  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.
