Modelling spatial heterogeneity in the effects of area-level covariates on income distributions using Bayesian nonparametric methods

2026-04-25

AI Summary

This study proposes a Bayesian nonparametric model, NLMFM-C, to characterize the heterogeneity of income distributions across space and with respect to regional covariates such as gender, race, and education level. The model represents multi-regional income densities as mixtures of latent factor densities, jointly incorporating spatial structure and covariate effects. It employs an adaptive Gibbs sampler to automatically infer the number of latent factors and introduces a posterior rotational alignment technique to ensure comparability of inferences across datasets. Empirical analysis using 2016 and 2020 U.S. Public Use Microdata Sample (PUMS) data from four states successfully identifies low-, middle-, and high-income latent factors, offering the first fine-grained characterization of spatiotemporal heterogeneity in covariate effects and providing a foundation for targeted policy design.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Understanding the how the distribution of an economic outcome, such as income, changes with respect to space and covariates is a key concern for policy makers. To address this, we develop a Bayesian nonparametric model, the Normalised Latent Measure Factor Model with Covariates (NLMFM-C), which expresses a large collection of related densities as mixtures of latent factor densities and allows for spatial and covariate effects. We propose an adaptive Gibbs sampler to automatically infer the number of latent factor distributions, and a rotation method to make posterior inference on different data sets comparable. We apply the NLMFM-C model to Public Use Microdata Sample (PUMS) data, focusing on income distributions for sub-areas of four U.S. states over to different years, 2016 and 2020. We show that the latent factor distributions can be interpreted by income level (e.g., low, medium, and high) and investigate the spatially- and time-changing impact of three covariates: gender, race and educational attainment.

Problem

• spatial heterogeneity
• income distribution
• area-level covariates
• Bayesian nonparametrics

Innovation

• Bayesian nonparametrics
• spatial heterogeneity
• latent factor model
• adaptive Gibbs sampler
• income distribution