Biology Reference
In-Depth Information
TABLE 6.2
CVA Classification Table for 119 Squirrel Jaws
A priori Assignments
A posteriori Assignments
Western Michigan
Eastern Michigan
Southern States
Total
Western Michigan
62
4
3
69
Eastern Michigan
1
22
0
23
Southern states
0
1
26
27
The
a priori
classifications are based on the geographic localities where specimens were collected. The
a posteriori
assignments are
based on Mahalanobis distances of individuals from the means of the
a priori
groups. Total is the total number of specimens in
each geographic sample. Thus, 62 specimens in the western Michigan sample were correctly classified using Mahalanobis
distance, and 7 were misclassified as members of one of the other geographic samples.
TABLE 6.3
CVA Classification Table for 119 Squirrel Jaws, using a Jackknife Cross-Validation Analysis
A priori Assignments
A posteriori Assignments
Western Michigan
Eastern Michigan
Southern states
Total
Western Michigan
56
6
7
69
Eastern Michigan
4
18
1
23
Southern states
1
5
21
27
Re-analysis of classification rates for the three geographic samples of squirrel jaws analyzed in
Table 6.2
. The overall rate of
correct classifications has dropped from 92% in the resubstitution rates to 80% in the jackknife.
Table 6.2
shows the resubstitution classification results based on CVA of the three sam-
ples of squirrel jaw discussed earlier. As shown in the first row, 62 of the 69 western
Michigan squirrels have jaws that are closer to the mean of their sample than to the mean
of another sample, based on the Mahalanobis distance. In contrast, only one specimen
from each of the other samples is farther from the mean of its own sample than it is from
the mean of another sample. Like the plot in
Figure 6.17
, this result contributes to the gen-
eral impression that the members of these three groups can usually be discriminated.
Using a jackknife cross-validation test, we can see that the samples may not be quite so
distinct (
Table 6.3
). The rate of correct classification drops by a little more than 10%. It is
still clear that the three groups can usually be discriminated, but it is also more apparent
that a substantial proportion of individuals on the fringes of the shape distributions are
apt to be misclassified based on shape alone.
CVA of Rank-Deficient Data
One issue that arises in working with CVA is the need to invert an estimated, pooled
variance
covariance matrix, which requires that the degrees of freedom in the matrix be
greater than the number of variables in the matrix. This is a problem at small sample sizes,
or when using semilandmarks (because each semilandmarks is represented by two
