bayespecon.diagnostics.lmtests.bayesian_panel_robust_lm_error_test¶
- bayespecon.diagnostics.lmtests.bayesian_panel_robust_lm_error_test(model)[source]¶
Bayesian panel robust LM-Error test (H₀: λ = 0, robust to ρ).
Follows Elhorst [2014]. Tests the null hypothesis that the spatial error coefficient is zero, robust to the local presence of a spatial lag.
The null model is a pooled/FE panel OLS. For each posterior draw,
\[\mathrm{LM}_R = \frac{ \left( \frac{\mathbf{e}^\top W_{NT} \mathbf{e}}{\sigma^2} - \frac{T \cdot \mathrm{tr}}{J} \cdot \frac{\mathbf{e}^\top W_{NT} \mathbf{y}}{\sigma^2} \right)^2 }{ T \cdot \mathrm{tr} \cdot \left(1 - \frac{T \cdot \mathrm{tr}}{J}\right) }\]where \(J\) is the information matrix from the panel LM-lag test and \(\mathrm{tr} = \mathrm{tr}(W'W + W^2)\).
The score is evaluated at the M_X-projected residual \(\mathbf{e}_\perp = M_X \mathbf{y}\) (constant across draws), because \(\beta\) is information-orthogonal to \((\rho,\lambda)\) under \(H_0\) and therefore \(\beta\)-posterior variance does not enter the LM reference distribution. This matches the cross-sectional correction documented in
bayesian_robust_lm_error_test().This is distributed as \(\chi^2_1\) under H₀.
- Parameters:¶
- model : SpatialPanelModel¶
Fitted panel model (e.g.
OLSPanelFE) withinference_dataattribute containing posterior draws forbetaandsigma.
- Returns:¶
Dataclass containing LM samples, summary statistics, and metadata.
- Return type:¶