statsmodels.robust.robust_linear_model.RLMResults¶
- class statsmodels.robust.robust_linear_model.RLMResults(model, params, normalized_cov_params, scale)[source]¶
Class to contain RLM results
- Attributes:
- bcov_scaled
ndarray
p x p scaled covariance matrix specified in the model fit method. The default is H1. H1 is defined as
k**2 * (1/df_resid*sum(M.psi(sresid)**2)*scale**2)/ ((1/nobs*sum(M.psi_deriv(sresid)))**2) * (X.T X)^(-1)
where
k = 1 + (df_model +1)/nobs * var_psiprime/m**2
wherem = mean(M.psi_deriv(sresid))
andvar_psiprime = var(M.psi_deriv(sresid))
H2 is defined as
k * (1/df_resid) * sum(M.psi(sresid)**2) *scale**2/ ((1/nobs)*sum(M.psi_deriv(sresid)))*W_inv
H3 is defined as
1/k * (1/df_resid * sum(M.psi(sresid)**2)*scale**2 * (W_inv X.T X W_inv))
where k is defined as above and
W_inv = (M.psi_deriv(sresid) exog.T exog)^(-1)
See the technical documentation for cleaner formulae.
- bcov_unscaled
ndarray
The usual p x p covariance matrix with scale set equal to 1. It is then just equivalent to normalized_cov_params.
- bse
ndarray
An array of the standard errors of the parameters. The standard errors are taken from the robust covariance matrix specified in the argument to fit.
- chisq
ndarray
An array of the chi-squared values of the parameter estimates.
- df_model
See RLM.df_model
- df_resid
See RLM.df_resid
- fit_history
dict
Contains information about the iterations. Its keys are deviance, params, iteration and the convergence criteria specified in RLM.fit, if different from deviance or params.
- fit_options
dict
Contains the options given to fit.
- fittedvalues
ndarray
The linear predicted values. dot(exog, params)
- model
statsmodels.rlm.RLM
A reference to the model instance
- nobs
float
The number of observations n
normalized_cov_params
ndarray
See specific model class docstring
- params
ndarray
The coefficients of the fitted model
- pinv_wexog
ndarray
See RLM.pinv_wexog
- pvalues
ndarray
The p values associated with tvalues. Note that tvalues are assumed to be distributed standard normal rather than Student’s t.
- resid
ndarray
The residuals of the fitted model. endog - fittedvalues
- scale
float
The type of scale is determined in the arguments to the fit method in RLM. The reported scale is taken from the residuals of the weighted least squares in the last IRLS iteration if update_scale is True. If update_scale is False, then it is the scale given by the first OLS fit before the IRLS iterations.
- sresid
ndarray
The scaled residuals.
- tvalues
ndarray
The “t-statistics” of params. These are defined as params/bse where bse are taken from the robust covariance matrix specified in the argument to fit.
- weights
ndarray
The reported weights are determined by passing the scaled residuals from the last weighted least squares fit in the IRLS algorithm.
- bcov_scaled
Methods
conf_int
([alpha, cols])Construct confidence interval for the fitted parameters.
cov_params
([r_matrix, column, scale, cov_p, ...])Compute the variance/covariance matrix.
f_test
(r_matrix[, cov_p, invcov])Compute the F-test for a joint linear hypothesis.
initialize
(model, params, **kwargs)Initialize (possibly re-initialize) a Results instance.
load
(fname)Load a pickled results instance
See specific model class docstring
predict
([exog, transform])Call self.model.predict with self.params as the first argument.
Remove data arrays, all nobs arrays from result and model.
save
(fname[, remove_data])Save a pickle of this instance.
summary
([yname, xname, title, alpha, return_fmt])This is for testing the new summary setup
summary2
([xname, yname, title, alpha, ...])Experimental summary function for regression results
t_test
(r_matrix[, cov_p, use_t])Compute a t-test for a each linear hypothesis of the form Rb = q.
t_test_pairwise
(term_name[, method, alpha, ...])Perform pairwise t_test with multiple testing corrected p-values.
wald_test
(r_matrix[, cov_p, invcov, use_f, ...])Compute a Wald-test for a joint linear hypothesis.
wald_test_terms
([skip_single, ...])Compute a sequence of Wald tests for terms over multiple columns.
Properties
Log-likelihood of model
Return the t-statistic for a given parameter estimate.
Flag indicating to use the Student's distribution in inference.