bayespecon.diagnostics.bayesian_lmtests.bayesian_panel_lm_error_test¶

bayespecon.diagnostics.bayesian_lmtests.bayesian_panel_lm_error_test(model)[source]¶

Bayesian panel LM test for omitted spatial error (H₀: λ = 0).

Follows Anselin et al. [2008] and the Bayesian framework of Doğan et al. [2021]. (2021). Tests whether a spatial error term should be added to a panel regression.

The null model is a pooled/FE panel OLS. For each posterior draw, residuals are computed (demeaned for FE, alpha-adjusted for RE).

The score for each draw is:

\[S = \mathbf{e}^\top W_{NT} \mathbf{e}\]

The variance is:

\[V = \sigma^4 \cdot T \cdot \mathrm{tr}(W'W + W^2)\]

The LM statistic for each draw is:

\[\mathrm{LM} = \frac{S^2}{V}\]

which is distributed as \(\chi^2_1\) under H₀.

Parameters:¶

model : SpatialPanelModel¶

Fitted panel model (e.g. OLSPanelFE, OLSPanelRE) with inference_data attribute containing posterior draws for beta and sigma.

Returns:¶

Dataclass containing LM samples, summary statistics, and metadata.

Return type:¶

BayesianLMTestResult