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

TL;DR

This paper develops a new concordance coefficient for lattice data, specifically applied to compare poverty measurement methodologies in Chile, incorporating Bayesian inference and accounting for spatial dependencies.

Contribution

It introduces a novel agreement coefficient for multivariate lattice data that accounts for dependencies using a GMCAR process and Bayesian inference, addressing a methodological gap.

Findings

The new coefficient effectively measures agreement between poverty indices.

Application to Chilean regions demonstrates practical utility.

Provides Bayesian estimates with HPD intervals for poverty rates.

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.