Tools for Statistical Inference with Geo-Coded Data

Fast computation of Conley (1999) spatial heteroskedasticity and autocorrelation consistent (HAC) standard errors for linear regression models with geo-coded data, with a fast C++ implementation by Christensen, Hartman, and Samii (2021) . Performance-critical distance calculations, kernel weighting, and variance component accumulation are implemented in C++ via 'Rcpp' and 'RcppArmadillo'. Includes tools for estimating the spatial correlation range from covariograms and correlograms following the bandwidth selection method proposed in Lehner (2026) , and diagnostic visualizations for bandwidth selection.

SpatialInference

Fast computation of Conley (1999) spatial HAC standard errors for regression models with geo-coded data, using the C++ implementation by Darin Christensen (Christensen, Hartman, and Samii 2021). Includes a data-driven bandwidth selection method based on the covariogram range of regression residuals (Lehner 2026).

Features

Conley spatial HAC standard errors with six kernel functions (Bartlett, Epanechnikov, Gaussian, Parzen, Biweight, Uniform) and Haversine great-circle distances
Covariogram-based bandwidth selection — estimates the spatial correlation range from the empirical covariogram, providing a principled cutoff distance as proposed by Lehner (2026)
Inverse-U diagnostic plot — visualises how the Conley SE varies with the bandwidth, revealing the inverse-U relationship documented in Lehner (2026)
Performance — distance matrix computation, kernel weighting, and variance component accumulation are implemented in C++ via Rcpp/RcppArmadillo

Installation

Install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("axlehner/SpatialInference")

macOS note

A Fortran compiler is required for LAPACK/BLAS. If you encounter gfortran issues, see this thread.

Quick start

library(SpatialInference)
library(lfe)
data("US_counties_centroids")

# 1. Estimate the correlation range from the covariogram
covgm_range(US_counties_centroids)

# 2. Compute Conley standard errors at the estimated bandwidth
reg <- felm(noise1 ~ noise2 | unit + year | 0 | lat + lon,
            data = US_counties_centroids, keepCX = TRUE)

vcvs <- conley_SE(reg, unit = "unit", time = "year",
                  lat = "lat", lon = "lon",
                  kernel = "epanechnikov", dist_cutoff = 831)

# Spatial standard errors:
sqrt(diag(vcvs$Spatial))

# Convenience wrapper (returns a single SE):
compute_conley_lfe(reg, cutoff = 831, kernel_choice = "epanechnikov")

# 3. Visualise the inverse-U relationship
inverseu_plot_conleyrange(US_counties_centroids,
                          cutoffrange = seq(1, 2501, by = 200))

Key functions

Function	Description
`conley_SE()`	Conley spatial HAC variance-covariance matrices (spatial, serial, and combined)
`compute_conley_lfe()`	Convenience wrapper returning a single Conley SE
`covgm_range()`	Estimate and plot the correlation range from a covariogram
`extract_corr_range()`	Extract the zero-crossing range from a covariogram or correlogram
`inverseu_plot_conleyrange()`	Diagnostic plot of SE vs. bandwidth (inverse-U)
`lm_sac()`	All-in-one: regression + Moran's I + Conley SEs
`DistMat()`	Kernel-weighted spatial distance matrix (C++)

References

Lehner, A. (2026). Bandwidth selection for spatial HAC standard errors. arXiv preprint arXiv:2603.03997. doi:10.48550/arXiv.2603.03997

Conley, T. G. (1999). GMM estimation with cross sectional dependence. Journal of Econometrics, 92(1), 1--45. doi:10.1016/S0304-4076(98)00084-0

Christensen, D., Hartman, A. C. and Samii, C. (2021). Legibility and external investment: An institutional natural experiment in Liberia. International Organization, 75(4), 1087--1108. doi:10.1017/S0020818321000187