Spatial Regime Models

ChowRegimeTest

Test of coefficient equality across regimes, returned by regime_chow_test.

Fields: stat, df, p_value, and the two log-likelihoods ll_pooled and ll_regime. Failing to reject means the pooled model is adequate and the regime split is not buying anything.

ExogenousRegimes(labels)

Regime membership supplied directly, as an integer label per unit.

Use this when the grouping is known in advance — states, planning regions, pre- and post-reform periods. When it is not, skater_regimes derives spatially contiguous regimes from the data instead.

Examples

fit_spatial_regime(W, X, y, ExogenousRegimes(region_id))

SpatialRegimeModel

A spatial regime model, returned by fit_spatial_regime: coefficients are allowed to differ across groups of units rather than being held constant over the whole map.

A discrete alternative to GWR — where fit_gwr lets coefficients vary smoothly with location, this estimates one set per regime, which is easier to interpret and test when the groups are meaningful. Use regime_chow_test to ask whether the split is warranted.

fit_spatial_regime(W, X, y, regimes; spatial_lag=true, varnames=nothing, method=ChebyshevApprox())

Fit a spatial regime model where coefficients vary across regimes: y = ρWy + Xr βr + ε (spatiallag=true) y = Xr βr + ε (spatiallag=false)

Each regime gets its own intercept and slope coefficients. Anselin (1988, 1990).

regime_chow_test(pooled_model, regime_model)

Likelihood ratio test for structural stability across spatial regimes. H₀: coefficients are equal across all regimes.

skater_regimes(W, X, n_regimes; min_size=1, rng=Random.default_rng())

Spatially constrained clustering via SKATER minimum spanning tree partitioning. Returns an ExogenousRegimes assignment with n_regimes contiguous groups, each guaranteed to be a connected region of W.

A minimum spanning tree is built over the contiguity graph with edge weights given by Euclidean distance between the standardised rows of X. The tree is then split n_regimes - 1 times, each time choosing the edge whose removal most reduces the within-group sum of squared deviations.

min_size is the smallest admissible region; cuts that would leave a smaller component are skipped. Raise it when the regions feed a regime regression, which needs enough units per region to identify its own coefficients.

Assunção et al. (2006) "Efficient regionalization techniques for socio‐economic geographical units using minimum spanning trees."