By Stefan Stoyanov, Solutions Manager, Experian Decision Analytics

Both linear and logistic regression models were built in order to determine which of them
provides the best estimate of the observed LGD.
•    Linear regression - continuous dependent variable
In order to meet the statistical requirements of the OLS regression an attempt was made to
transform the LGD to normality or at least symmetry by using Box – Cox type of transformation function
•    Logistic regression – the LGD was transformed to a binary dependent variable using two methods:
o    Uniform random number: if LGD > random number then LGD_ Binary = 1 (Bads) ; else LGD_Binary = 0 (Goods)


Set import_data;
Bin_lgd=1;
_freq=LGD;
Output;
Bin_lgd=0;
_freq=1-LGD;
Output;
Run;

•    Manual Cut-Off: if LGD > 0.2 then LGD_Binary = 1 (Bads) ; else LGD_Binary = 0

(Goods)

Power transformation of the LGD distribution
•    Usually the LGD has highly non-normal distribution, often with an U shape and spikes at the two tails of the distribution
•    However, the basic properties of the least squares regression do not require normality
•    Non-normality does not affect the estimation of the regression parameters. The least 
squares estimates are still BLUE (best linear unbiased estimates) if the other regression assumptions are met
•    Non-normality affects the tests of significance and the confidence interval estimates of the regression parameters

Binary transformation of the LGD using uniform random Numbers
Theoretical Beta distribution parameters:
The estimation of the alpha (a) and beta
(b) parameters of the theoretical beta distribution was based on the first two
moments of the observed LGD distribution
 


Functional calibration of the logistic regression scores to estimated LGD

o    The OLS regression model provides direct LGD estimates whereas the
logistic regression models provide indirect LGD estimates. Hence, it is
necessary to calibrate the logistic regression scores to direct LGD estimates in
order to be able to compare the two types of models
o    After obtaining the functional relationship between the logistic regression
scores and LGD it is possible to assign an estimated LGD to each individual
score
Due to the small sample size all data were used for model development. The
models were validated using bootstrap techniques
o    The following calibration tests were used to validate the LGD models:
–Spearman’s Rank Correlation
–Mean Squared Error
–R-square