bayespecon.models.SEMPanelTobit¶

class bayespecon.models.SEMPanelTobit(*args, censoring=0.0, **kwargs)[source]¶

Bayesian spatial error panel Tobit model.

\[y^* = X\beta + u,\quad u = \lambda W u + \varepsilon, \quad \varepsilon \sim N(0,\sigma^2 I)\]

with observed outcome y = max(c, y*).

Robust regression

When robust=True, the error distribution is changed from Normal to Student-t. For uncensored observations the density becomes:

\[f(y^*_i \mid \mu_i, \sigma, \nu) = \frac{1}{\sigma} \, t_\nu\!\left(\frac{y^*_i - \mu_i}{\sigma}\right)\]

and for censored observations:

\[P(y^*_i \le c) = T_\nu\!\left(\frac{c - \mu_i}{\sigma}\right)\]

where \(T_\nu\) is the Student-t CDF and \(\nu \sim \mathrm{TruncExp}(\lambda_\nu, \mathrm{lower}=2)\) with rate nu_lam (default 1/30).

__init__(*args, censoring=0.0, **kwargs)[source]¶

Methods

`__init__`(*args[, censoring])
`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 Tobit model uses pm.Potential for both the error log-likelihood and the Jacobian, so nothing is auto-captured. We compute the complete pointwise log-likelihood manually after sampling, using the Tobit censoring formula:

Uncensored: log N(y | mu, sigma^2)
Censored: log Phi((c - mu) / sigma)

where mu = X@beta and the spatial filtering is absorbed into the Jacobian.

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.