SpatialPack: Tools for assessment the association between two spatial processes

SpatialPack provides tools to assess the association between two spatial processes. Currently, several methodologies are implemented: A modified t-test to perform hypothesis testing about the independence between the processes, a suitable nonparametric correlation coefficient, the codispersion coefficient, and an F test for assessing the multiple correlation between one spatial process and several others. Functions for image processing and computing the spatial association between images are also provided. SpatialPack gives methods to complement methodologies that are available in geoR for one spatial process.

Tjostheim's Coefficient.
- Tjostheim, D., 1978. A measure of association for spatial variables. Biometrika 65, 109-114.
A Modified Correlation Coefficient Test.
- Clifford, P., Richardson, S., Hemon, D., 1989. Assessing the significance of the correlation between two spatial processes. Biometrics 45, 123-134.
The Codispersion Coefficient.
- Matheron, G., 1965. Les Variables Regionalisees et leur Estimation. Masson, Paris.
- Rukhin, A., Vallejos, R., 2008. Codispersion coefficients for spatial and temporal series. Statistics and Probability Letters 78, 1290-1300.
Modified F Test for assessing multiple correlation.
- Dutilleul, P., Pelletier, B., Alpargu, G., 2008. Modified F test for assessing the multiple correlation between one spatial process and several others. Journal of Statistical Planning and Inference 138, 1402-1415.

A detailed description of each of these techniques is presented in the book:

Vallejos, R., Osorio, F., Bevilacqua, M. (2020). Spatial Relationships Between Two Georeferenced Variables: with Applications in R. Springer, Cham. DOI: 10.1007/978-3-030-56681-4

Currently, the SpatialPack provides support for the following R packages:

Resources

Latest binaries and sources can be found at the CRAN package repository:

SpatialPack_0.4-1.tar.gz - Package sources
SpatialPack_0.4-1.zip - Windows binaries (R-release)
SpatialPack_0.4-1.tgz - MacOS binaries (R-release, arm64)
SpatialPack_0.4-1.tgz - MacOS binaries (R-release, x86_64)

Reference Manual

PDF manual | HTML manual

Features

Computes Tjostheim's coefficient and its asymptotic variance for two spatial sequences defined on the same locations on the plane.
Performs an hypothesis testing based on a modified version of the correlation coefficient. The test provides a decision rule to elucidate whether the two processes are spatially correlated or not. The spatial sequences need to be defined on the same locations on the plane.
Computes de codispersion coefficient for a specific direction h on the plane.
Provides a plot for the codispersion coefficient versus the lag distance h for isotropic processes.
Functions for image processing and computing the spatial association between images are also provided.

Installation instructions

Install SpatialPack from CRAN using.

install.packages("SpatialPack")

You can install the latest development version from github with:

# install.packages("devtools")
# devtools::install_github("faosorios/SpatialPack")
install.packages("SpatialPack", repos = c('https://faosorios.r-universe.dev', 'https://cloud.r-project.org'))

Alternatively, you can download the source as a tarball or as a zip file. Unpack the tarball or zipfile (thereby creating a directory named, SpatialPack) and install the package source by executing (at the console prompt)

R CMD INSTALL SpatialPack

Next, you can load the package by using the command library(SpatialPack)

Providing Feedback

Please report any bugs/suggestions/improvements to Felipe Osorio. If you find these routines useful or not then please let me know. Also, acknowledgement of the use of the routines is appreciated.

To cite package `SpatialPack` in publications use:

To cite the SpatialPack package in publications use:

  Vallejos, R., Osorio, F., Bevilacqua, M. (2020). Spatial
  Relationships Between Two Georeferenced Variables: with Applications
  in R. Springer, New York. ISBN 978-3-030-56680-7

A BibTeX entry for LaTeX users is

  @Book{,
    title = {Spatial Relationships Between Two Georeferenced Variables: with Applications in R},
    author = {R. Vallejos and F. Osorio and M. Bevilacqua},
    publisher = {Springer},
    address = {New York},
    year = {2020},
    note = {ISBN 978-3-030-56680-7},
    url = {http://srb2gv.mat.utfsm.cl/},
  }

References

Osorio, F., Vallejos, R., Barraza, W., Ojeda, S.M., Landi, M.A. (2022). Statistical estimation of the structural similarity index for image quality assessment. Signal, Image and Video Processing 16, 1035-1042.
Acosta, J., Vallejos, R. (2018). Effective sample size for spatial regression processes. Electronic Journal of Statistics 12, 3147-3180.
Vallejos, R., Osorio, F., Mancilla, D. (2015). The codispersion map: A graphical tool to visualize the association between two spatial variables. Statistica Neerlandica 69, 298-314.
Cuevas, F., Porcu, E., Vallejos, R. (2013). Study of spatial relationships between two sets of variables: A nonparametric approach. Journal of Nonparametric Statistics 25, 695-714.
Ojeda, S., Vallejos, R., Lamberti, P. (2012). Measure of similarity between images based on the codispersion coefficient. Journal of Electronic Imaging 21, 023019.

Papers using SpatialPack

Stephens, P.R., Farrell, M.J., Davies, T.J., Gittleman, J.L., Meiri, S., Moreira, M.O., Roll, U., Wiens, J.J. (2025). Global diversity patterns are explained by diversification rates and dispersal at ancient, not shallow, timescales. Systematic Biology syaf018.
Habeeb, R., Almazah, M.M.A., Hussain, I., Al-Ansari, N., Al-Rezami, A.Y., Sammen, S.Sh. (2023). Modified standardized precipitation evapotranspiration index: spatiotemporal analysis of drought. Geomatics, Natural Hazards and Risk 14 (1), 2195532.
Moura, M.R., do Nascimento, F.A.O., Paolucci, L.N., Silva, D.P., Santos, B.A. (2023). Pervasive impacts of climate change on the woodiness and ecological generalism of dry forest plant assemblages. Journal of Ecology 111, 1762-1776.
Tehreem, Z., Ali, Z., Al-Ansari, N., Niaz, R., Hussain, I., Sammen, S.Sh. (2022). A novel appraisal protocol for spatiotemporal patterns of rainfall by reconnaissance the precipitation concentration index (PCI) with global warming context. Mathematical Problems in Engineering 2022, ID 3012100.
Buss, D.L., Hearne, E., Loy, R.H.Y., Manica, A., O'Connell, T.C., Jackson, J.A. (2022). Evidence of resource partitioning between fin and sei whales during the twentieth-century whaling period. Marine Biology 169, 150.
Ali, Z., Hussain, I., Faisal, M., Shad, M.Y., Elashkar, E.E., Gani, S. (2019). An ensemble procedure for pattern recognition of regional drought. The International Journal of Climatology 40, 94-114.