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Myfanwy
Alisdair
Jane
Clerical
F
Scotland
Wales
Fair
University
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School
Brown
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Professional
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Harriet
Grey
M
England
Ivor
George
Jeremy
Figure 8.8 Biplot based on the EMC plotting U J for the samples and ( I 11 L / n ) VJ
for the CLPs, where G 11 L / n = U V . The quality of the two-dimensional display
is 59.77%, which on adding a third dimension increases to 77.49%, suggesting that a
three-dimensional plot may be worthwhile.
we may adopt from the Jaccard and simple matching families. In other cases there will
be slight differences but it makes sense to use the EMC, which is the simplest choice.
The EMC matrix may be analysed by any method of multidimensional scaling but
most simply by the principal component analysis of G . Then, the CLPs for the EMC are
given by the L × L unit matrix I . Unlike with MCA, where the first eigenvector of the
SVD and spectral decompositions adjusts for deviations from the mean, special attention
has to be given to allow for this in handling the CLPs. Expressing G in deviations from the
column means gives
( I 11 / n ) G = G 11 L / n . The same adjustment must be made
to the CLPs to give I
11 L
11 L
V ,weplot U
/
n . Thus if G
/
n has SVD U
J
=
11 L
11 L
VJ for the CLPs. This biplot is shown
in Figure 8.8 and is a result of setting mca.variant = "EMC" in the call to MCAbipl .
(
G
/
n
)
VJ for the samples and
(
I
/
n
)
8.5 Category-level points
Category-level points have been used extensively above. Here, we supply an ampli-
fied discussion and an introduction to the concept of prediction regions. Every dummy
variable of the indicator matrix takes either zero or unit values, so the usual idea of
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