Identifying latent groups in spatial panel data using a Markov random field constrained product partition model

TL;DR

This paper introduces a novel Bayesian nonparametric prior combining Markov random fields with product partition models to identify latent spatial groups, effectively capturing spatial dependence in panel data.

Contribution

The paper proposes the MRF-PPM prior, a new method that improves latent group detection in spatial panel data by integrating spatial dependence into the clustering process.

Findings

MRF-PPM accurately identifies latent spatial groups.

The method demonstrates superior performance in simulations.

Applications to real data show effective spatial clustering.

Abstract

Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.