e. Notice for this data, as the cut-point gets larger the
specificity also gets larger (or stays the same). For
example, a cut-point of 0.200 yields a specificity of
92.0% while a cut-point of 0.300 yields a specificity
of 97.6%. Is it possible (using different data) that an
increase of a cut-point could actually decrease the
specificity? Explain.
f. In the classification table provided above, a cut-
point of 0.200 yields a false positive percentage of
58.1% whereas 1 minus the specificity at this cut
point is 8.0%. Since 1 minus specificity percentage
is defined as 100 times the proportion of true non-
cases that are falsely classified as cases, i.e., the
numerator in this proportion is the number of
false-positive noncases, why is not the false positive
percentage (58.1%) shown in the output equal to
1 minus specificity (8.0%)? Is the computer pro-
gram in error?
- Based on the output,
a. What is the area under the ROC curve? How would
you grade this area in terms of the discriminatory
power of the model being fitted?
b. In the output provided under the heading “Associa-
tion of Predicted Probabilities and Observed
Responses,” the number of pairs is 38,198. How is
this number computed?
c. In the output provided under the same heading in
question 2b, how are the Percent Concordant and
the Percent Tied computed?
d. Using the information given by the number of
pairs, the Percent Concordant and the Percent
Tied described in parts (b) and (c), compute the
area under the ROC curve (AUC) and verify that it
is equal to your answer to part 2a.
e. The ROC curves for the interaction model described
above and the no interaction model that does not
contain the CC or CH (interaction) variables are
shown below. The area under the ROC curve for
the no-interaction model is 0.705. Why is the latter
AUC less than the AUC for the interaction model?
Test 379
