# Comparing Spatial Regression to Random Forests for Large Environmental Data Sets

## TL;DR

This study compares spatial regression and random forests for large environmental datasets, finding spatial regression with transformations slightly outperforms random forests in predictive accuracy and produces narrower, more consistent prediction intervals.

## Contribution

Introduces a novel transformation procedure for spatial regression and provides a comprehensive comparison with random forests on large-scale environmental data.

## Key findings

- Spatial regression with transformations slightly outperforms random forests in cross-validation.
- Prediction intervals from spatial regression are narrower and less variable.
- Simulation study clarifies the advantages of each modeling approach.

## Abstract

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.