class statsmodels.regression.linear_model.GLS(endog, exog, sigma=None, missing='none', hasconst=None, **kwargs)
[source]
Generalized least squares model with a general covariance structure.
Parameters: 


Attributes
pinv_wexog : array
pinv_wexog
is the p x n MoorePenrose pseudoinverse of wexog
.cholsimgainv : array
df_model : float
df_resid : float
llf : float
nobs : float
normalized_cov_params : array
results : RegressionResults instance
sigma : array
sigma
is the n x n covariance structure of the error terms.wexog : array
cholsigmainv
wendog : array
cholsigmainv
If sigma is a function of the data making one of the regressors a constant, then the current postestimation statistics will not be correct.
>>> import numpy as np >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load() >>> data.exog = sm.add_constant(data.exog) >>> ols_resid = sm.OLS(data.endog, data.exog).fit().resid >>> res_fit = sm.OLS(ols_resid[1:], ols_resid[:1]).fit() >>> rho = res_fit.params
rho
is a consistent estimator of the correlation of the residuals from an OLS fit of the longley data. It is assumed that this is the true rho of the AR process data.
>>> from scipy.linalg import toeplitz >>> order = toeplitz(np.arange(16)) >>> sigma = rho**order
sigma
is an n x n matrix of the autocorrelation structure of the data.
>>> gls_model = sm.GLS(data.endog, data.exog, sigma=sigma) >>> gls_results = gls_model.fit() >>> print(gls_results.summary())
fit ([method, cov_type, cov_kwds, use_t])  Full fit of the model. 
fit_regularized ([method, alpha, L1_wt, …])  Return a regularized fit to a linear regression model. 
from_formula (formula, data[, subset, drop_cols])  Create a Model from a formula and dataframe. 
get_distribution (params, scale[, exog, …])  Returns a random number generator for the predictive distribution. 
hessian (params)  The Hessian matrix of the model 
hessian_factor (params[, scale, observed])  Weights for calculating Hessian 
information (params)  Fisher information matrix of model 
initialize ()  Initialize (possibly reinitialize) a Model instance. 
loglike (params)  Returns the value of the Gaussian loglikelihood function at params. 
predict (params[, exog])  Return linear predicted values from a design matrix. 
score (params)  Score vector of model. 
whiten (X)  GLS whiten method. 
df_model  The model degree of freedom, defined as the rank of the regressor matrix minus 1 if a constant is included. 
df_resid  The residual degree of freedom, defined as the number of observations minus the rank of the regressor matrix. 
endog_names  Names of endogenous variables 
exog_names  Names of exogenous variables 
© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3clause BSD License.
http://www.statsmodels.org/stable/generated/statsmodels.regression.linear_model.GLS.html