Spatial Empirical Dynamic Modeling

Inferring causation from spatial cross-sectional data through empirical dynamic modeling (EDM), with methodological extensions including geographical convergent cross mapping from Gao et al. (2023) , geographical cross mapping cardinality as introduced by Lyu et al. (2026) , as well as the spatial causality test following the approach of Herrera et al. (2016) , together with geographical pattern causality proposed in Zhang & Wang (2025) .

spEDM

Spatial Empirical Dynamic Modeling

spEDM is an R package for spatial causal discovery. It extends Empirical Dynamic Modeling (EDM) from time series to spatial cross-sectional data, provides seamless support for vector and raster spatial data via tight integration with the sf and terra packages, and enables data-driven causal inference from spatial snapshots.

Refer to the package documentation https://stscl.github.io/spEDM/ for more detailed information.

Installation

Install from CRAN with:

install.packages("spEDM", dependencies = TRUE)

Install binary version from R-universe with:

install.packages("spEDM",
                 repos = c("https://stscl.r-universe.dev",
                           "https://cloud.r-project.org"),
                 dependencies = TRUE)

Install from source code on GitHub with:

if (!requireNamespace("pak", quietly = TRUE)) {
    install.packages("pak")
}
pak::pak("stscl/spEDM", dependencies = TRUE)

CITATION

Please cite spEDM as:

Lyu, W., Dai, S., Song, Y., Zhao, W., Yi, W., Xiao, Y., Jia, N., 2026. Measuring causal strengths from spatial cross-sectional data with geographical cross mapping cardinality. International Journal of Geographical Information Science 1–23. https://doi.org/10.1080/13658816.2026.2687121

A BibTeX entry for LaTeX users is:

@article{lyu2026gcmc, 
    title = {Measuring causal strengths from spatial cross-sectional data with geographical cross mapping cardinality}, 
    ISSN = {1362-3087}, 
    DOI = {10.1080/13658816.2026.2687121}, 
    journal = {International Journal of Geographical Information Science}, 
    publisher = {Informa UK Limited}, 
    author = {Lyu, Wenbo and Dai, Shaoqing and Song, Yongze and Zhao, Wufan and Yi, Wen and Xiao, Yumiao and Jia, Nan}, 
    year = {2026}, 
    month = {June}, 
    pages = {1–23} 
}

Reference

Lyu, W., Dai, S., Song, Y., Zhao, W., Yi, W., Xiao, Y., Jia, N., 2026. Measuring causal strengths from spatial cross-sectional data with geographical cross mapping cardinality. International Journal of Geographical Information Science 1–23. https://doi.org/10.1080/13658816.2026.2687121.

Lyu, W., Lei, Y., Yi, W., Song, Y., Li, X., Dai, S., Qin, Y., Zhao, W., 2026. Causal discovery in urban data with temporal empirical dynamic modeling: The R package tEDM. Computers, Environment and Urban Systems 127, 102435. https://doi.org/10.1016/j.compenvurbsys.2026.102435.

Gao, B., Yang, J., Chen, Z., Sugihara, G., Li, M., Stein, A., Kwan, M.-P., Wang, J., 2023. Causal inference from cross-sectional earth system data with geographical convergent cross mapping. Nature Communications 14. https://doi.org/10.1038/s41467-023-41619-6.

Herrera, M., Mur, J., Ruiz, M., 2016. Detecting causal relationships between spatial processes. Papers in Regional Science 95, 577–595. https://doi.org/10.1111/pirs.12144.

Sugihara, G., May, R., Ye, H., Hsieh, C., Deyle, E., Fogarty, M., Munch, S., 2012. Detecting Causality in Complex Ecosystems. Science 338, 496–500. https://doi.org/10.1126/science.1227079.