bayespecon.models.SEMPanelRE¶

class bayespecon.models.SEMPanelRE(**kwargs)[source]¶

Bayesian spatial error panel model with unit random effects.

\[y_{it} = X_{it}\beta + \alpha_i + u_{it}, \quad u_{it} = \lambda (Wu)_{it} + \varepsilon_{it}\]

Equivalently the spatially-filtered residual is i.i.d.:

\[\varepsilon_{it} = (I - \lambda W)(y - X\beta - \alpha)_{it} \sim N(0, \sigma^2)\]

Parameters:¶

formula

data

y

X

W

unit_col

time_col

N

T

priors

logdet_method

[ : _spatial_diagnostics_tests =

(lambda m: __import__(: “bayespecon.diagnostics.bayesian_lmtests”, fromlist=[“bayesian_panel_lm_lag_test”],

).bayesian_panel_lm_lag_test(m), “Panel-LM-Lag”), (lambda m: __import__(

”bayespecon.diagnostics.bayesian_lmtests”, fromlist=[“bayesian_panel_lm_wx_sem_test”],

).bayesian_panel_lm_wx_sem_test(m), “Panel-LM-WX”),

]

See SpatialPanelModel. model is forced to 0.

Notes

The priors dict supports the following keys:

lam_lower, lam_upper (float, default -1, 1): Bounds for the Uniform prior on lambda.
beta_mu (float, default 0): Prior mean for beta.
beta_sigma (float, default 1e6): Prior std for beta.
sigma_sigma (float, default 10): Scale for HalfNormal prior on sigma.
sigma_alpha_sigma (float, default 10): Scale for HalfNormal prior on sigma_alpha.

Robust regression

When robust=True, the spatially-filtered error distribution is changed from Normal to Student-t, yielding a model that is robust to heavy-tailed outliers:

\[\varepsilon_{it} = (I - \lambda W)(y - X\beta - \alpha_i) \sim t_\nu(0, \sigma^2)\]

where \(\nu \sim \mathrm{TruncExp}(\lambda_\nu, \mathrm{lower}=2)\) with rate nu_lam (default 1/30). The default nu_lam = 1/30 gives a prior mean of approximately 30, favouring near-Normal tails. The lower bound of 2 ensures the variance exists.

__init__(**kwargs)[source]¶

Methods

`__init__`(**kwargs)
`fit`([draws, tune, chains, target_accept, ...])	Sample posterior and attach pointwise log-likelihood for IC metrics.
`fitted_values`()	Return fitted values at posterior mean parameters.
`residuals`()	Return transformed residuals `y - fitted`.
`spatial_diagnostics`()	Run Bayesian LM specification tests and return a summary table.
`spatial_diagnostics_decision`([alpha])	Return a model-selection decision from Bayesian LM test results.
`spatial_effects`([return_posterior_samples])	Compute Bayesian inference for direct, indirect, and total impacts.
`summary`([var_names])	Return posterior summary table.

Attributes

`inference_data`	Return the ArviZ InferenceData from the most recent fit.
`pymc_model`	Return the PyMC model object built for the most recent fit.

fit(draws=2000, tune=1000, chains=4, target_accept=0.9, random_seed=None, idata_kwargs=None, **sample_kwargs)[source]¶

Sample posterior and attach pointwise log-likelihood for IC metrics.

The SEM panel RE model uses pm.Potential for both the Gaussian error log-likelihood and the Jacobian, so neither is auto-captured. We compute the complete pointwise log-likelihood manually after sampling, including the random effects alpha[unit_idx].

fitted_values()[source]¶

Return fitted values at posterior mean parameters.

Returns:¶: Fitted values on transformed panel scale.
Return type:¶: np.ndarray

property inference_data : arviz.data.inference_data.InferenceData | None[source]¶

Return the ArviZ InferenceData from the most recent fit.

Returns:¶: The inference data object, or None if the model has not been fit yet.
Return type:¶: arviz.InferenceData or None

property pymc_model : pymc.model.core.Model | None[source]¶

Return the PyMC model object built for the most recent fit.

Returns:¶: The model object used by fit(), or None if the instance has not been fit yet.
Return type:¶: pymc.Model or None

residuals()[source]¶

Return transformed residuals y - fitted.

Returns:¶: Residual vector on transformed panel scale.
Return type:¶: np.ndarray

spatial_diagnostics()[source]¶

Run Bayesian LM specification tests and return a summary table.

Iterates over the class-level _spatial_diagnostics_tests registry and calls each test function on this fitted model, collecting the results into a tidy DataFrame. The set of tests depends on the model type — for example, an OLSPanelFE model runs Panel-LM-Lag, Panel-LM-Error, Panel-LM-SDM-Joint, and Panel-LM-SLX-Error-Joint.

Requires the model to have been fit (.fit() called) and a spatial weights matrix W to have been supplied at construction time.

Returns:¶

DataFrame indexed by test name with columns:

Column	Description
statistic	Posterior mean of the LM statistic
median	Posterior median of the LM statistic
df	Degrees of freedom for the \(\chi^2\) reference
p_value	Bayesian p-value: `1 - chi2.cdf(mean, df)`
ci_lower	Lower bound of 95% credible interval (2.5%)
ci_upper	Upper bound of 95% credible interval (97.5%)

The DataFrame has attrs["model_type"] (class name) and attrs["n_draws"] (total posterior draws) metadata.

Return type:¶

pandas.DataFrame

Raises:¶

RuntimeError – If the model has not been fit yet.