# Introduction to the spEDM package

#### Wenbo Lv

####
Last update: 2025-08-31
Last run: 2025-08-31

## Overview

The spEDM package is an open-source, computationally efficient toolkit designed to provide a unified API for Spatial Empirical Dynamic Modeling. It supports a suite of prediction-based causal discovery algorithms, including spatial (granger) causality test, geographically convergent cross mapping, and geographical cross mapping cardinality.

To support both learning and practical application, spEDM offers four carefully curated spatial cross-sectional datasets, each paired with a detailed example showcasing the use of key algorithms in the package.

## Installation

Install the stable version from CRAN with:

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

Alternatively, you can install the development version from R-universe with:

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

## Data

The spEDM package includes four illustrative datasets with well-known causation to demonstrate key functionalities:

1. Columbus, OH dataset — A classic spatial dataset widely used in spatial econometrics, included here for benchmarking and demonstration purposes. Data files: `columbus.gpkg`

2. Population density and its potential drivers in mainland China — A county-level dataset capturing population density alongside relevant socio-environmental drivers. Data files: `popd.csv`, `popd_nb.gal`

3. Soil copper (Cu) contamination — A raster-based dataset representing soil Cu concentrations, with associated layers on nighttime light intensity and industrial density, useful for exploring the influence of human activities on environmental pollution. Data files: `cu.tif`

4. Farmland NPP and related variables — A raster dataset capturing net primary productivity (NPP) of farmland, key climatic variables, elevation, and human activity footprints across mainland China, suitable for analyzing the interactions between agricultural productivity, environmental conditions, and human activities. Data files: `npp.tif`

These datasets can be loaded as shown below:

### Columbus OH spatial analysis dataset

    library(spEDM)

    columbus = sf::read_sf(system.file("case/columbus.gpkg", package="spEDM"))
    columbus
    ## Simple feature collection with 49 features and 6 fields
    ## Geometry type: POLYGON
    ## Dimension:     XY
    ## Bounding box:  xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245
    ## Projected CRS: Undefined Cartesian SRS with unknown unit
    ## # A tibble: 49 × 7
    ##    hoval   inc  crime  open plumb discbd                                     geom
    ##    <dbl> <dbl>  <dbl> <dbl> <dbl>  <dbl>                                <POLYGON>
    ##  1  80.5 19.5  15.7   2.85  0.217   5.03 ((8.624129 14.23698, 8.5597 14.74245, 8…
    ##  2  44.6 21.2  18.8   5.30  0.321   4.27 ((8.25279 14.23694, 8.282758 14.22994, …
    ##  3  26.4 16.0  30.6   4.53  0.374   3.89 ((8.653305 14.00809, 8.81814 14.00205, …
    ##  4  33.2  4.48 32.4   0.394 1.19    3.7  ((8.459499 13.82035, 8.473408 13.83227,…
    ##  5  23.2 11.3  50.7   0.406 0.625   2.83 ((8.685274 13.63952, 8.677577 13.72221,…
    ##  6  28.8 16.0  26.1   0.563 0.254   3.78 ((9.401384 13.5504, 9.434411 13.69427, …
    ##  7  75    8.44  0.178 0     2.40    2.74 ((8.037741 13.60752, 8.062716 13.60452,…
    ##  8  37.1 11.3  38.4   3.48  2.74    2.89 ((8.247527 13.58651, 8.2795 13.5965, 8.…
    ##  9  52.6 17.6  30.5   0.527 0.891   3.17 ((9.333297 13.27242, 9.671007 13.27361,…
    ## 10  96.4 13.6  34.0   1.55  0.558   4.33 ((10.08251 13.03377, 10.0925 13.05275, …
    ## # ℹ 39 more rows

### County-level population density in mainland China

    library(spEDM)

    popd_nb = spdep::read.gal(system.file("case/popd_nb.gal",package = "spEDM"))
    ## Warning in spdep::read.gal(system.file("case/popd_nb.gal", package = "spEDM")):
    ## neighbour object has 4 sub-graphs
    popd_nb
    ## Neighbour list object:
    ## Number of regions: 2806
    ## Number of nonzero links: 15942
    ## Percentage nonzero weights: 0.2024732
    ## Average number of links: 5.681397
    ## 4 disjoint connected subgraphs

    popd = readr::read_csv(system.file("case/popd.csv",package = "spEDM"))
    ## Rows: 2806 Columns: 7
    ## ── Column specification ─────────────────────────────────────────────────────────
    ## Delimiter: ","
    ## dbl (7): lon, lat, popd, elev, tem, pre, slope
    ##
    ## ℹ Use `spec()` to retrieve the full column specification for this data.
    ## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
    popd
    ## # A tibble: 2,806 × 7
    ##      lon   lat  popd  elev   tem   pre slope
    ##    <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
    ##  1  117.  30.5  780.     8  17.4 1528. 0.452
    ##  2  117.  30.6  395.    48  17.2 1487. 0.842
    ##  3  117.  30.8  261.    49  16.0 1456. 3.56
    ##  4  116.  30.1  258.    23  17.4 1555. 0.932
    ##  5  116.  30.5  211.   101  16.3 1494. 3.34
    ##  6  117.  31.0  386.    10  16.6 1382. 1.65
    ##  7  117.  30.2  350.    23  17.5 1569. 0.346
    ##  8  117.  30.7  470.    22  17.1 1493. 1.88
    ##  9  117.  30.6 1226.    11  17.4 1526. 0.208
    ## 10  116.  30.9  137.   598  13.9 1458. 5.92
    ## # ℹ 2,796 more rows

    popd_sf = sf::st_as_sf(popd, coords = c("lon","lat"), crs = 4326)
    popd_sf
    ## Simple feature collection with 2806 features and 5 fields
    ## Geometry type: POINT
    ## Dimension:     XY
    ## Bounding box:  xmin: 74.9055 ymin: 18.2698 xmax: 134.269 ymax: 52.9346
    ## Geodetic CRS:  WGS 84
    ## # A tibble: 2,806 × 6
    ##     popd  elev   tem   pre slope          geometry
    ##  * <dbl> <dbl> <dbl> <dbl> <dbl>       <POINT [°]>
    ##  1  780.     8  17.4 1528. 0.452 (116.912 30.4879)
    ##  2  395.    48  17.2 1487. 0.842 (116.755 30.5877)
    ##  3  261.    49  16.0 1456. 3.56  (116.541 30.7548)
    ##  4  258.    23  17.4 1555. 0.932  (116.241 30.104)
    ##  5  211.   101  16.3 1494. 3.34   (116.173 30.495)
    ##  6  386.    10  16.6 1382. 1.65  (116.935 30.9839)
    ##  7  350.    23  17.5 1569. 0.346 (116.677 30.2412)
    ##  8  470.    22  17.1 1493. 1.88  (117.066 30.6514)
    ##  9 1226.    11  17.4 1526. 0.208 (117.171 30.5558)
    ## 10  137.   598  13.9 1458. 5.92  (116.208 30.8983)
    ## # ℹ 2,796 more rows

### Soil Cu heavy metal contamination

    library(spEDM)

    cu = terra::rast(system.file("case/cu.tif", package="spEDM"))
    cu
    ## class       : SpatRaster
    ## size        : 131, 125, 3  (nrow, ncol, nlyr)
    ## resolution  : 5000, 5000  (x, y)
    ## extent      : 360000, 985000, 1555000, 2210000  (xmin, xmax, ymin, ymax)
    ## coord. ref. : North_American_1983_Albers
    ## source      : cu.tif
    ## names       :         cu, industry, ntl
    ## min values  :   1.201607,    0.000,   0
    ## max values  : 319.599274,    0.615,  63

### Farmland NPP and related variables in mainland China

    library(spEDM)
    npp = terra::rast(system.file("case/npp.tif", package = "spEDM"))
    npp
    ## class       : SpatRaster
    ## size        : 404, 483, 5  (nrow, ncol, nlyr)
    ## resolution  : 10000, 10000  (x, y)
    ## extent      : -2625763, 2204237, 1877078, 5917078  (xmin, xmax, ymin, ymax)
    ## coord. ref. : CGCS2000_Albers
    ## source      : npp.tif
    ## names       :      npp,        pre,      tem,      elev,         hfp
    ## min values  :   164.00,   384.3409, -47.8194, -122.2004,  0.03390418
    ## max values  : 16606.33, 23878.3555, 263.6938, 5350.4902, 44.90312195

## Usage

Users can refer to several additional vignettes for more detailed examples of using spEDM, namely:

Method | Vignette
--- | ---
State Space Reconstruction | SSR
Spatial Logistic Map | SLM
Geographical Convergent Cross Mapping | GCCM
Geographical Cross Mapping Cardinality | GCMC
Spatial Causality Test | SCT

In addition to the spatial extensions provided by spEDM, several other R packages support Empirical Dynamic Modeling (EDM) for time series data:

- tEDM: An R package developed by the author of `spEDM`, designed to implement the Temporal Empirical Dynamic Modeling framework. It aims for maximal consistency with `spEDM` in terms of API design and modeling workflow, facilitating seamless transition between spatial and temporal EDM applications.
- rEDM: A foundational EDM package implementing simplex projection, S-map, and convergent cross mapping (CCM), widely used for analyzing nonlinear time series dynamics.
- multispatialCCM: Implements CCM for collections of short time series using bootstrapping, enabling causal inference across replicated or multi-site time series.
- fastEDM: A high-performance EDM package with a multi-threaded C++ backend. It supports large-scale time series analysis, handles panel data, and provides robust options for dealing with missing values using delay-tolerant algorithms or data exclusion.

## References

Takens, F. (1981). Detecting strange attractors in turbulence. Dynamical Systems and Turbulence, Warwick 1980, 366–381. https://doi.org/10.1007/bfb0091924

Mañé, R. (1981). On the dimension of the compact invariant sets of certain non-linear maps. Dynamical Systems and Turbulence, Warwick 1980, 230–242. https://doi.org/10.1007/bfb0091916

Willeboordse, F.H., 2003. The spatial logistic map as a simple prototype for spatiotemporal chaos. Chaos: An Interdisciplinary Journal of Nonlinear Science 13, 533–540. https://doi.org/10.1063/1.1568692

Herrera, M., Mur, J., & Ruiz, M. (2016). Detecting causal relationships between spatial processes. Papers in Regional Science, 95(3), 577–595. https://doi.org/10.1111/pirs.12144

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(1). https://doi.org/10.1038/s41467-023-41619-6