linearmodels.system.covariance.ClusteredCovariance¶

class linearmodels.system.covariance.ClusteredCovariance(x: list[numpy.ndarray], eps: linearmodels.typing.data.Float64Array, sigma: linearmodels.typing.data.Float64Array, full_sigma: linearmodels.typing.data.Float64Array, *, gls: bool = False, debiased: bool = False, constraints: LinearConstraint | None = None, clusters: linearmodels.typing.data.IntArray | None = None, group_debias: bool = False)[source]¶

Heteroskedastic covariance estimation for system regression

Parameters:¶

x: list[numpy.ndarray]¶: ndependent element list of regressor
eps: linearmodels.typing.data.Float64Array¶: Model residuals, ndependent by nobs
sigma: linearmodels.typing.data.Float64Array¶: Covariance matrix estimator of eps
gls: bool = False¶: Flag indicating to compute the GLS covariance estimator. If False, assume OLS was used
debiased: bool = False¶: Flag indicating to apply a small sample adjustment
constraints: LinearConstraint | None = None¶: Constraints used in estimation, if any
clusters: linearmodels.typing.data.IntArray | None = None¶: Optional array of cluster id. Must be integer valued, and have shape (nobs, ncluster) where ncluster is 1 or 2.
group_debias: bool = False¶: Flag indicating whether to debias by the number of groups.

Notes

If GLS is used, the covariance is estimated by

\[(X'\Omega^{-1}X)^{-1}\tilde{S}_{\mathcal{G}}(X'\Omega^{-1}X)^{-1}\]

where X is a block diagonal matrix of exogenous variables and where \(\tilde{S}_{\mathcal{G}}\) is a clustered estimator of the model scores based on the model residuals and the weighted X matrix \(\Omega^{-1/2}X\).

When GLS is not used, the covariance is estimated by

\[(X'X)^{-1}\hat{S}_{\mathcal{G}}(X'X)^{-1}\]

where \(\hat{S}\) is a clustered estimator of the covariance of the model scores.

`cov`	Parameter covariance
`cov_config`	Optional configuration information used in covariance
`sigma`	Error covariance