Panel Diagnostics

Spatial Hausman Test

Compare two spatial panel specifications; a rejection favours the first.

ht = spatial_hausman_test(m_fe, m_pooled)
# ht.stat      — Hausman statistic
# ht.df        — number of coefficients compared
# ht.coefnames — which coefficients those were
# ht.p_value   — reject H₀ → the first specification is preferred

Coefficients are matched by name, using the names the two models share in the order they appear in the first model. ht.coefnames records what was compared, so the contrast is auditable.

This matters because the specifications need not carry the same terms. A NoFE fit has an intercept that an FE fit does not:

coefnames(m_fe)      # ["income", "density", "ρ"]
coefnames(m_pooled)  # ["(Intercept)", "income", "density", "ρ"]

The intercept is dropped, and income is compared with income. Matching positionally instead would contrast income with the intercept and build a large statistic out of unrelated parameters — a decisive-looking rejection that means nothing.

Pass names to restrict the comparison; an unknown name raises an error rather than silently shrinking it.

ht = spatial_hausman_test(m_fe, m_pooled; names = ["income", "density"])

Spatial Chow Test

Test for structural breaks across time periods:

ct = spatial_chow_test(y, X, W, N, T, break_period)
# ct.stat — F-statistic
# ct.p_value — reject H₀ → structural break exists

Joint LM Tests for Panels

Simultaneously test for spatial lag, spatial error, and random effects (Baltagi, Song & Koh 2003):

plm = panel_lm_tests(y, X_with_intercept, W, N, T)
# plm.joint_stat — joint test (χ², df=3)
# plm.lag_stat   — marginal spatial lag test
# plm.error_stat — marginal spatial error test
# plm.re_stat    — marginal random effects test

Panel Moran's I

Period-by-period and pooled Moran statistics on panel residuals:

pm = panel_moran(residuals(m), W, N, T)
# pm.period_results — vector of per-period MoranResult
# pm.pooled — meta-analytic pooled statistic