neighbayes.diagnostics.lmtests.bayesian_glm_lm_wx_test¶
- neighbayes.diagnostics.lmtests.bayesian_glm_lm_wx_test(model)[source]¶
Bayesian LM test for omitted WX coefficients in a GLM (H₀: γ = 0).
PG-augmented analog of
bayesian_lm_wx_test(). Tests whether spatially lagged covariates \(WX\) should be added to the GLM mean. The score in the weighted pseudo-regression is\[\mathbf{g}_\gamma^{(d)} = (WX)^\top \Omega^{(d)} \tilde e^{(d)},\]with variance under H₀
\[V_{\gamma\gamma} = (WX)^\top \bar\Omega\, M_X^{\bar\Omega}\, (WX) = (WX)^\top \bar\Omega (WX) - (WX)^\top \bar\Omega X (X^\top \bar\Omega X)^{-1} X^\top \bar\Omega (WX).\]Reduces to the spreg
lm_wxformula when \(\bar\Omega = \sigma^{-2} I\).