Bias-variance decomposition of errors in data-driven land cover change modeling

Abstract

Careful model evaluation is essential for using the results of data-driven land cover change (LCC) models. A useful evaluation should help the analyst understand model behavior and improve model performance. Conventional error analysis methods provide limited insights on these two issues. We propose the use of bias-variance error decomposition (BVD) for LCC model evaluation and investigate its value through a pilot study. We examined the mathematical underpinnings of BVD and applied the approach to a model describing the expansion of development for a county in southeastern Michigan, USA. The spatial structure of the BVD error component maps effectively informed the design of model improvement efforts. We found that bias maps can help detect and eliminate the negative influence of spatial non-stationarity in LCC models, and variance maps can shed light on optimal training sample allocation and ways to mitigate model instability. In our case study, model improvements suggested by BVD showed potential to substantially reduce estimation error. Our analysis also revealed that fast and slow developments can result from different mechanisms even when they are geographically near to each other, and different development types may be best analyzed with separate models. BVD has advantages over conventional error analysis and can deepen our understanding of the underlying LCC process and the sources of modeling error. The BVD insights can help effectively design and apply model improvement strategies. These results and the BVD approach have great generality and are applicable to many other geospatial models.