Cross-Sectional Spatial Models

SAR (Spatial Autoregressive)

\[y = \rho W y + X \beta + \varepsilon\]

m = fit_spatial(SAR(), W, X, y)

SDM (Spatial Durbin Model)

\[y = \rho W y + X \beta + W X \theta + \varepsilon\]

m = fit_spatial(SDM(), W, X, y)

Estimation Methods

Both models support exact (LU decomposition) and approximate (Chebyshev) log-determinant computation:

# Exact (default, good for N < 5000)
m = fit_spatial(SAR(), W, X, y)

# Chebyshev approximation (for large N)
m = fit_spatial(SAR(), W, X, y;
    method=ChebyshevApprox(order=7))

Spatial Effects

For SDM, coefficients alone are not interpretable — use spatial_effects:

effects = spatial_effects(m)
# effects.direct   — average direct effect per variable
# effects.indirect — average indirect (spillover) effect
# effects.total    — direct + indirect