Formula Interface

Every estimator that takes matrices also takes a @formula, re-exported from StatsModels.jl, plus three spatial terms this package adds. The formula methods take a table — any Tables.jl-compatible source, such as a DataFrame — and build the design matrices, the spatial lags and the fixed-effects projection from the column names, so the stacking order does not have to be managed by hand.

The spatial terms

Term	Meaning
`slag(x1 + x2)`	Spatially lagged regressors `W*x`, giving a Durbin specification
`fe(region)`	Absorb fixed effects for a grouping column
`endo(x, z1 + z2)`	Mark `x` endogenous and name its instruments

fe appearing twice, as fe(region) + fe(year), is how a two-way specification is written; the panel and time keywords then name which columns carry the panel and period identifiers.

Examples

# SDM panel with two-way FE
m = fit_spatial_panel(
    @formula(y ~ x1 + x2 + slag(x1 + x2) + fe(region) + fe(year)),
    table, W; panel = :region, time = :year)

# GS2SLS with an endogenous regressor and its instruments
m = fit_gs2sls_panel(
    @formula(y ~ x1 + endo(tax, z1 + z2) + fe(region) + fe(year)),
    table, W; panel = :region, time = :year)

# Cross-section SDM
m = fit_spatial(
    @formula(y ~ x1 + x2 + slag(x1 + x2)),
    table, W)

# SEM, cross-section
m = fit_spatial_error(@formula(y ~ x1 + x2 + fe(region)), table, W)

# SEM panel
m = fit_spatial_error(@formula(y ~ x1 + x2 + fe(region) + fe(year)),
    table, W; panel = :region, time = :year)

# Gravity
m = fit_gravity(PoissonGravity(),
    @formula(flows ~ log_dist + common_lang), table;
    origin = :exporter, dest = :importer)

Panel ordering

The matrix interfaces expect a panel stacked unit-within-period, that is [unit₁t₁, unit₂t₁, …, unitₙt₁, unit₁t₂, …]. Data rarely arrives that way, and a silently mis-stacked panel produces plausible-looking nonsense rather than an error, so the reordering is available directly:

perm, N, T_per = extract_panel_permutation(table, :region, :year)

It returns the permutation together with the panel dimensions it inferred, and throws an ArgumentError on an unbalanced panel rather than guessing. The formula methods apply this themselves.