Generalized least squares model with a general covariance structure.
Parameters : | endog : array-like
exog : array-like
sigma : scalar or array
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Notes
If sigma is a function of the data making one of the regressors a constant, then the current postestimation statistics will not be correct.
Examples
>>> import numpy as np
>>> import scikits.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.results
Attributes
pinv_wexog | array | pinv_wexog is the p x n Moore-Penrose pseudoinverse of wexog. |
cholsimgainv | array | The transpose of the Cholesky decomposition of the pseudoinverse. |
df_model | float | p - 1, where p is the number of regressors including the intercept. of freedom. |
df_resid | float | Number of observations n less the number of parameters p. |
llf | float | The value of the likelihood function of the fitted model. |
nobs | float | The number of observations n. |
normalized_cov_params | array | p x p array (X^{T}\Sigma^{-1}X)^{-1} |
results | RegressionResults instance | A property that returns the RegressionResults class if fit. |
sigma | array | sigma is the n x n covariance structure of the error terms. |
wexog | array | Design matrix whitened by cholsigmainv |
wendog | array | Response variable whitened by cholsigmainv |
Methods
fit([method]) | Full fit of the model. |
hessian(params) | The Hessian matrix of the model |
information(params) | Fisher information matrix of model |
initialize() | |
loglike(params) | Returns the value of the gaussian loglikelihood function at params. |
predict(exog[, params]) | Return linear predicted values from a design matrix. |
score(params) | Score vector of model. |
whiten(X) | GLS whiten method. |