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Comparing spatial regression to random forests for large environmental data sets
Fox, EricW, J. Ver Hoef, AND Tony Olsen. Comparing spatial regression to random forests for large environmental data sets. Joint Statistical Meeting, Baltimore, MD, July 29 - August 03, 2017.
This research investigates different approaches for modeling and mapping national stream condition. We use MMI data from the EPA's National Rivers and Streams Assessment and predictors from StreamCat (Hill et al., 2015). Previous studies have focused on modeling the MMI condition classes (i.e., good, fair, and poor) for stream sites using random forests. A major contribution of this work is modeling the MMI scores directly and focusing on the corresponding regression problem. We also quantify the uncertainty of the MMI predictions, and produce maps of the MMI predictions and standard errors at all perennial stream reaches across the USA. This is an extra product under SSWR 3.01B.
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, whereas spatial regression, when using reduced rank methods, has a reputation for good predictive performance when using many records. 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. Our primary goal is predicting MMI at over 1.1 million perennial stream reaches across the USA. For spatial regression modeling, we develop two new methods to accommodate large data: (1) a procedure that estimates optimal Box-Cox transformations to linearize covariate relationships; and (2) a computationally efficient covariate selection routine that takes into account spatial autocorrelation. We show that our new methods lead to cross-validated performance similar to random forests, but that there is an advantage for spatial regression when quantifying the uncertainty of the predictions. Simulations are used to clarify advantages for each method.