Information Technology Reference
In-Depth Information
1.1 Types of biplots
We may distinguish two main types of biplot:
•
asymmetric
(biplots giving information on sample units and variables of a data
matrix);
•
symmetric
(biplots giving information on rows and columns of a two-way table).
In symmetric biplots, rows and columns may be interchanged without loss of information,
while in asymmetric biplots variables and sample units are different kinds of object that
may not be interchanged.
Consider the data on four variables measured on 21 aircraft in Table 1.1. The cor-
responding biplot in Figure 1.1 represents the 21 aircraft as sample points and the four
variables as biplot axes. It will not be sensible to exchange the two sets, representing
the aircraft as continuous axes and the variables as points. Next, consider the two-way
table in Table 1.2. Exchanging the rows and columns of this table will have no effect
on the information contained therein. For such a symmetric data set, both the rows and
columns are represented as points as shown in Figure 1.2. Details on the construction of
these biplots are deferred to later chapters.
Ta b l e 1 . 1
Values of four variables,
SPR
(specific power, proportional to power per
unit weight),
RGF
(flight range factor),
PLF
(payload as a fraction of gross weight of
aircraft) and
SLF
(sustained load factor), for 21 aircraft labelled in column 2. From
Cook and Weisberg (1982, Table 2.3.1), derived from 1979 RAND Corporation report.
Aircraft
SPR
RGF
PLF
SLF
A
FH-1
1.468
3.30
0.166
0.10
B
FJ-1
1.605
3.64
0.154
0.10
C
F-86A
2.168
4.87
0.177
2.90
D
F9F-2
2.054
4.72
0.275
1.10
E
F-94A
2.467
4.11
0.298
1.00
F
F3D-1
1.294
3.75
0.150
0.90
G
F-89A
2.183
3.97
0.000
2.40
H
XF10F-1
2.426
4.65
0.117
1.80
I
F9F-6
2.607
3.84
0.155
2.30
J
F100-A
4.567
4.92
0.138
3.20
K
F4D-1
4.588
3.82
0.249
3.50
M
F11F-1
3.618
4.32
0.143
2.80
N
F-101A
5.855
4.53
0.172
2.50
P
F3H-2
2.898
4.48
0.178
3.00
Q
F102-A
3.880
5.39
0.101
3.00
R
F-8A
0.455
4.99
0.008
2.64
S
F-104A
8.088
4.50
0.251
2.70
T
F-105B
6.502
5.20
0.366
2.90
U
YF-107A
6.081
5.65
0.106
2.90
V
F-106A
7.105
5.40
0.089
3.20
W
F-4B
8.548
4.20
0.222
2.90
