linearmodels.system.covariance.ClusteredCovariance¶

class linearmodels.system.covariance.ClusteredCovariance(x, eps, sigma, full_sigma, *, gls=False, debiased=False, constraints=None, clusters=None, group_debias=False)[source]¶

Heteroskedastic covariance estimation for system regression

Parameters:¶

x : list[ndarray]¶

ndependent element list of regressor

eps : ndarray¶

Model residuals, ndependent by nobs

sigma : ndarray¶

Covariance matrix estimator of eps

gls : bool¶

Flag indicating to compute the GLS covariance estimator. If False, assume OLS was used

debiased : bool¶

Flag indicating to apply a small sample adjustment

constraints : {None, LinearConstraint}¶

Constraints used in estimation, if any

clusters : ndarray¶

Optional array of cluster id. Must be integer valued, and have shape (nobs, ncluster) where ncluster is 1 or 2.

group_debias : bool¶

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.

See also

linearmodels.shared.covariance.cov_cluster, linearmodels.shared.covariance.group_debias_coefficient

Methods

Properties

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