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Class vs Individual Rating: Means vs Patterns in Linear Models

This article explores the limitations of simple linear relationships in class-based rating models and highlights the importance of considering patterns, curves, interruptions, and higher-order interactions. It discusses the concept of homogenous Euclidean space and how it may not hold in reality, leading to differences in dynamics and structure among subgroups. Additionally, it examines the calculation of effective sample size and the challenges in fitting models that accurately represent the underlying data. The article concludes by discussing the importance of credibility in model fit and suggests alternative measures, such as the Gini Index, for underwriting decisions.

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Class vs Individual Rating: Means vs Patterns in Linear Models

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  1. From Class to Individual RatingDaniel Finnegan, PresidentISO Innovative Analytics

  2. CLASS vs INDIVIDUAL RATING

  3. Means vs Patterns • GLM’s Assume Simple Linear Relationships in Homogenous Euclidean Space that Spans the Decision Space • This Complex Set of Assumptions Seldom Holds in Reality

  4. “Simple Linear Relationships” • Curves • Interrupts • Higher-Order Interactions • Categorical Independent Variables Converge to Conditional Means

  5. Example Residuals

  6. Corrected Residuals

  7. “Homogenous Euclidean Space” • Different Structure for Subgroups • Dynamics Change at Extremes

  8. “Spans the Decision Space” • Sample Generalizability • Stability of Underlying Structure • Stability at Extremes • Interpolation vs Extrapolation

  9. Number of Independent Variables • For traditional, class-based approaches, effective sample size is: np/(∏CV) • For GLM-based approaches, effective sample size is: np - (nv+ 1) • GLM’s span entire population, mean-based approaches span subgroups

  10. Calculating Rates vs Fitting a Model • Models are complex combinations of theory, data, equations. • Arbitrary model decisions are inevitable. • Failures of these assumptions can be dangerous

  11. Linear and Log Linear Models

  12. Non-Unique Solutions • Complex models seldom allow unique solutions • Continuous improvement likely • Causal models have longest life spans

  13. Creditability vs Fit • Model fit is not statistical significance • r2 is often not good measure of fit • Aggregate standard error of prediction measures often appropriate • Gini Index may be appropriate for underwriting decision

  14. Example Gini Index

  15. From Class to Individual RatingDaniel Finnegan, PresidentISO Innovative Analytics

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