Package Extensions

Two optional feature sets ship as Julia package extensions. They are not installed with SpatialEconometrics; each one activates automatically once its trigger packages are in the session.

How the entry points work

All eight function names are declared and exported by SpatialEconometrics itself; the extensions only add methods to them. This matters in practice: nothing ever writes using SpatialEconometricsMakieExt, so a function an extension declared on its own would be unreachable no matter how it was exported. You therefore never need to import anything but the parent:

using SpatialEconometrics
using CairoMakie            # the Makie methods appear here
plot_coefficients(m)

Calling one of them before its trigger packages are loaded raises an error that names the package to load, rather than a bare MethodError:

julia> using SpatialEconometrics

julia> plot_coefficients(m)
ERROR: plot_coefficients requires Makie: run `using Makie` to load the
SpatialEconometricsMakieExt extension, then call it again.

To check whether an extension is active:

Base.get_extension(SpatialEconometrics, :SpatialEconometricsMakieExt) !== nothing

Visualization (Makie)

Install a backend rather than Makie itself — CairoMakie for files, GLMakie for an interactive window:

using Pkg; Pkg.add("CairoMakie")

Every function returns a Makie.Figure, so the results compose with the rest of Makie (save, further axes, custom layouts).

using SpatialEconometrics, CairoMakie

m = fit_spatial(SAR(), W, X, y; varnames = ["income", "density"])

save("coefs.png", plot_coefficients(m))              # 95% CI by default
save("coefs99.png", plot_coefficients(m; level = 0.99))
save("moran.png",  plot_moran_scatter(y, W))
save("lisa.png",   plot_local_moran(moran_local(y, W), coords))
save("gwr.png",    plot_gwr_coefficients(m_gwr, "income"))
save("effects.png", plot_spatial_effects(spatial_effects(m)))

plot_coefficients(m; level = 0.95)

Horizontal coefficient plot with confidence intervals, for any StatsAPI.RegressionModel. The critical value is the normal quantile for level, so changing level genuinely changes the interval drawn. A level outside (0, 1) raises an ArgumentError.

plot_moran_scatter(y, W)

Standardized y against its spatial lag Wy, with the fitted slope drawn through it. When W is row-standardized that slope is Moran's I, so it should match moran_global(y, W).I_stat.

plot_local_moran(lisa, coords)

LISA cluster map, colouring HH, LL, HL, LH and non-significant units. coords must be an N × 2 matrix describing the same units as lisa; a mismatch raises a DimensionMismatch rather than plotting the shorter of the two.

plot_gwr_coefficients(m, varname)

Maps one GWR local coefficient over the estimation coordinates. varname must be one of m.coefnames; an unknown name raises an error listing the names available.

plot_spatial_effects(effects)

Grouped bar chart of the direct, indirect and total effects from spatial_effects.

See examples/18_visualization.jl for a runnable walk-through, and notebooks/interactive_extensions_explorer.jl for a Pluto version.

Bayesian estimation (Turing)

using Pkg; Pkg.add(["Turing", "Distributions"])

Three models are sampled by NUTS:

using SpatialEconometrics, Turing, Distributions

r = bayesian_sar(W, X, y; n_samples = 1000, n_chains = 2,
                 varnames = ["income", "density"], rng = MersenneTwister(11))
r = bayesian_sem(W, X, y)    # dependence in the errors
r = bayesian_sdm(W, X, y)    # design augmented with WX

An intercept is added for you, so X holds the covariates only.

Priors

β ~ MvNormal(0, 10I)
ρ, λ ~ Uniform(-0.99, 0.99)
σ ~ truncated(Normal(0, 5), 0, Inf)

These are deliberately diffuse, which is why the posterior mean lands on the maximum-likelihood estimate for the same data — the most useful check to run on a fit. They are not offered as a considered prior for any particular application, and they are not currently configurable.

The result

BayesianSpatialResult, a subtype of AbstractBayesianSpatialResult — which the parent package declares, so your own code can dispatch on it without depending on Turing.

coefnames runs intercept, slopes, then the spatial parameter and σ. For bayesian_sdm the WX terms appear between the slopes and ρ, prefixed W_:

["(Intercept)", "income", "density", "W_income", "W_density", "ρ", "σ"]

AbstractBayesianSpatialResult

Why it is affordable

Each likelihood evaluation needs log|I - ρW|, and NUTS asks for thousands of them at a new ρ every time. A dense factorization per draw would be prohibitive, so the extension uses the Chebyshev approximation (SpatialEconometrics.CrossSection.chebyshev_logdet), which precomputes traces once and then costs a polynomial evaluation per draw. At order 12 it agrees with the exact log-determinant to several decimal places across the whole parameter space, so this is the likelihood rather than a stand-in for it.

See examples/19_bayesian.jl for a runnable walk-through that checks the posterior against the MLE.

Tested versions

The compatibility bounds in Project.toml are wide, but the extension testsets are run against both ends of each range:

Testsets 25 and 26 of the suite cover the extensions. They skip themselves when the trigger packages are absent, so a plain Pkg.test() does not have to build Makie and Turing; the extensions CI job installs them and runs the suite again with both live.