bayespecon.models.SEMTobit¶

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

Bayesian spatial error 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*). Censored observations contribute their CDF; uncensored observations contribute the spatially-filtered density of \(y^*\).

Parameters:¶

formula : str, optional

Wilkinson-style formula. Requires data.

data : pandas.DataFrame or geopandas.GeoDataFrame, optional

Data source for formula mode.

y : array-like, optional

Observed (censored) response. Required in matrix mode.

X : array-like or pandas.DataFrame, optional

Design matrix. Required in matrix mode.

W : libpysal.graph.Graph or scipy.sparse matrix

Spatial weights of shape (n, n); see SAR for accepted formats.

censoring : float, default 0.0¶

Left-censoring threshold c.

priors : dict, optional

Override default priors. Supported keys:

lam_lower (float, default -1.0): Lower bound of Uniform prior on \(\lambda\).
lam_upper (float, default 1.0): Upper bound of Uniform prior on \(\lambda\).
beta_mu (float, default 0.0): Normal prior mean for \(\beta\).
beta_sigma (float, default 1e6): Normal prior std for \(\beta\).
sigma_sigma (float, default 10.0): HalfNormal prior std for \(\sigma\).
censor_sigma (float, default 10.0): HalfNormal scale for the latent y_cens_gap.
nu_lam (float, default 1/30): Rate of TruncExp(lower=2) prior on \(\nu\) (only used when robust=True).

logdet_method : str, optional

How to compute \(\log|I - \lambda W|\); auto-selected when None (default).

robust : bool, default False

If True, replace the Normal innovation with Student-t.

Notes

Robust regression

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

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

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 residuals on the observed (or transformed-panel) scale.
`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 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.

property inference_data : arviz.data.inference_data.InferenceData | None[source]¶: Return the ArviZ InferenceData from the most recent fit.

property pymc_model : pymc.model.core.Model | None[source]¶: Return the PyMC model object built for the most recent fit.

residuals()[source]¶: Return residuals on the observed (or transformed-panel) scale.

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.

Requires the model to have been fit (.fit() called). For cross-sectional models a spatial weights matrix W must also have been supplied at construction time.

Returns:¶

DataFrame indexed by test name with columns statistic (posterior mean), median, df (degrees of freedom for the \(\chi^2\) reference), p_value (Bayesian p-value 1 - chi2.cdf(mean, df)), and ci_lower / ci_upper (95% credible interval). The DataFrame carries attrs["model_type"] and attrs["n_draws"] metadata.

Return type:¶

pandas.DataFrame

Raises:¶

RuntimeError – If the model has not been fit yet.
ValueError – If a cross-sectional model was constructed without W.