Identifying Latent Groups in Spatial Panel Data Using a Markov Random Field Constrained Product Partition Model

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 panel data analysis, where repeated measurements are collected time at various locations. We propose a novel class of nonparametric priors combines Markov random field (MRF) with product partition model (PPM), show resulting prior, called by MRF-PPM, capable identifying latent group structure among while efficiently utilizing dependence information. derive closed-form conditional distribution proposed prior introduce new way to compute marginal likelihood renders efficient Bayesian inference. further study theoretical properties MRF-PPM clustering consistency result posterior distribution. demonstrate excellent empirical performance our method via extensive simulation studies US precipitation California median household income study.