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: |
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Attributes
pinv_wexog : array
pinv_wexog
is the p x n Moore-Penrose 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 re-initialize) a Model instance. |
loglike (params) | Returns the value of the Gaussian log-likelihood 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 3-clause BSD License.
http://www.statsmodels.org/stable/generated/statsmodels.regression.linear_model.GLS.html