Information Technology Reference
In-Depth Information
RAC
Gaut
CrJk
KZN
CmRb
AtMr
DrgR
WCpe
InAs
CmAs
PubV
Arsn
Mrd
BR s
BNRs
Rape
Mpml
NWst
NCpe
FrSt
Lim p
ECpe
AGBH
Figure 7.3
Two-dimensional CA biplot for the 2007/08 crime contingency table.
Proportional to Pearson residuals in deviation form
R
−
1
/
2
(
X
−
E
)
C
−
1
/
2
; constructed from
1
/
2
. Both rows and columns are represented as points: points representing
rows are in green and points representing columns are in red.
1
/
2
U
and
V
Changing the function call to
cabipl (X = as.matrix(SACrime08.data), axis.col = "grey",
marker.col = "black", offset = c(2, 2, 0.5, 0.5), ort.lty = 2,
predictions.sample = 9, offset.m = rep(-0.2, 14))
produces Figure 7.5. Here we show how to obtain predictions for the Western Cape
province. Predictions for all the provinces can be obtained simultaneously by changing
argument
predictions.sample
to
predictions.sample = 1:9
. In Table 7.10 we
give the full set of predictions made from the two-dimensional biplot in Figure 7.5.
Remember that
n
1
/
2
times the elements of
R
−
1
/
2
(
X
−
E
)
C
−
1
/
2
gives exactly the
2
for a contingency table. Therefore, the
values of
n
1
/
2
times the calibrations on the biplot axes of Figures 7.4 and 7.5 can be
interpreted in terms of Pearson residuals associated with the row points (the provinces
in our data set). However, as we saw in Chapter 2, it is easy to calibrate the axes
square roots of the contributions to Pearson's
χ
