Information Technology Reference
In-Depth Information
BMSWA
EXFFBB
BMCFF
BMCFD
RMOF
RMP
Figure 10.7
Coefficient of variation monoplot of the flotation data. This is constructed
as the covariance biplot of the matrix (10.2). With
E
E
=
V
V
the red filled circles
have coordinates given by
V
J
. Straight lines through the origin and each red filled
circle show the variables in the form of uncalibrated monoplot axes.
coefficients of variation and if we do a covariance monoplot of
E
it is these quantities that
are approximated. In Figure 10.7 we show an example of a CV monoplot obtained with
the function call
MonoPlot.coefvar(X = Flotation.data[,-1], as.axes = TRUE, pos = "Hor",
offset = c(0.1, 0.3, 0.2, 0.1))
10.2.4 Other representations of correlations
The representation of correlations, as described above, suffers from the unnecessary
approximation of the known unit diagonals. It is not just that it is unnecessary to reproduce
the diagonals but also that, for symmetric matrices, the Eckart-Young approximation gives
twice the weight to approximating the off-diagonal terms compared with the diagonals.
The unequal weighting is in the right direction but is arbitrary - see Bailey and Gower
(1990) for a fuller analysis of differential weighting. This drawback is the same as
that found in an even more extreme form for MCA, where whole diagonal blocks are
approximated unless one uses the JCA variant of MCA (see Chapter 8). A similar solution
to using JCA is available for correlation matrices, and is the basis of some of the simpler
