Scorecard Model Development-a standard scorecard implementation based on logistic regression

By the basic principle of logistic regression, we represent the probability of customer default as P, then the normal probability is 1-p. As a result, you can get:

At this point, the probability p for a customer default can be expressed as: The score scale set by the

Scorecard can be defined by a linear expression that represents a fraction of the ratio logarithm, which is represented as follows:

where A and B are constants. The negative sign in the formula can make the probability of default less, the higher the score. Usually, this is the ideal direction of the score, that is, the high score represents the low risk, the low score represents the high risk. The
Logistic regression model calculates the ratio as follows:

The model parameter β0,β1,...,βn can be obtained by fitting model with modeling parameters. Β_0,β_1,...,β_n. The values of constants A and B in the
formula can be calculated by bringing two known or assumed scores into the calculation. Typically, you need to set two assumptions:
(1) sets a specific expected score for a particular ratio;
(2) determines the percentage doubling (PDO)
based on the above analysis, we first assume that the score is p for a particular point with a ratio of x. Then the points with a ratio of 2x should be p+pdo. In the surrogate, the following two equations can be obtained:

Assuming that the rating card scale is set to the ratio of {1:20} (default normal ratio) when the score is 50 points, PDO is 10 points, in the substituting formula: b=14.43,a=6.78
The calculation formula of the score can be expressed as:
After the
Scorecard scale parameters A and B are determined, you can calculate the ratio and default probability, as well as the corresponding score. Constant A is often called compensation, and constant b is called a scale.
The scorecard's score can be expressed as:

: The variable x1...xn x_1...x_n is the independent variable that appears in the final model, which is the in-mold indicator. Since all variables are converted with woe conversions, each of these arguments can be written in the form of Δij (Βiωij) (Β_iω_{ij}) Δ_{ij}:

, Ωijω_{ij} is the woe of the J variable in line I, and is a known variable; βiβ The _i is the coefficient in the logistic regression equation, the known variable, and the Δijδ_{ij} is a two variable that indicates whether the variable I takes the first J value. The above can be re-represented as:

This is the final scorecard formula. If the X1...XN x_1...x_n variable does not take the same line and calculates its woe value, the standard scorecard format represented in the formula is shown in table 3.20:
Table 3.20 shows that the variable x1 has a K1 row, the variable x2 has k2 rows x_1 There are k_1 rows, the variable x_2 has k_2 rows, and so on The base score equals (a−bβ0) (a-bβ_0); Because of the minus sign in the score distribution formula, the model parameter β0,β1,...,βn