Bayesian Logistic Regression Models for Credit Scoring by Gregg Webster

Table 4.8
Correlation matrix of the numerical independent variables on the “new” data.
 Variable 
LOAN MORTDUE VALUE YOJ 
DEROG DELINQ CLAGE NINQ CLNO DEBTINC 
LOAN 
1.00 
0.23 
0.33 
0.08 
-0.02 
-0.04 
0.10 
0.08 
0.08 
0.07 
MORTDUE 
0.23 
1.00 
0.85 
0.01 
-0.01 
-0.02 
0.11 
0.05 
0.31 
0.14 
VALUE 
0.33 
0.85 
1.00 
0.06 
-0.04 
0.04 
0.13 
0.04 
0.33 
0.12 
YOJ 
0.08 
0.01 
0.06 
1.00 
-0.05 
0.01 
0.16 
-0.06 
-0.01 
-0.09 
DEROG 
-0.02 
-0.01 
-0.04 
-0.05 
1.00 
0.14 
-0.02 
0.07 
0.00 
0.07 
DELINQ 
-0.04 
-0.02 
0.04 
0.01 
0.14 
1.00 
0.06 
0.02 
0.07 
0.06 
CLAGE 
0.10 
0.11 
0.13 
0.16 
-0.02 
0.06 
1.00 
-0.1 
0.21 
-0.07 
NINQ 
0.08 
0.05 
0.04 
-0.06 
0.07 
0.02 
-0.1 
1.00 
0.07 
0.20 
CLNO 
0.08 
0.31 
0.33 
-0.01 
0.00 
0.07 
0.21 
0.07 
1.00 
0.17 
DEBTINC 
0.07 
0.14 
0.12 
-0.09 
0.07 
0.06 
-0.07 
0.20 
0.17 
1.00 

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80 
From this correlation matrix, we see that there are no large pair-wise correlations. The 
largest correlation is 0.85 between VALUE and MORTDUE. The other pair-wise 
correlations are all very small and insignificant. Worrying correlations will occur when the 
correlation between two variables is greater than 0.9. The variance inflation factors for 
each numerical variable are given in Table 4.9. 
Table 4.9
Variance inflation factors (VIF) of numerical independent variables on the 
“new” data. 
Variable 
VIF 
LOAN 
1.156804 
MORTDUE 3.84004 
VALUE 
4.112173 
YOJ 
1.047812 
DEROG 
1.03521 
DELINQ 
1.046096 
CLAGE 
1.108899 
NINQ 
1.063397 
CLNO 
1.202153 
DEBTINC 
1.100282 
From Table 4.9, there are no large variance inflation factors. Therefore, there is no serious 
problem with collinearity in the “new” data.
Outliers and influential observations in the model are now considered. A half-normal plot 
of the residuals is given in Figure 4.17.

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81 
Fig. 4.17
Half-normal plot of residuals for the “new” data.
Figure 4.17 shows no indication of outliers. Secondly, a half-normal plot of the leverages 
is given in Figure 4.18. 
Fig. 4.18
Half-normal plot of leverages for the “new” data.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0
1
2
3
4
Half-normal quantiles
So
rte
d 
D
at
a
240
245
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.
0
0.
1
0.
2
0.
3
0.
4
0.
5
Half-normal quantiles
So
rte
d 
Da
ta
49
86

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82 
Figure 4.18 shows that there may be some indication of leverage from observations 
numbered 49 and 86. Finally a half-normal plot of the Cook’s distance statistics is given in 
Figure 4.19. 
Fig. 4.19
Half-normal plot of the Cook’s distance statistics for the “new” data.
From Figure 4.19, there may be some leverage from observations numbered 220 and 245. 
Thus, observations numbered 49, 86, 220 and 245 may be influential observations. In order 
to see whether these observations are influential we delete them from the “new” data and 
re-fit the model. The estimated parameters of this model are then compared to the 
parameters of the model with no observations deleted. Table 4.10 shows the estimated 
coefficients.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.
00
0.
02
0.
04
0.
06
0.
08
0.
10
Half-normal quantiles
So
rte
d 
Da
ta
220
245

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83