This is the homepage for the R package

developed in
the Department of Mathematics
at Universidad Técnica Federico Santa María, Chile by
Felipe Osorio and Ronny
Vallejos, with contributions of Francisco
Cuevas, Diego Mancilla and Jonathan Acosta.
**SpatialPack**

It 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., Hémon, D., 1989. Assessing the significance of the correlation between two spatial processes. Biometrics 45, 123-134.

- The Codispersion Coefficient.
- Matheron, G., 1965. Les Variables Régionalisées et leur Estimation, Masson, Paris.
- Rukhin, A., Vallejos, R., 2008. Codispersion coefficient 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:

- 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

- 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 isopropic processes.
- Functions for image processing and computing the spatial association between images are also provided.

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

Latest binaries and sources for SpatialPack are availables from CRAN package repository .

- SpatialPack_0.4.tar.gz - Package sources
- not available - Windows binaries (R-release)
- not available - MacOS binaries (R-release, arm64)
- not available - MacOS binaries (R-release, x86_64)
- SpatialPack.pdf - Reference Manual

Source code is also available at GitHub: github.com/faosorios/SpatialPack

To install this package, start R and enter:

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)

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

The package is provided under the GPL. SpatialPack is under active development: new features are being added and old features are being improved.

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

Osorio, F., Vallejos, R., Cuevas, F. (2016). SpatialPack: Computing the association between two spatial processes. arXiv:1611.05289

- 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. Files: R Functions | Datasets
- 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.

- Bernadou, A., Espadaler, X., Le Goff, A., Fourcassié, V. (2015). Ant community organization along elevational gradients in a temperate ecosystem. Insectes Sociaux 62, 59-71.
- Koorem, K., Gazol, A., Öpik, M., Moora, M., Saks, Ü., Uibopuu, A., Sõber, V., Zobel, M. (2014). Soil nutrient content influences the abundance of soil microbes but not plant biomass at the small-scale. PLoS ONE 9(3): e91998.
- Zhang, J., Nielsen, S.E., Mao, L., Chen, S., Svenning, J.-C. (2015). Regional and historical factors supplement current climate in shaping global forest canopy height. Journal of Ecology 104, 469-478.

See more papers using/citing SpatialPack...

Felipe Osorio is Assistant Professor at Department of Mathematics of the Universidad Técnica Federico Santa María, Chile.

- Webpage: fosorios.mat.utfsm.cl
- Email: felipe.osorios AT usm.cl

Ronny Vallejos is Associate Professor at Department of Mathematics of the Universidad Técnica Federico Santa María, Chile.

- Webpage: rvallejos.mat.utfsm.cl
- Email: ronny.vallejos AT usm.cl

Felipe and Ronny contribute as developers/maintainers of the following R packages:

- fastmatrix - Fast computation of some matrices useful in statistics
- HEAVY - Robust estimation using heavy-tailed distributions.
- L1pack - Routines for L1 estimation.
- MVT - Estimation and testing for the multivariate t-distribution.