Titles.3d
