How to convert coefficients of logistic regression into score values when constructing scorecard?

Question

I have built a logistic regression model which takes a dataframe of dummy values as an input and produces binary classification (0 for accept, 1 for default). I have already split all variables into ranges and calculated logistic regression coefficients for each of these ranges.

Here is the sample of what my input looks like:

(pictures are taken from this article)

And coefficients for these inputs (which are taken from the coefficients of logistic regression model):

I want to convert these values into scores, but I am not sure how to accomplish this. I saw some texts and questions here that mention PDO and linear scaling. But I cant figure out how to actually produce score values.

Any help would be appreciated

Answer 1

I have a lot of experience with credit scorecard models.

In response to the above comment, it is common to bin continuous variables in credit scoring models (scorecards) to improve usability and interpretation, e.g. a person with income > 100k is assigned 10 scorecard points, which you then aggregate across all predictor vairables to get the final score.

Regarding transforming variable coefficients to scores, you need to change the structure of your logistic regression model. Follow the steps below:

1. Instead of using dummy variables for your variable categories, use a single categorical variable, but instead of the category values (Grade A,B,C etc.) substitute in the Weight of Evidence (WoE) of the category. You will then have numeric values as your categories (i.e. separate WoE values per category). WoE transformed variables are industry practice when it comes to building logistic regression scorecards.

2. Run your regression on your bad flag = 1 on the WoE transformed categorical variables. These variables are treated as continous numeric variables rather than categorical variables (e.g. in SAS you no longer need the CLASS statement on PROC LOGISTIC).

3. Define what your overall scorecard parameters are, e.g. base score = 500, base odds = 1:1, points to double the odds (PDO) = 20.

4. Derive the intercept score based on your logistic regression output: intercept score = base score + PDO/LN(2) * Intercept coefficient - 1. You'll use this value to sum up all the variable category points (+ intercept score) to get your final scorecard score.

5. For each of the categories in a given variables, calculate the category score: category score = category coefficient * category WoE * -1 * PDO/LN(2)

6. For a given account or customer, sum up the different variable scores to get your final scorecard score.

7. As a sense check, take your account level logistic regression output which will be a probability of default between 0 and 1 and apply the following formula:

Scorecard score = Base Score - (PDO/LN(2)) * LN(Base Odds) + (PDO/LN(2)) * LN(P(Good)/P(Bad))

This should match the score derived from adding up the individual variable categories per account.

Good luck!

Answer 2

You need to take some course in logistic regression and not only follow tutorials as the one you linked. Several points:

• You seem to bin continuous variables before using them as predictors. That is mostly a bad idea, a better idea is to model using regression splines. See What is the benefit of breaking up a continuous predictor variable? and Violation of linearity assumption in Logistic Regression (and search this site).

• You say I want to convert these values into scores, but I am not sure how to accomplish this, which is strange. The predicted value for each case in LR is a probability value, and that is your score. See Why P>0.5 cutoff is not "optimal" for logistic regression? and Why isn't Logistic Regression called Logistic Classification?