Spatial Aggregation with Respect to a Population Distribution

Spatial aggregation with respect to a population distribution involves estimating aggregate quantities for a population based on an observation of individuals in a subpopulation. In this context, a geostatistical workflow must account for three major sources of `aggregation error': aggregation weights, fine scale variation, and finite population variation. However, common practice is to treat the unknown population distribution as a known population density and ignore empirical variability in outcomes. We improve common practice by introducing a `sampling frame model' that allows aggregation models to account for the three sources of aggregation error simply and transparently. We compare the proposed and the traditional approach using two simulation studies that mimic neonatal mortality rate (NMR) data from the 2014 Kenya Demographic and Health Survey (KDHS2014). For the traditional approach, undercoverage/overcoverage depends arbitrarily on the aggregation grid resolution, while the new approach exhibits low sensitivity. The differences between the two aggregation approaches increase as the population of an area decreases. The differences are substantial at the second administrative level and finer, but also at the first administrative level for some population quantities. We find differences between the proposed and traditional approach are consistent with those we observe in an application to NMR data from the KDHS2014.