bayespecon.diagnostics.bayesian_lmtests.bayesian_panel_lm_lag_test¶

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

Bayesian panel LM test for omitted spatial lag (H₀: ρ = 0).

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

The null model is a pooled/FE panel OLS. For each posterior draw, residuals are:

\[\mathbf{e} = \mathbf{y} - X \beta\]

(demeaned for FE models; with alpha subtracted for RE models).

The score for each draw is:

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

where \(W_{NT} = W \otimes I_T\) is the block-diagonal panel weights matrix.

The information matrix (Anselin et al. [2008]) is:

\[J = \frac{1}{\sigma^2} \left( (W\hat{y})^\top M (W\hat{y}) + T \cdot \mathrm{tr}(W'W + W^2) \right)\]

where \(M = I - X(X^\top X)^{-1} X^\top\) and \(\hat{y} = X\bar{\beta}\).

The LM statistic for each draw is:

\[\mathrm{LM} = \frac{S^2}{\sigma^2 \cdot J}\]

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