linearmodels.system.covariance.ClusteredCovariance

class ClusteredCovariance(x, eps, sigma, full_sigma, *, gls=False, debiased=False, constraints=None, clusters=None, group_debias=False)

Heteroskedastic covariance estimation for system regression

Parameters

xList[ndarray]

ndependent element list of regressor

epsndarray

Model residuals, ndependent by nobs

sigmandarray

Covariance matrix estimator of eps

glsbool

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

debiasedbool

Flag indicating to apply a small sample adjustment

constraints{None, LinearConstraint}

Constraints used in estimation, if any

clustersndarray

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

group_debiasbool

Flag indicating whether to debias by the number of groups.

See also

linearmodels.shared.covariance.cov_cluster

linearmodels.shared.covariance.group_debias_coefficient

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.

Attributes

cov

Parameter covariance

cov_config

Optional configuration information used in covariance

sigma

Error covariance

Methods

Properties

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