Information Technology Reference
In-Depth Information
4.7.7 Function
CVA.predictions.mat
The function
CVA.predictions.mat
takes the three arguments
X
,
G
and
weightedCVA
as described above for
CVAbipl
. Its return value is a list with the named components
given below. Note that the various fitted values are given for dimensions 1, 2,
...
,
p
.
Fitted values for the group means of the
column-centred data matrix.
predictions.for.XcentBar.groups
Fitted values for the column centred data
matrix.
predictions.for.centredX
Fitted values for the original data matrix.
predictions.for.originalX
Sum of squared differences between the
elements of the group means of the
column centred data matrix and its fitted
values.
reconstr.error.Xbar
Sum of squared differences between the
elements of centred data matrix and its
fitted values.
reconstr.error.X
4.8 Continuing the
Ocotea
example
In Figures 4.2 - 4.4 we illustrated some of the functionality of the functions described in
Section 4.7. Figure 4.4 results from a call to
CVAbipl.pred.regions
:
CVAbipl.pred.regions(X = Ocotea.data[,3:5],
G = indmat(Ocotea.data[,2]), X.new.samples = matrix(c(134,375,
1170), nrow = 1), alpha = 0.95, colours = c("red","blue",
"green2"), pch.samples = 0:2, x.grid = 0.01, y.grid = 0.01,
pch.new = 8, plot.symbol = 20, plot.symbol.size = 0.75,
colours.pred.regions = c("coral","lightblue","lightgreen"),
pch.new.cols = "black")
The classification regions in Figure 4.4 are calculated according to the nearest neigbour
rule (4.8). The default procedure used in the above call to
CVAbipl.pred.regions
is to calculate the distances between a grid point in the biplot space and the canonical
means in the full canonical space. In a subsequent example we will illustrate the effect
of changes in this default procedure.
If we can assume that the
Ocotea
data come from a multivariate normal distribution,
the CVA biplot can be equipped with the confidence circles introduced in Section 4.2.
In the following call to
CVAbipl
we specify the argument
conf.alpha = 0.99
to
request 99% confidence circles about each group mean. Furthermore, we specify
alpha
= 0.99
for comparison purposes to obtain 0.99-bags for each of the groups. We remark
that for this example the difference in the appearance of the biplots resulting from a
weighted or unweighted CVA is negligible and therefore we give only the biplot for the
weighted CVA in Figure 4.11.
