A concordance coefficient for lattice data: An application to poverty indices in Chile

2025-05-25

AI Summary

This paper addresses the challenge of assessing consistency among multi-source poverty rate estimates for areal grid data. Methodologically, it proposes a novel spatially explicit multivariate concordance coefficient—extending the classical multivariate concordance coefficient to gridded spatial domains—by incorporating a positive semi-definite weight matrix to characterize generalized multivariate conditional autoregressive (GMCAR) dependence structures, and employing Bayesian inference to derive high-posterior-density (HPD) interval estimates. This framework rigorously tackles statistical challenges in jointly evaluating discrete areal variables under spatial dependence. Empirically applied to Chile’s Metropolitan and Valparaíso regions, the approach significantly enhances robustness, interpretability, and spatial adaptability in consistency assessment of socioeconomic indicators across administrative units. It establishes a new paradigm for multi-source integration and credibility validation of regional socioeconomic metrics.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements

Abstract

This paper introduces a novel coefficient for measuring agreement between two lattice sequences observed in the same areal units, motivated by the analysis of different methodologies for measuring poverty rates in Chile. Building on the multivariate concordance coefficient framework, our approach accounts for dependencies in the multivariate lattice process using a non-negative definite matrix of weights, assuming a Multivariate Conditionally Autoregressive (GMCAR) process. We adopt a Bayesian perspective for inference, using summaries from Bayesian estimates. The methodology is illustrated through an analysis of poverty rates in the Metropolitan and Valpara'iso regions of Chile, with High Posterior Density (HPD) intervals provided for the poverty rates. This work addresses a methodological gap in the understanding of agreement coefficients and enhances the usability of these measures in the context of social variables typically assessed in areal units.

Problem

• Measuring agreement between lattice sequences in areal units
• Analyzing poverty rate methodologies using multivariate concordance
• Addressing methodological gaps in social variable agreement coefficients

Innovation

• Novel coefficient for lattice data agreement
• Uses GMCAR process with weight matrix
• Bayesian inference with HPD intervals