bayespecon.models.OLSPanelRE¶

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

Bayesian random effects panel regression (non-spatial).

\[y_{it} = X_{it}\beta + \alpha_i + \varepsilon_{it}\]

where \(\alpha_i \sim N(0, \sigma_\alpha^2)\) are unit-level random effects and \(\varepsilon_{it} \sim N(0, \sigma^2)\).

Parameters:¶

formula

Either formula mode (formula + data) or matrix mode (y + X).

data

Either formula mode (formula + data) or matrix mode (y + X).

y

Either formula mode (formula + data) or matrix mode (y + X).

X

Either formula mode (formula + data) or matrix mode (y + X).

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

Spatial weights of shape (N, N). Accepts a libpysal.graph.Graph (the modern libpysal graph API) or any scipy.sparse matrix. The legacy libpysal.weights.W object is not accepted directly; pass w.sparse or convert with

[ : _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_error_test”],

).bayesian_panel_lm_error_test(m), “Panel-LM-Error”), (lambda m: __import__(

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

).bayesian_panel_lm_sdm_joint_test(m), “Panel-LM-SDM-Joint”), (lambda m: __import__(

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

).bayesian_panel_lm_slx_error_joint_test(m), “Panel-LM-SLX-Error-Joint”),

]

libpysal.graph.Graph.from_W(w). Unused in the RE likelihood but required by the base class for consistency (e.g. computing spatial lags for SDM/SDEM variants). W should be row-standardised; a UserWarning is raised if not.

unit_col

Required in formula mode.

time_col

Required in formula mode.

N

Required in matrix mode.

T

Required in matrix mode.

priors : dict, optional

Override default priors. Supported keys:

beta_mu (default 0), beta_sigma (default 1e6), sigma_sigma (default 10), sigma_alpha_sigma (default 10).

Notes

Data are not demeaned — the random effects absorb the unit-level mean structure probabilistically. This is the Bayesian analogue of the classical GLS random-effects estimator in prandom.m.

Robust regression

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

\[\varepsilon_{it} \sim t_\nu(0, \sigma^2)\]

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 the posterior for the panel model.
`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, **sample_kwargs)[source]¶

Sample the posterior for the panel model.

Parameters:¶

draws : int, default=2000¶: Number of post-tuning draws per chain.
tune : int, default=1000¶: Number of tuning draws per chain.
chains : int, default=4¶: Number of chains.
target_accept : float, default=0.9¶: NUTS target acceptance probability.
random_seed : int, optional¶: Random seed used by PyMC.
**sample_kwargs¶: Extra keyword arguments forwarded to pymc.sample().

Returns:¶

Posterior samples and diagnostics.

Return type:¶

arviz.InferenceData

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.