Bayesian Logistic Regression Models for Credit Scoring by Gregg Webster

Table 4.19 
Classification table of the Bayesian logistic regression model with non-
informative prior and cut-off probability of 0.3.
Predicted 
Good 
Bad 
Actual 
Good 
1141 
181 
Bad 
101 
239 
Of the 1,662 applicants on the test set, the Bayesian logistic regression model with non-
informative prior (Model 3) rejected 420 and accepted 1,242 applicants (Table 4.19). Of 
the rejected applicants, 181 (43.1%) are in fact good - missed out profits for the financial 
institution. Of the accepted applicants, 101 (8.1%) were bad - losses for the financial 
institution. 8.1% is thus the classification error rate realized by the financial institution. 
The overall classification error rate is 17.0%. 
Comparison of the 3 models 
Table 4.20 compares Models 1, 2 and 3.
Table 4.20 
Comparison of Models 1, 2 and 3 when the cut-off probability is 0.3. 
Model 1 Model 2 Model 3 
Accepted 
1226 
1261 
1242 
Rejected 
436 
401 
420 
Error rate among accepted 
8.2% 
8.4% 
8.1% 
Error rate among rejected 
45.0% 
41.6% 
43.1% 
Total error rate 
17.8% 
16.4% 
17.0% 

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95 
From Table 4.20, the following can be deduced: 
-
Model 2 accepts the most applicants. 
-
Model 1 rejects the most applicants. 
-
Model 3 has the lowest error rate among the accepted applicants.
-
Model 2 has the lowest error rate among the rejected applicants. 
-
Model 2 has the lowest total error rate. 
In terms of total error rate, the best model is Model 2 and the second best model is Model 
3. Therefore, both the Bayesian models perform better than the logistic regression model. 
For the error rates among the accepted applicants (the error realized by the financial 
institution), the error rates are fairly close to each other. Model 2 is thus the best model to 
use as it would result in the most profit for the financial institution.