A Supplementary R Package to to "A Linear Mixed Model Formulation for Spatio-Temporal Random Processes with Computational Advances for the Product, Sum, and Product-Sum Covariance Functions"
The published journal article is available here.
To properly characterize a spatio-temporal random process, it is necessary to understand the process’ dependence structure. It is common to describe this dependence using a single random error having a complicated covariance. Instead of using the single random error approach, we describe spatio-temporal random processes using linear mixed models having several random errors; each random error describes a specific quality of the covariance. This linear mixed model formulation is general, intuitive, and contains many commonly used covariance functions as special cases. We focus on using the linear mixed model formulation to express three covariance functions: product (separable), sum (linear), and product–sum. We discuss benefits and drawbacks of each covariance function and propose novel algorithms using Stegle eigendecompositions, a recursive application of the Sherman–Morrison–Woodbury formula, and Helmert–Wolf blocking to efficiently invert their covariance matrices, even when every spatial location is not observed at every time point. Via a simulation study and an analysis of temperature data in Oregon, USA, we assess model performance and computational efficiency of these covariance functions when estimated using restricted maximum likelihood (likelihood-based) and Cressie’s weighted least squares (semivariogram-based). We end by offering guidelines for choosing among combinations of the covariance functions and estimation methods based on properties of observed data and the desired balance between model performance and computational efficiency.
This supplementary R package contains all files used in creation of this document.
The easiest way to install this R package is to run
install.packages("devtools")
library(devtools)
devtools::install_github("michaeldumelle/DumelleEtAl2021STLMM@main")
After installation, the associated package files can be located on your machine via the system.file() function.
The preprint is available at
system.file("preprint/main.pdf", package = "DumelleEtAl2021STLMM")
or alternatively can be downloaded here.
Supplementary material for the preprint is available at
system.file("preprint/supplementary.pdf", package = "DumelleEtAl2021STLMM")
or alternatively can be downloaded here.
All images can be found at
system.file("images", package = "DumelleEtAl2021STLMM")
All R scripts used to create the images can be found at
system.file("scripts/images", package = "DumelleEtAl2021STLMM")
These files are named corresponding to the figure numbers in the preprint.
All R scripts used to study inversion and empirical semivariogram computational benchmarks (Section 4.3) can be found at
system.file("scripts/inverses", package = "DumelleEtAl2021STLMM")
All output from these R scripts can be found at
system.file("output/inverses", package = "DumelleEtAl2021STLMM")
All R scripts used in the simulation study (Section 5) can be found at
system.file("scripts/simulations", package = "DumelleEtAl2021STLMM")
All output from these R scripts can be found at
system.file("output/simulations", package = "DumelleEtAl2021STLMM")
The data can be loaded after installing the R package and running
library(DumelleEtAl2021STLMM)
data("or_data")
All R scripts used in the data analysis (Section 6) can be found at
system.file("scripts/dataanalysis", package = "DumelleEtAl2021STLMM")
All output from these R scripts can be found at
system.file("output/dataanalysis", package = "DumelleEtAl2021STLMM")