Discriminative analysis is a statistical model that can be used to accept or reject a prospective credit customer. The discriminant analysis is similar to regression analysis but it assumed that the observations come from two different universal sets (in credit analysis, the good and bad customers). To illustrate let us assume that two factors are important in evaluating a credit applicant the quick ratio and net worth to total assets ratio.
The discriminant function will be of the form.
ft = a1(X1) + a2(X2)
Where: X1 is quick ratio
X2 is the network to total assets
a1 and a2 are parameters
The parameters can be computed by the use of the following equations:
a1 = Szz dx – Sxzdz
Sxx Sxx – Sxz²
a2 = Szz dx – Sxzdz
Szz Sxx – Sxz²
Where: Sxx represents the variances of X1
Szz represents the variances of X2
Sxz is the covariance of variables of X1 and X2
dx is the difference between the average of X1’s bad accounts and X2’s good accounts
dz represents the difference between the average of X’s bad accounts and X’s good accounts.
The next step is to determine the minimum cut-off value of the function below at which credit will not be given. This value is referred to as the discriminant value and is denoted by f*.
Once the discriminant function has been developed it can then be used to analyse credit applicants. The important assumption here is that new credit applicants will have the same characteristics as the ones used to develop the mode.
More than two variables can be used to determine the discriminant function. In such a case the discriminant function will be of the form.
ft = a1x1 + a2x2 + … + anxn