A comparison of the spatial linear model to Nearest Neighbor (k-NN) methods for forestry applications

Forest surveys provide critical information for many diverse interests. Data are often collected from samples, and from these samples, maps of resources and estimates of aerial totals or averages are required. In this paper, two approaches for mapping and estimating totals; the spatial linear model (SLM) and k-NN (k-Nearest Neighbor) are compared, theoretically, through simulations, and as applied to real forestry data. While both methods have desirable properties, a review shows that the SLM has prediction optimality properties, and can be quite robust. Simulations of artificial populations and resamplings of real forestry data show that the SLM has smaller empirical root-mean-squared prediction errors (RMSPE) for a wide variety of data types, with generally less bias and better interval coverage than k-NN. These patterns held for both point predictions and for population totals or averages, with the SLM reducing RMSPE from 9% to 67% over some popular k-NN methods, with SLM also more robust to spatially imbalanced sampling. Estimating prediction standard errors remains a problem for k-NN predictors, despite recent attempts using model-based methods. Our conclusions are that the SLM should generally be used rather than k-NN if the goal is accurate mapping or estimation of population totals or averages.