Information Technology Reference
In-Depth Information
Ta b l e 7 . 1 2
Axis predictivities for the 2007/2008 crime contingency table in weighted
deviation form
R
−
1
/
2
(
X
−
E
)
C
−
1
/
2
.
Arsn
AGBH
AtMr
BNRs
BRs
CrJk
CmAs
CmRb
DrgR
InAs
Mrd
PubV
Rape
RAC
Dim_1
0.392
0.221
0.151
0.000
0.007
0.179
0.103
0.668
0.992
0.855
0.017
0.337
0.217
0.161
Dim_2
0.621
0.934
0.213
0.230
0.054
0.951
0.103
0.799
0.998
0.863
0.034
0.440
0.680
0.985
Dim_3
0.813
0.974
0.674
0.302
0.065
0.983
0.800
0.882
1.000
0.863
0.767
0.509
0.796
0.993
Dim_4
0.851
0.977
0.867
0.303
0.763
0.988
0.965
0.965
1.000
0.883
0.805
0.640
0.797
0.993
Dim_5
0.915
0.980
0.878
0.997
0.886
0.994
0.984
0.972
1.000
0.957
0.852
0.640
0.904
0.993
Dim_6
0.968
1.000
0.880
0.997
0.949
0.995
1.000
0.976
1.000
0.980
0.972
0.859
0.965
0.998
Dim_7
0.998
1.000
0.999
0.999
0.999
0.999
1.000
0.982
1.000
0.985
0.995
0.874
0.990
1.000
Dim_8
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Dim_9
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Ta b l e 7 . 1 3
Sample predictivities for the 2007/2008 crime contingency
table in weighted deviation form
R
−
1
/
2
(
X
−
E
)
C
−
1
/
2
.
ECpe
FrSt
Gaut
KZN
Limp
Mpml
NWst
NCpe
WCpe
Dim_1
0.147
0.099
0.499
0.177
0.107
0.583
0.009
0.031
0.984
Dim_2
0.783
0.503
0.984
0.541
0.760
0.837
0.680
0.766
0.988
Dim_3
0.927
0.864
0.996
0.891
0.811
0.840
0.700
0.780
0.997
Dim_4
0.933
0.958
0.997
0.956
0.811
0.947
0.772
0.885
0.999
Dim_5
0.989
0.981
0.997
0.974
0.983
0.950
0.904
0.885
1.000
Dim_6
0.991
0.997
0.999
0.995
0.994
0.952
0.948
0.991
1.000
Dim_7
0.999
0.998
1.000
0.999
0.995
1.000
0.973
0.999
1.000
Dim_8
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Dim_9
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Specifying in
cabipl
the argument
ca.variant = IndepDev
leads to what might
be called an independence deviations CA biplot (see (7.8)). We illustrate this type of
biplot with the two-dimensional biplot given in Figure 7.9 for the 2007/08 crime data set.
For
approximating
the
contingency
ratio
our
function
cabipl
provides
for
constructing biplots using
R
−
1
/
2
U
1
/
2
and
C
−
1
/
2
V
1
/
2
as well as
R
−
1
/
2
U
and
C
−
1
/
2
V
. Furthermore, users have the option to calibrate axes in terms of the contingency
ratios or in terms of contingency ratio minus 1. The computed contingency ratio matrix
of the 2007/08 crime data is given in Table 7.14.
The two-dimensional contingency approximating biplot can be obtained either by
specifying in the function
cabipl
the argument
ca.variant = "ConRatioA"
as in
Figure 7.10, or
ca.variant = "ConRatioB"
resulting in Figure 7.11. Both these
biplots give exactly the same predictions as are given in Table 7.15. The user can set
argument
ConRatioMinOne = TRUE
to obtain the calibrations of the axes (as well as
the predictions) in terms of the deviations of
x
ij
from independence relative to the approx-
imation
e
ij
under independence. It is clear that Figures 7.9 and 7.10 are similar but that
the provinces (the row points) are squeezed in towards the origin of the biplot axes,
while the column points (the red squares) are relatively more spread out. Again, setting
argument
lambda = TRUE
will result in a biplot in which the row points appear more
spread out. This is illustrated with the biplot given in Figure 7.12. By specifying the
