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When a Credit Risk Models like PAY& NO-PAY (Binary) Models are developed, we get the probability whether an account/customer can pay. Only on Paid customers we develop
"Payment projection Scorecard"(Linear Model).

At the time of Implementation, how do we combine the information?

First Model gives P(Pay) and the second Model provides Expected Payment value?

If the customer who can pay falls in bottom decile, and if his payment
value is high, how this can be justified by using two Models?

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### Replies to This Discussion

To combine the information from the two models, you can simply multiply the two model scores, which will give you an expected value.

You've got two populations of customers (payers and non-payers). In your first model, you are coming up with a probability for each customer that they will be a payer. In your second model, you are predicting payment value for payers only. So, a customer's payment probability multiplied by their expected payment value (conditional on them being a payer), would give you an 'expected value' score for each customer.
Thank you for the information. This worked

E[Payment value of each customer] = SUM { E[Payment value | Payer] * P[Payer].}

The total predicted payment value for the population is almost equal to the predicted payment value of the population. When sorted by the combined score, predicted payment value is high at initial pentiles when compared to lower pentiles?. I think the combined score accumulates customers with high probability and high payment value, where as it is reverse in lower pentiles?
The total predicted payment value for the population is almost equal to the total actual payment value of the population.

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