A score for how far a variable's distribution has shifted between two samples, usually training and production: bin the variable, then sum (actual% − expected%) × ln(actual% / expected%) over the bins. Below 0.1 is usually read as stable and above 0.25 as a major shift.
Card 1 of 228. Answer: A score for how far a variable's distribution has shifted between two samples, usually training and production: bin the variable, then sum (actual% − expected%) × ln(actual% / expected%) over the bins. Below 0.1 is usually read as stable and above 0.25 as a major shift.
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The population stability index comes from credit scoring, where it compares the score distribution of current applicants with the sample the scorecard was built on. Split the variable into bins, often deciles of the expected sample, and sum (a − e) × ln(a / e), where a and e are each bin's share in the actual and expected samples. It is the KL divergence measured in both directions and added, so it is symmetric.
Example with three bins: training shares are 50%, 30% and 20%; this month's are 30%, 40% and 30%. The terms are (0.3 − 0.5) × ln(0.3/0.5) = 0.102, (0.4 − 0.3) × ln(0.4/0.3) = 0.029 and (0.3 − 0.2) × ln(0.3/0.2) = 0.041, so PSI = 0.17: a moderate shift by the usual rule of thumb, worth a look but not an alarm.
Caveats interviewers probe: the 0.1 and 0.25 cut-offs are industry conventions, not a statistical test; the value depends on the binning; an empty bin makes the log undefined, so a small floor is added; and PSI measures how much one variable moved, not whether the model's performance suffered. It is one of several drift measures, next to the Kolmogorov-Smirnov test and the Jensen-Shannon distance.
