uniformly distributed over the deciles. In contrast,
good discrimination would be indicated by an
increasing trend in the observed cases and a
corresponding decreasing trend in the observed
noncases as the deciles of predicted risk increase
from low to high. The table indicates poor GOF
since, when considered collectively, corresponding
observed and expected cases differ substantially
over most deciles; similarly corresponding observed
and expected and noncases also differ substantially.
d. The table provided for this part indicates that the
model discriminates poorly but provides good fit.
Poor discrimination is indicated by the uniform
distributions of both observed cases and noncases
over the deciles. Good fit is indicated by the
closeness of corresponding observed and expected
cases and noncases over the deciles.
e. Yes, it is possible that a model might provide good
discrimination but have poor fit. An example is
given of data in which there is interaction, but a
no-interaction model provides good discrimination
despite not having good fit:
V¼ 1 V¼ 0E¼ 1 E¼ 0 E¼ 1 E¼ 0D¼113 12 D¼138 70
D¼0 8 171 D¼0 12 102ORcV¼ 1 ¼ 23 : 16 ORcV¼ 0 ¼ 4 : 61
Model:logit PðXÞ¼b 0 þb 1 Eþb 2 V
From the edited output shown below it can be seen
that the AUC¼0.759, which indicates “fair” discrimi-
nation (Grade C), whereas the Hosmer GOF test indi-
cates poor lack of fit (P¼0.0416):
Analysis of Maximum Likelihood EstimatesParameter DF Estimate Std ErrorWald
Chi‐Sq Pr>ChiSq
Intercept 1 2.6484 0.2676 97.9353 <.0001
E 1 2.1026 0.3218 42.7024 <.0001
V 1 0.0872 0.3291 0.0702 0.7911
Odds Ratio Estimates
Effect Pt Estimate 95% Wald Confidence Limits
E 8.188 4.358 15.383
V 1.091 0.572 2.080684 Test Answers