Spatial Correlogram Tutorial (R)

A short, self-contained tutorial for building spatial correlograms in R—computing Moran’s I and Geary’s C across distance bins using the built-in meuse dataset (no external files). This is a good follow-up or precursor to the variogram tutorial.

What you'll learn

• What correlograms show (vs. semivariograms)
• Building equal-width distance bins (rings)
• Moran’s I by distance (with permutation p-values)
• Optional: Geary’s C correlogram

Quick start

A) View-only (R script shown, but already run for you)

Open the rendered HTML tutorial:

• https://parker-group.github.io/spcorrelogram_tutorial1/
• correlogram_tutorial1.html (in this repo)

B) Hands-on (R installed on your computer - you run the script)

In R:

install.packages(c("spdep", "sp", "sf", "ggplot2", "rmarkdown"))  # first time
rmarkdown::render("correlogram_tutorial1.rmd", output_format = "html_document")

C) Hands-on in your browser (no install - you run R from your browser)

Click to launch an interactive RStudio session with Binder:

When RStudio opens in the browser:

1. In the Files pane, click correlogram_tutorial1.rmd
2. Click Knit to render, or use Run ▶ to step through

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Reproducing directly from the README in R

If you want to quickly reproduce the core correlogram example without opening the .Rmd, copy/paste this into your R console:

# Install required packages (skip if already installed)
install.packages(c("spdep", "sp"))

# Load libraries
library(sp)
library(spdep)

# Load the example data
data(meuse)
coords <- as.matrix(meuse[, c("x","y")])   # numeric matrix of coordinates
x <- meuse$zinc                             # variable to analyze

# Build equal-width distance bins (e.g., 0–3000 m into 12 bins)
max_distance <- 3000
n_bins <- 12
edges <- seq(0, max_distance, length.out = n_bins + 1)

# Compute Moran's I by ring with permutation p-values
set.seed(123)
res <- do.call(rbind, lapply(seq_len(n_bins), function(i) {
  dmin <- edges[i]; dmax <- edges[i+1]
  nb <- dnearneigh(coords, d1 = dmin, d2 = dmax, longlat = FALSE)
  lw <- nb2listw(nb, style = "B", zero.policy = TRUE)  # binary weights
  if (sum(unlist(lw$weights)) == 0) {
    data.frame(bin=i, dmin=dmin, dmax=dmax, mid=(dmin+dmax)/2, I=NA_real_, p=NA_real_)
  } else {
    mc <- moran.mc(x, lw, nsim = 499, zero.policy = TRUE, alternative = "two.sided")
    data.frame(bin=i, dmin=dmin, dmax=dmax, mid=(dmin+dmax)/2,
               I=as.numeric(mc$statistic), p=mc$p.value)
  }
}))

# Quick base R plot
plot(res$mid, res$I, type="b", xlab="Distance (bin mid, m)", ylab="Moran's I")
abline(h=0, lty=2)

This minimal example runs the core correlogram workflow without needing any extra files.

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Next Step

Continue to Spatial Dependence Part 2
▶️ View the live tutorial here

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Notes

• Binder setup files (runtime.txt and install.R) are included for reproducibility.
• First Binder launch may take 1–3 minutes while it builds the environment.