6.7.4.4.14. statsmodels.sandbox.regression.gmm.RegressionResults¶
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class
statsmodels.sandbox.regression.gmm.
RegressionResults
(model, params, normalized_cov_params=None, scale=1.0, cov_type='nonrobust', cov_kwds=None, use_t=None)[source]¶ This class summarizes the fit of a linear regression model.
It handles the output of contrasts, estimates of covariance, etc.
Returns: Attributes
aic
Aikake’s information criteria. For a model with a constant \(-2llf + 2(df_model + 1)\). For a model without a constant \(-2llf + 2(df_model)\).
bic
Bayes’ information criteria For a model with a constant \(-2llf + \log(n)(df_model+1)\). For a model without a constant \(-2llf + \log(n)(df_model)\)
bse
The standard errors of the parameter estimates.
pinv_wexog
See specific model class docstring
centered_tss
The total (weighted) sum of squares centered about the mean.
cov_HC0
Heteroscedasticity robust covariance matrix. See HC0_se below.
cov_HC1
Heteroscedasticity robust covariance matrix. See HC1_se below.
cov_HC2
Heteroscedasticity robust covariance matrix. See HC2_se below.
cov_HC3
Heteroscedasticity robust covariance matrix. See HC3_se below.
cov_type
Parameter covariance estimator used for standard errors and t-stats
df_model
Model degress of freedom. The number of regressors p. Does not include the constant if one is present
df_resid
Residual degrees of freedom. n - p - 1, if a constant is present. n - p if a constant is not included.
ess
Explained sum of squares. If a constant is present, the centered total sum of squares minus the sum of squared residuals. If there is no constant, the uncentered total sum of squares is used.
fvalue
F-statistic of the fully specified model. Calculated as the mean squared error of the model divided by the mean squared error of the residuals.
f_pvalue
p-value of the F-statistic
fittedvalues
The predicted the values for the original (unwhitened) design.
het_scale
adjusted squared residuals for heteroscedasticity robust standard errors. Is only available after HC#_se or cov_HC# is called. See HC#_se for more information.
HC0_se
White’s (1980) heteroskedasticity robust standard errors. Defined as sqrt(diag(X.T X)^(-1)X.T diag(e_i^(2)) X(X.T X)^(-1) where e_i = resid[i] HC0_se is a cached property. When HC0_se or cov_HC0 is called the RegressionResults instance will then have another attribute het_scale, which is in this case is just resid**2.
HC1_se
MacKinnon and White’s (1985) alternative heteroskedasticity robust standard errors. Defined as sqrt(diag(n/(n-p)*HC_0) HC1_see is a cached property. When HC1_se or cov_HC1 is called the RegressionResults instance will then have another attribute het_scale, which is in this case is n/(n-p)*resid**2.
HC2_se
MacKinnon and White’s (1985) alternative heteroskedasticity robust standard errors. Defined as (X.T X)^(-1)X.T diag(e_i^(2)/(1-h_ii)) X(X.T X)^(-1) where h_ii = x_i(X.T X)^(-1)x_i.T HC2_see is a cached property. When HC2_se or cov_HC2 is called the RegressionResults instance will then have another attribute het_scale, which is in this case is resid^(2)/(1-h_ii).
HC3_se
MacKinnon and White’s (1985) alternative heteroskedasticity robust standard errors. Defined as (X.T X)^(-1)X.T diag(e_i^(2)/(1-h_ii)^(2)) X(X.T X)^(-1) where h_ii = x_i(X.T X)^(-1)x_i.T HC3_see is a cached property. When HC3_se or cov_HC3 is called the RegressionResults instance will then have another attribute het_scale, which is in this case is resid^(2)/(1-h_ii)^(2).
model
A pointer to the model instance that called fit() or results.
mse_model
Mean squared error the model. This is the explained sum of squares divided by the model degrees of freedom.
mse_resid
Mean squared error of the residuals. The sum of squared residuals divided by the residual degrees of freedom.
mse_total
Total mean squared error. Defined as the uncentered total sum of squares divided by n the number of observations.
nobs
Number of observations n.
normalized_cov_params
See specific model class docstring
params
The linear coefficients that minimize the least squares criterion. This is usually called Beta for the classical linear model.
pvalues
The two-tailed p values for the t-stats of the params.
resid
The residuals of the model.
resid_pearson
wresid normalized to have unit variance.
rsquared
R-squared of a model with an intercept. This is defined here as 1 - ssr/centered_tss if the constant is included in the model and 1 - ssr/uncentered_tss if the constant is omitted.
rsquared_adj
Adjusted R-squared. This is defined here as 1 - (nobs-1)/df_resid * (1-rsquared) if a constant is included and 1 - nobs/df_resid * (1-rsquared) if no constant is included.
scale
A scale factor for the covariance matrix. Default value is ssr/(n-p). Note that the square root of scale is often called the standard error of the regression.
ssr
Sum of squared (whitened) residuals.
uncentered_tss
Uncentered sum of squares. Sum of the squared values of the (whitened) endogenous response variable.
wresid
The residuals of the transformed/whitened regressand and regressor(s)
6.7.4.4.14.1. Methods¶
HC0_se () |
See statsmodels.RegressionResults |
HC1_se () |
See statsmodels.RegressionResults |
HC2_se () |
See statsmodels.RegressionResults |
HC3_se () |
See statsmodels.RegressionResults |
__init__ (model, params[, ...]) |
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aic () |
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bic () |
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bse () |
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centered_tss () |
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compare_f_test (restricted) |
use F test to test whether restricted model is correct |
compare_lm_test (restricted[, demean, use_lr]) |
Use Lagrange Multiplier test to test whether restricted model is correct |
compare_lr_test (restricted[, large_sample]) |
Likelihood ratio test to test whether restricted model is correct |
condition_number () |
Return condition number of exogenous matrix. |
conf_int ([alpha, cols]) |
Returns the confidence interval of the fitted parameters. |
cov_HC0 () |
See statsmodels.RegressionResults |
cov_HC1 () |
See statsmodels.RegressionResults |
cov_HC2 () |
See statsmodels.RegressionResults |
cov_HC3 () |
See statsmodels.RegressionResults |
cov_params ([r_matrix, column, scale, cov_p, ...]) |
Returns the variance/covariance matrix. |
eigenvals () |
Return eigenvalues sorted in decreasing order. |
ess () |
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f_pvalue () |
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f_test (r_matrix[, cov_p, scale, invcov]) |
Compute the F-test for a joint linear hypothesis. |
fittedvalues () |
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fvalue () |
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get_robustcov_results ([cov_type, use_t]) |
create new results instance with robust covariance as default |
initialize (model, params, **kwd) |
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llf () |
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load (fname) |
load a pickle, (class method) |
mse_model () |
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mse_resid () |
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mse_total () |
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nobs () |
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normalized_cov_params () |
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predict ([exog, transform]) |
Call self.model.predict with self.params as the first argument. |
pvalues () |
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remove_data () |
remove data arrays, all nobs arrays from result and model |
resid () |
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resid_pearson () |
Residuals, normalized to have unit variance. |
rsquared () |
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rsquared_adj () |
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save (fname[, remove_data]) |
save a pickle of this instance |
scale () |
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ssr () |
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summary ([yname, xname, title, alpha]) |
Summarize the Regression Results |
summary2 ([yname, xname, title, alpha, ...]) |
Experimental summary function to summarize the 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 |
tvalues () |
Return the t-statistic for a given parameter estimate. |
uncentered_tss () |
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wald_test (r_matrix[, cov_p, scale, invcov, ...]) |
Compute a Wald-test for a joint linear hypothesis. |
wresid () |