Citation:

Fox, E., J. Ver Hoef, AND Tony Olsen. Comparing Spatial Regression to Random Forests for Large Environmental Data Sets. PLOS ONE . Public Library of Science, San Francisco, CA, 15(3):e0229509, (2020). https://doi.org/10.1371/journal.pone.0229509

Impact/Purpose:

This research compares spatial regression and random forest approaches for modeling and mapping national stream condition. The response variable for the models is a multimetric index (MMI) that is indicative of the health of macroinvertebrate assemblages sampled at stream sites for 2008/2009 National Rivers and Streams Assessment (NARS). The covariates for the models consist of over 200 landscape features from the StreamCat data set. Previous studies have used random forests to model the MMI condition classes (good, fair, and poor) with StreamCat covariates. This research focuses instead on directly modeling the MMI scores, which range between 0-100, and includes both random forests and spatial regression. We also develop new methods for transforming and selecting covariates for the spatial regression models, and quantify the uncertainty in the MMI predictions. A primary application is mapping the MMI predictions and prediction errors at 1.1 million perennial streams across the conterminous United States.

Description:

Environmental data may be large due to number of records, number of covariates, or both. Random forests has a reputation for good predictive performance when using many covariates with nonlinear relationships, whereas spatial regression, when using reduced rank methods, has a reputation for good predictive performance when using many records that are spatially autocorrelated. In this study, we compare these two techniques using a data set containing the macroinvertebrate multimetric index (MMI) at 1859 stream sites with over 200 landscape covariates. A primary application is mapping MMI predictions and prediction errors at 1.1 million perennial stream reaches across the conterminous United States. For the spatial regression model, we develop a novel transformation procedure that estimates Box-Cox transformations to linearize covariate relationships and handles possibly zero-inflated covariates. We find that the spatial regression model with transformations, and a subsequent selection of significant covariates, has cross-validation performance slightly better than random forests. We also find that prediction interval coverage is close to nominal for each method, but that spatial regression prediction intervals tend to be narrower and have less variability than quantile regression forest prediction intervals. A simulation study is used to generalize results and clarify advantages of each modeling approach.

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