Information Technology Reference
In-Depth Information
VesD
180
160
0
100
140
200
300
1000
120
1200
400
400
1400
500
500
100
1600
FibL
1800
600
80
700
Obul; n
=
20
Oken; n
=
7. (C hull)
Opor; n
=
10
800
60
VesL
Figure 4.10
Vector-sum method for adding a new point to a CVA biplot. The biplot
shown is similar to Figure 4.4, but with interpolation axes instead. The black triangle
and red arrow illustrate the vector-sum method leading to the solid circle coinciding
with the position of the star marking the position of the specimen of unknown origin in
Figure 4.4.
that
x
∗
has been centred in the same way as the other variables in
X
andthatithas
group means
x
k
. Then, we require the regression
b
of
C
1
/
2
x
∗
on the
(
k
=
1,
...
,
K
)
fitted values
C
1
/
2
XMJ
. Thus,
b
=
(
JM
X
CXMJ
)
−
1
JM
X
Cx
∗
=
(
J
J
)
−
1
JM
X
Cx
∗
.
(4.10)
As a check, we examine what happens when
x
∗
is replaced by
x
k
,themeansof
the
k
th variable in
X
. We now have
b
)
−
1
JM
X
CXe
k
=
(
J
J
)
−
1
J
M
−
1
e
k
from the two-sided eigenvector equation (4.5) for CVA. Therefore
b
)
−
1
JM
X
Cx
k
=
(
J
J
=
(
J
J
JM
−
1
e
k
, agreeing with the expression for predictive CVA biplot axes derived in
Section 4.4.2.
=
4.6 Measures of fit for CVA biplots
We saw in (4.1) and (4.2) that CVA is based on the decomposition
T
=
B
+
W
.We
G
G
)
−
1
G
and note that
HX
gives a matrix of the group means
shall write
H
=
G
(
