The connection of the stability of the binary choice model with its discriminatory power

Paper: arXiv 2507.04866

Authors: M. Pomazanov

Abstract

The key indicators of model stability are the population stability index (PSI), which uses the difference in population distribution, and the Kolmogorov-Smirnov statistic (KS) between two distributions. When deriving a binary choice model, the question arises about the real Gini index for any new model. The paper shows that when the Gini changes, the real Gini index should be less than the obtained Gini index. This type is included in the equation using a formula, and the PSI formula in KS is also included based on the scoring indicator. The error in calculating the Gini index of the equation is unavoidable, so it is necessary to always rely on the calculation formula. This type of research is suitable for a wide range of tasks where it is necessary to consider the error in scoring the indicator at any length.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a theoretical mathematical framework linking model instability metrics (PSI, KS) directly to the decay in discriminatory power (Gini coefficient). However, the empirical validation is minimal, relying on a basic illustration using historical Moody’s rating transition counts rather than a rigorous, full-scale backtest.

Research Flowchart

  flowchart TD
    A[Research Goal: Assess Binary Choice Model Stability vs. Discriminatory Power] --> B[Inputs: Population Distribution, Scoring Indicators & Distributions]
    B --> C[Methodology: Calculate Baseline Gini, KS Statistic & PSI]
    C --> D[Adjust Gini Index for Model Instability/Shift]
    D --> E[Incorporate PSI & KS Metrics into Adjustment Equations]
    E --> F[Outcomes: Real Gini < Obtained Gini Due to Unavoidable Scoring Error]