RandomForestsGLS (version 0.1.5)

RFGLS_predict_spatial: Spatial response prediction at new location with RF-GLS

Description

The function RFGLS_predict_spatial performs fast prediction on a set of new locations by combining non-linear mean estimate from a fitted RF-GLS model in Saha et al. 2020 with spatial kriging estimate obtained by using Nearest Neighbor Gaussian Processes (NNGP) (Datta et al., 2016).

Some code blocks are borrowed from the R packages: spNNGP: Spatial Regression Models for Large Datasets using Nearest Neighbor Gaussian Processes
https://CRAN.R-project.org/package=spNNGP and randomForest: Breiman and Cutler's Random Forests for Classification and Regression
https://CRAN.R-project.org/package=randomForest .

Usage

RFGLS_predict_spatial(RFGLS_out, coords.0, Xtest,
                      h = 1, verbose = FALSE)

Value

A list comprising:

prediction

predicted spatial response corresponding to Xtest and coords.0.

Arguments

RFGLS_out

an object obtained from RFGLS_estimate_spatial.

coords.0

the spatial coordinates corresponding to prediction locations.
Its structure should be same as that of coords in BRISC_estimation. Default covariate value is a column of \(1\) to adjust for the mean (intercept).

Xtest

an \(ntest \times p\) matrix of covariates for prediction. Its Structure should be identical (including intercept) with that of covariates provided for estimation purpose in X in RFGLS_out.

h

number of core to be used in parallel computing setup for bootstrap samples. If h = 1, there is no parallelization. Default value is 1.

verbose

if TRUE, model specifications along with information regarding OpenMP support and progress of the algorithm is printed to the screen. Otherwise, nothing is printed to the screen. Default value is FALSE.

Author

Arkajyoti Saha ,
Sumanta Basu ,
Abhirup Datta

References

Saha, A., Basu, S., & Datta, A. (2020). Random Forests for dependent data. arXiv preprint arXiv:2007.15421.

Saha, A., & Datta, A. (2018). BRISC: bootstrap for rapid inference on spatial covariances. Stat, e184, DOI: 10.1002/sta4.184.

Datta, A., S. Banerjee, A.O. Finley, and A.E. Gelfand. (2016) Hierarchical Nearest-Neighbor Gaussian process models for large geostatistical datasets. Journal of the American Statistical Association, 111:800-812.

Andrew Finley, Abhirup Datta and Sudipto Banerjee (2017). spNNGP: Spatial Regression Models for Large Datasets using Nearest Neighbor Gaussian Processes. R package version 0.1.1. https://CRAN.R-project.org/package=spNNGP

Andy Liaw, and Matthew Wiener (2015). randomForest: Breiman and Cutler's Random Forests for Classification and Regression. R package version 4.6-14.
https://CRAN.R-project.org/package=randomForest

Examples

rmvn <- function(n, mu = 0, V = matrix(1)){
  p <- length(mu)
  if(any(is.na(match(dim(V),p))))
    stop("Dimension not right!")
  D <- chol(V)
  t(matrix(rnorm(n*p), ncol=p)%*%D + rep(mu,rep(n,p)))
}

set.seed(1)
n <- 250
coords <- cbind(runif(n,0,1), runif(n,0,1))

set.seed(2)
x <- as.matrix(rnorm(n),n,1)

sigma.sq = 1
phi = 5
tau.sq = 0.1

D <- as.matrix(dist(coords))
R <- exp(-phi*D)
w <- rmvn(1, rep(0,n), sigma.sq*R)

y <- rnorm(n, 10*sin(pi * x) + w, sqrt(tau.sq))

estimation_result <- RFGLS_estimate_spatial(coords[1:200,], y[1:200],
                                 matrix(x[1:200,],200,1), ntree = 10)
prediction_result <- RFGLS_predict_spatial(estimation_result,
                           coords[201:250,], matrix(x[201:250,],50,1))