The “Heisenberg uncertainty” of spatial analysis: tradeoffs between spatial and estimator precision in small area estimation

Abstract

Industry, government, and conservation groups alike increasingly rely on remote sensing and small area estimation methods to generate forest biometric estimates for small areas, raster cells, and even individual trees. In many places these techniques may replace traditional field surveying. This practice necessitates difficult conversations about the impacts of measurement, positioning, and model errors; the modifiable areal unit problem; and the ecological fallacy in the field of forestry. There are two broad classes of small area estimation (SAE) models that combine survey data and auxiliary data: unit-level models, which first fit prediction models to plot level survey and auxiliary data and then aggregate the predictions to the small areas; and area level models which first aggregate all the data to the small area, then fit prediction models to that aggregated data. Given the wealth of high-resolution data available, it is easy to assume that unit level models are preferable and that the results of these models may be applied to increasingly small areas. However, those data and model errors at the unit level require more caution when considering unit level models and interpreting model results. These issues are illustrated using a case study from small area estimation of mangrove forests in Florida.