Direct and Indirect Discrimination in Generalized Linear Models

2026-06-22

AI Summary

Generalized linear models (GLMs) are widely used in actuarial modeling, yet their nonlinear link functions render existing fairness diagnostics—typically grounded in linear intuition—inapplicable. This work proposes the first fairness decomposition framework tailored to GLMs by extending the Wasserstein barycenter criterion to the distributional level and integrating moment decomposition with curvature analysis of the inverse link function. The resulting interpretable “four-channel plus dual-curvature” effect decomposition yields explicit formulas for logistic, Poisson, and Tweedie models. Empirical application to healthcare expenditure data demonstrates that the method effectively disentangles sources of prediction disparities, including the direct effect of sensitive attributes, mediation through proxy variables, differences in covariance structure, and amplification effects induced by nonlinear link coupling, thereby offering a practical tool for fairness auditing in actuarial practice.

Abstract

Generalized linear models are central to actuarial modelling of binary risk, claim frequency, utilization, and cost-related outcomes. Yet fairness diagnostics often rely on linear-model intuitions, although GLM predictions are obtained by transporting a latent score through a nonlinear inverse link. We develop a moment-based decomposition framework for diagnosing group disparities in fitted GLM predictions. In an exact linear-Gaussian benchmark, the Wasserstein barycentric criterion for distributional demographic-parity violation reduces to a two-moment criterion and decomposes into direct mean, indirect mean, interaction, and structural components. For GLMs, we distinguish the empirical output-scale criterion $U_2(f)$, a within-group proxy $\widetilde U_2(f)$, and a leading decomposition $D_1(f)$. This leading term preserves the four linear channels and adds two curvature components induced by the inverse link: curvature coupling and curvature amplification. We derive explicit formulas for logistic, Poisson, and Tweedie specifications and illustrate the diagnostic on medical-expenditure survey data. The framework is not a legal test of discrimination, nor a full characterization of distributional parity outside the linear-Gaussian case. It is a tractable actuarial diagnostic for identifying whether fitted prediction disparities arise from explicit sensitive effects, proxy-mediated covariate profiles, covariance-structure differences, or nonlinear link effects.

Problem

• discrimination
• generalized linear models
• fairness
• demographic parity
• nonlinear link

Innovation

• moment-based decomposition
• generalized linear models
• distributional fairness
• curvature effects
• demographic parity