statsmodels.genmod.generalized_estimating_equations.GEEResults

class statsmodels.genmod.generalized_estimating_equations.GEEResults(model, params, cov_params, scale, cov_type='robust', use_t=False, regularized=False, **kwds)

This class summarizes the fit of a marginal regression model using GEE.

Attributes

cov_params_defaultndarray

default covariance of the parameter estimates. Is chosen among one of the following three based on cov_type

cov_robustndarray

covariance of the parameter estimates that is robust

cov_naivendarray

covariance of the parameter estimates that is not robust to correlation or variance misspecification

cov_robust_bcndarray

covariance of the parameter estimates that is robust and bias reduced

convergedbool

indicator for convergence of the optimization. True if the norm of the score is smaller than a threshold

cov_typestr

string indicating whether a “robust”, “naive” or “bias_reduced” covariance is used as default

fit_historydict

Contains information about the iterations.

fittedvaluesndarray

Linear predicted values for the fitted model. dot(exog, params)

modelclass instance

Pointer to GEE model instance that called fit.

normalized_cov_paramsndarray

See specific model class docstring

paramsndarray

The coefficients of the fitted model. Note that interpretation of the coefficients often depends on the distribution family and the data.

scalefloat

The estimate of the scale / dispersion for the model fit. See GEE.fit for more information.

score_normfloat

norm of the score at the end of the iterative estimation.

bsendarray

The standard errors of the fitted GEE parameters.

Methods

conf_int([alpha, cols, cov_type])	Returns confidence intervals for the fitted parameters.
cov_params([r_matrix, column, scale, cov_p, …])	Compute the variance/covariance matrix.
f_test(r_matrix[, cov_p, scale, invcov])	Compute the F-test for a joint linear hypothesis.
get_hat_matrix_diag([observed])	Compute the diagonal of the hat matrix
get_influence([observed])	Get an instance of GLMInfluence with influence and outlier measures
get_margeff([at, method, atexog, dummy, count])	Get marginal effects of the fitted model.
get_prediction([exog, exposure, offset, …])	compute prediction results
initialize(model, params, **kwargs)	Initialize (possibly re-initialize) a Results instance.
load(fname)	Load a pickled results instance
normalized_cov_params()	See specific model class docstring
params_sensitivity(dep_params_first, …)	Refits the GEE model using a sequence of values for the dependence parameters.
plot_added_variable(focus_exog[, …])	Create an added variable plot for a fitted regression model.
plot_ceres_residuals(focus_exog[, frac, …])	Conditional Expectation Partial Residuals (CERES) plot.
plot_isotropic_dependence([ax, xpoints, min_n])	Create a plot of the pairwise products of within-group residuals against the corresponding time differences.
plot_partial_residuals(focus_exog[, ax])	Create a partial residual, or ‘component plus residual’ plot for a fitted regression model.
predict([exog, transform])	Call self.model.predict with self.params as the first argument.
qic([scale])	Returns the QIC and QICu information criteria.
remove_data()	Remove data arrays, all nobs arrays from result and model.
save(fname[, remove_data])	Save a pickle of this instance.
score_test()	Return the results of a score test for a linear constraint.
sensitivity_params(dep_params_first, …)	Refits the GEE model using a sequence of values for the dependence parameters.
standard_errors([cov_type])	This is a convenience function that returns the standard errors for any covariance type.
summary([yname, xname, title, alpha])	Summarize the GEE regression results
summary2([yname, xname, title, alpha, …])	Experimental summary for regression Results
t_test(r_matrix[, cov_p, scale, 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, scale, invcov, …])	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.

Methods

conf_int([alpha, cols, cov_type])	Returns confidence intervals for the fitted parameters.
cov_params([r_matrix, column, scale, cov_p, …])	Compute the variance/covariance matrix.
f_test(r_matrix[, cov_p, scale, invcov])	Compute the F-test for a joint linear hypothesis.
get_hat_matrix_diag([observed])	Compute the diagonal of the hat matrix
get_influence([observed])	Get an instance of GLMInfluence with influence and outlier measures
get_margeff([at, method, atexog, dummy, count])	Get marginal effects of the fitted model.
get_prediction([exog, exposure, offset, …])	compute prediction results
initialize(model, params, **kwargs)	Initialize (possibly re-initialize) a Results instance.
load(fname)	Load a pickled results instance
normalized_cov_params()	See specific model class docstring
params_sensitivity(dep_params_first, …)	Refits the GEE model using a sequence of values for the dependence parameters.
plot_added_variable(focus_exog[, …])	Create an added variable plot for a fitted regression model.
plot_ceres_residuals(focus_exog[, frac, …])	Conditional Expectation Partial Residuals (CERES) plot.
plot_isotropic_dependence([ax, xpoints, min_n])	Create a plot of the pairwise products of within-group residuals against the corresponding time differences.
plot_partial_residuals(focus_exog[, ax])	Create a partial residual, or ‘component plus residual’ plot for a fitted regression model.
predict([exog, transform])	Call self.model.predict with self.params as the first argument.
qic([scale])	Returns the QIC and QICu information criteria.
remove_data()	Remove data arrays, all nobs arrays from result and model.
save(fname[, remove_data])	Save a pickle of this instance.
score_test()	Return the results of a score test for a linear constraint.
sensitivity_params(dep_params_first, …)	Refits the GEE model using a sequence of values for the dependence parameters.
standard_errors([cov_type])	This is a convenience function that returns the standard errors for any covariance type.
summary([yname, xname, title, alpha])	Summarize the GEE regression results
summary2([yname, xname, title, alpha, …])	Experimental summary for regression Results
t_test(r_matrix[, cov_p, scale, 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, scale, invcov, …])	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

aic	Akaike Information Criterion -2 * llf + 2 * (df_model + 1)
bic	Bayes Information Criterion
bic_deviance	Bayes Information Criterion
bic_llf	Bayes Information Criterion
bse
centered_resid	Returns the residuals centered within each group.
deviance	See statsmodels.families.family for the distribution-specific deviance functions.
fittedvalues	The estimated mean response.
llf	Value of the loglikelihood function evalued at params.
llnull	Log-likelihood of the model fit with a constant as the only regressor
mu	See GLM docstring.
null	Fitted values of the null model
null_deviance	The value of the deviance function for the model fit with a constant as the only regressor.
pearson_chi2	Pearson’s Chi-Squared statistic is defined as the sum of the squares of the Pearson residuals.
pvalues	The two-tailed p values for the t-stats of the params.
resid	The response residuals.
resid_anscombe	Anscombe residuals.
resid_anscombe_scaled	Scaled Anscombe residuals.
resid_anscombe_unscaled	Unscaled Anscombe residuals.
resid_centered	Returns the residuals centered within each group.
resid_centered_split	Returns the residuals centered within each group.
resid_deviance	Deviance residuals.
resid_pearson	Pearson residuals.
resid_response	Response residuals.
resid_split	Returns the residuals, the endogeneous data minus the fitted values from the model.
resid_working	Working residuals.
split_centered_resid	Returns the residuals centered within each group.
split_resid	Returns the residuals, the endogeneous data minus the fitted values from the model.
tvalues	Return the t-statistic for a given parameter estimate.
use_t	Flag indicating to use the Student’s distribution in inference.