Spatial proportional data often exhibit localized regions with elevated variability, where some areas display substantially higher dispersion than the surrounding domain. Such two-regime spatial heteroscedasticity arises in mining, environmental, and geostatistical applications, but is difficult to accommodate using standard spatial beta regression models. We propose a spatial beta mixture model that jointly models mean and precision regimes through a shared latent spatial process, allowing the identification of spatially contiguous high-dispersion regions. Bayesian inference is performed using MCMC implemented in NIMBLE. Simulation studies demonstrate improved predictive performance and accurate recovery of latent variance regimes relative to conventional spatial beta models. An application to iron ore (Fe) concentration data from Western Australia illustrates the ability of the proposed framework to identify regions with elevated spatial variability.
In causal inference with point-referenced data, two problems arise. First, standard synthetic control methods are typically formulated for panel data in which outcomes are repeatedly observed for the same spatial units over time. In many applications, however, point-referenced data are observed at irregular and time-varying locations (for example, housing transactions occur at different addresses in each period), so there is no fixed spatial panel. Second, when treatment effects vary spatially, aggregating outcomes into a single treated unit can introduce aggregation bias: the resulting estimates depend on how that unit is defined and may mask offsetting local effects.We address both challenges by using block kriging to construct a panel for interpretable spatial units and applying synthetic control methods to the resulting panel. Assuming spatial smoothness, the estimand corresponds to the area-average treatment effect within each treated region, and varying the spatial partition yields an interpretable profile of spatially heterogeneous effects. Simulation experiments illustrate that the proposed approach can reveal causal effects that are obscured when the entire area is aggregated into a single treated unit. As an empirical illustration, we apply the method to quantify the influence of the Toei Oedo Line opening in Tokyo on residential land prices. We find sizable gains near western inner-city stations and relative declines near eastern and waterfront areas, suggesting a spatial reallocation of residential demand.
Analyzing, interpreting, and understanding the dynamics of air pollution data and their meteorological drivers is challenging due to the complex multivariate spatio-temporal nature of the phenomenon. By finding a lower dimensional representation of the data, modeling and interpretation tasks become substantially easier. In this paper, nonlinear spatio-temporal blind source separation methods based on identifiable variational autoencoder, are applied with the aim of finding the generative latent components behind the meteorological and air pollution data over Northern Italy. A simulation study, generated over the same spatio-temporal domain as the real data, first confirms that both methods are able to recover synthetic ground-truth latent components accurately, with iVAEar consistently outperforming iVAE under varying degrees of mixing nonlinearity and missing data. The importance and contributions of the retained latent components estimated from the real data are interpreted through their scaled mean absolute Shapley values, and the temporal and spatial patterns are visually analyzed. Four most important recovered components are detected, namely (i) stagnation component, (ii) combustion-related emission component (iii) wet deposition component and (iv) photochemical pollution component. The found components are easily interpretable and in line with established environmental knowledge.
This paper examines spatial spillovers in voting concentration across Italian municipalities, a key aspect for understanding electoral competition and political representation. To estimate heterogeneous spatial dependencies at the cluster level, while accounting for a broad set of socio-economic and institutional covariates, we adopt the recently introduced spatially-clustered spatial autoregressive (SCSAR) model. The standard SCSAR requires the evaluation of log-determinants of matrices whose dimension grows with the number of spatial units. Due to the large number of Italian municipalities, we address the computational burden of maximizing the log-likelihood function in SCSAR by means of matrix factorization methods. A computational benchmarking experiment shows that sparse factorization substantially improves scalability relative to the eigenvalue-based implementation, making SCSAR feasible for large municipal systems. This approach therefore enables a fast identification of clusters of Italian municipalities characterized by similar structural relationships. We find that global SAR models provide limited explanatory power of voting concentration compared to clustered specifications. Moreover, spatial spillovers are positive in the main specifications but vary substantially across clusters and electoral chambers, confirming that a single global spatial autoregressive coefficient masks important territorial heterogeneity. Economic and demographic variables are the most robust predictors of voting concentration, while several covariates display heterogeneous or even opposite effects across local contexts.
