bayespecon.diagnostics.bayesian_lmtests.bayesian_lm_lag_test¶
- bayespecon.diagnostics.bayesian_lmtests.bayesian_lm_lag_test(model)[source]¶
Bayesian LM test for omitted spatial lag (SAR) model.
Follows Doğan et al. [2021]. Implements the Bayesian LM test for omitted spatial lag (SAR) effects.
The test statistic for each posterior draw is:
\[S = \mathbf{e}^\top W \mathbf{y}\]where \(\mathbf{e}\) are residuals, \(W\) is the spatial weights matrix, and \(\mathbf{y}\) is the outcome vector.
The variance is:
\[V = T_{WW} \bar{\sigma}^2 + \|W\mathbf{y}\|^2\]where \(T_{WW} = \mathrm{tr}(W^\top W + W^2)\) and \(\bar{\sigma}^2\) is the posterior mean of \(\sigma^2\). This matches the Fisher information denominator of the classical LM-lag test ([]).
The LM statistic is:
\[\mathrm{LM} = \frac{S^2}{V}\]The Bayesian p-value is computed at the posterior mean of the LM statistic:
1 - chi2.cdf(mean, df)([Doğan et al., 2021]).- Parameters:¶
- model : SpatialModel¶
Fitted spatial model instance with
inference_dataattribute.
- Returns:¶
Dataclass containing LM samples, summary statistics, and metadata.
- Return type:¶