ABSTRACT
Handling spatial misalignment and the notion that statistical inference could change with spatial scale is a long-standing issue. By spatial misalignment we mean the summary or analysis of spatial data at a scale different from that at which it was originally collected. More generally, with the increased collection of spatial data layers, synthesis of such layers has moved to the forefront of spatial data analysis. In some cases the issue is merely interpolation-given data at one scale, inferring about data at a different scale, different locations, or different areal units. In other cases, the data layers are examining the same variable and the synthesis can be viewed as a fusion to better understand the behavior of the variable across space. In yet other settings, the data layers record different variables. Now the objective is regression, utilizing some data layers to explain others. In each of these settings, we can envision procedures that range from ad hoc, offering computational simplicity and convenience but limited in inference to fully model-based that require detailed stochastic specification and more demanding computation but allowing richer inference. In practice, valid inference requires assumptions that may not be possible to check from the available data.
