Spatial Product Partition Models

When modeling geostatistical or areal data, spatial structure is commonly accommodated via a covariance function for the former and a neighborhood structure for the latter. In both cases the resulting spatial structure is a consequence of implicit spatial grouping in that observations near in space are assumed to behave similarly. It would be desirable to develop spatial methods that explicitly model the partitioning of spatial locations providing more control over resulting spatial structures and being able to better balance global vs local spatial dependence. To this end, we extend product partition models to a spatial setting so that the partitioning of locations into spatially dependent clusters is explicitly modeled. We explore the spatial structures that result from employing a spatial product partition model and demonstrate its flexibility in accommodating many types of spatial dependencies. We illustrate the method's utility through simulation studies and an education application.