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
Parameter covariance
Optional configuration information used in covariance
Error covariance