Bayesian modeling and clustering for spatio-temporal areal data: An application to Italian unemployment

TL;DR

This paper introduces a Bayesian spatio-temporal model with clustering for areal data, effectively capturing regional unemployment patterns in Italy and providing richer economic insights.

Contribution

It develops a novel Bayesian framework combining Gaussian Markov random fields with nonparametric clustering for spatio-temporal areal data analysis.

Findings

More precise estimates than competitors

Effective clustering reveals meaningful regional groups

Enhanced economic interpretation of unemployment patterns

Abstract

Spatio-temporal areal data can be seen as a collection of time series which are spatially correlated according to a specific neighboring structure. Incorporating the temporal and spatial dimension into a statistical model poses challenges regarding the underlying theoretical framework as well as the implementation of efficient computational methods. We propose to include spatio-temporal random effects using a conditional autoregressive prior, where the temporal correlation is modeled through an autoregressive mean decomposition and the spatial correlation by the precision matrix inheriting the neighboring structure. Their joint distribution constitutes a Gaussian Markov random field, whose sparse precision matrix enables the usage of efficient sampling algorithms. We cluster the areal units using a nonparametric prior, thereby learning latent partitions of the areal units. The performance of the model is assessed via an application to study regional unemployment patterns in Italy. When compared to other spatial and spatio-temporal competitors, the proposed model shows more precise estimates and the additional information obtained from the clustering allows for an extended economic interpretation of the unemployment rates of the Italian provinces.