Population stability index (PSI)
Population stability index (PSI) measures how far the distribution of a score or characteristic has shifted between two samples, such as development data and recent applications. It describes a change in the population distribution, not whether a score ranks risk worse.
Example
For illustration, suppose two score bins have expected shares of 60% and 40%, and actual shares of 50% and 50%. PSI = (0.50 − 0.60) × ln(0.50 ÷ 0.60) + (0.50 − 0.40) × ln(0.50 ÷ 0.40), which is approximately 0.041.
How PSI is calculated by bin
Start by dividing the score or characteristic into bins. For each bin, calculate its share in the reference sample, called the expected share, and its share in the comparison sample, called the actual share.
For each bin, multiply the actual share minus the expected share by the natural log of the actual share divided by the expected share. Add the bin contributions to get the PSI for the two samples.
How lenders read PSI in score monitoring
A common reading treats PSI below 0.1 as little shift. From 0.1 to 0.25, it suggests some shift worth a look, and above 0.25 is commonly read as a major shift. These are rules of thumb, not regulatory thresholds.
A new marketing channel or a change to the application form can move the distribution. Policy changes and data faults can do so too. Check possible sources before attributing the shift to applicants. PSI does not show whether the score ranks risk worse; Gini on recent outcomes addresses that question.
Questions we get asked
Can PSI identify what caused a shift?
No. PSI measures the size of a distribution shift, not its cause. A change in marketing channel or application form may explain it, and a data fault is another possibility to check.
Does PSI describe an individual applicant?
No. PSI compares the distribution across samples, so it does not describe an individual applicant or determine that person’s credit outcome.
What does a PSI of zero mean?
A PSI of zero means the expected and actual shares match across the bins. The calculation shows no measured shift between those two sample distributions.
Decisimo’s PSI calculator calculates the index for a score or characteristic and shows each bin’s contribution and the size of the shift.
