Question

In: Math

You are trying to predict if audit clients will go bankrupt in the next year. Based...

You are trying to predict if audit clients will go bankrupt in the next year. Based on the results from a logistic regression, the actual vs predicted numbers for clients is as follows, when using a 50 percent cutoff probability for predicting that a client will go bankrupt:

Prediction from Model

Actual Status

Not Bankrupt

Bankrupt

Not Bankrupt

950

50

Bankrupt

40

60

One of your colleagues, John, suggests that you should use a 70 percent cutoff probability for predicting that a client will go bankrupt.

Another colleague, Mike, suggests that you should use a 30 percent cutoff probability for predicting that a client will go bankrupt.

Answer the following questions:

(a) Who is correct, in this situation? Explain your answer with appropriate logic.

(b) What will happen to the Actual vs Predicted matrix if you use:

(i) 70 percent cutoff probability suggested by John? That is, how would the total numbers in the two columns and two rows change, if at all they change?

(i) 30 percent cutoff probability suggested by Mike? That is, how would the total numbers in the two columns and two rows change, if at all they change?

Solutions

Expert Solution

We can explain the choice of a better cutoff point with the help of sensitivity and specificity values
Sensitivity is defined as the total number of bankrupts(in the current situation) who will be correctly classified as bankrupts
Specificity is defined as the total number of non bankrupts who will be correctly classified as non bankrupts.
Effect of shift in cut points on sensitivity and specificity:
Here, we have the contingency table (the table which contains the actual and predicted values) for the actual and predicted values.
Fixing the cutoff to a lower value than the one chosen presently will result in a greater sensitivity and lower specificity (more false positives) while fixing the cutoff to a higher value than the one chosen presently will result in a lower sensitivity and higher specificity (more false negatives).

a)
Here in the case of predicting bankrupts, there will be loss to be incurred if bankrupts are not correctly classified as bankrupts.
So we need a higher sensitivity value (or false positives should be reduced)
Mike's suggestion would serve better and give better results.

b)

30 percent cutoff probability suggested by Mike will give more false positives. ie Bankrupts predicted as Bankrupts will have a higher number.

70 percent cutoff probability suggested by John will give more false negatives. ie Non Bankrupts predicted as Non Bankrupts will have a higher number.


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