Information Technology Reference
In-Depth Information
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Figure 6.4
Biadditive biplot of the interaction matrix
Z
=
U
V
of the wheat data
(Table 6.2). Sites are plotted from first two dimensions of
U
1
/
2
and varieties from
2
using our R function
biadbipl
with arguments
X = wheat.data
,
biad.variant = "InteractionMat"
,
ax = NULL
,
SigmaHalf
= TRUE
. Note that exactly the same graph is obtained with the setting
X = t(wheat.
data)
. The origin is marked with a black cross.
1
/
V
first
two
dimensions
of
in his Figure 4, gives an inner product type biplot where the variables are represented as
vectors. Here, Figure 6.6 gives the equivalent biplot with calibrated axes.
In Figures 6.3 and 6.4 we show a biadditive biplot of the interaction matrix
Z
,where
we have used points to represent both varieties and sites, leaving users to attempt to
evaluate inner products. Previously we have emphasized the value of representing at
least one of the factors by a set of calibrated biplot axes. This we show in the top panel
of Figure 6.5, where the sites are shown as axes. To obtain approximate predictions for
the variety yields expected at each site, we merely project each variety onto the selected
site axis and read off the calibration. We might wish to do things the other way round and
predict which site is best for each variety. This requires that the varieties be represented
as axes as in the bottom panel of Figure 6.5. In Figure 6.5 the two-dimensional row and
column predictivities are shown. These are not as good as for the biplots of the original
data table nor for those of the mean-adjusted data. Full details of the predictivities are
