An R package in support of publication, "Kriging Models for Linear Networks and non-Euclidean Distances: Cautions and Solutions."
As a scientific work, and in keeping with common scientific practicies, I kindly request that you cite my research project and applicable publications if you use my work(s) or data in your publications or presentations. Additionally, I strongly encourage and welcome collaboration to promote use of these data in the proper context and scope. The publication is currently submitted:
Ver Hoef, Jay. M. Kriging Models for Linear Networks and non-Euclidean Distances: Cautions and Solutions. In press Methods in Ecology and Evolution.
- There are now many examples where ecological researchers used non-Euclidean distance metrics in geostatistical models that were designed for Euclidean distance, such as those used for kriging. This can lead to problems where predictions have negative variance estimates. Technically, this occurs because the spatial covariance matrix, which depends on the geostatistical models, is not guaranteed to be positive definite when non-Euclidean distance metrics are used. These are not permissible models, and should be avoided.
- I give a quick review of kriging and illustrate the problem with several simulated examples, including locations on a circle, locations on a linear dichotomous network (such as might be used for streams), and locations on a linear trail or road network. I re-examine the linear-network distance models from Ladle et al. (2017) and show that they are not guaranteed to have a positive-definite covariance matrix.
- I introduce the reduced-rank method, also called a predictive-process model, for creating valid spatial covariance matrices with non-Euclidean distance metrics. It has an additional advantage of fast computation for large data sets.
- I reanalyzed the data of Ladle et al. (2017), showing that fitted models that used linear network distance in geostatistical models, both with and without a nugget effect, had negative variances, poor predictive performance compared reduced-rank methods, and had improper coverage for the prediction intervals. The reduced-rank approach using linear network distances provided a class of permissible models that had better predictive performance and proper coverage for the prediction intervals, and could be combined with Euclidean distance models to provide the best overall predictive performance.
Installation of this R data package is done through the devtools::install_github() function or by downloading the source package from the latest release.
library("devtools")
install_github("jayverhoef/KrigLinCaution")
The knitr document used to create the manuscript can be found here on your computer system:
system.file("doc/KrigLinCaution.Rnw", package = "KrigLinCaution")
which contains all of the R code embedded in the Latex manuscript. Stripping out the R code with the "purl" command yields a pure R script, which can be found here:
system.file("doc/KrigLinCaution.R", package = "KrigLinCaution")
To run the whole script from within R use:
# set working directory to /doc path in package
setwd(system.file("doc", package = "KrigLinCaution"))
# make a list of files and directories
file.list <- list.files()
# copy files to R temporary directory (or change to a permanent one of your choice)
file.copy(file.list, tempdir(), recursive = TRUE)
# set working directory to R temporary directory (or whereever you copied stuff)
setwd(tempdir())
# Run the R script
source("KrigLinCaution.R")
A pure Latex document can be found here:
system.file("doc/KrigLinCaution.tex", package = "KrigLinCaution")
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