statsmodels.robust.robust_linear_model.RLM
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class statsmodels.robust.robust_linear_model.RLM(endog, exog, M=, missing='none', **kwargs)
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Robust Linear Models
Estimate a robust linear model via iteratively reweighted least squares given a robust criterion estimator.
Parameters: endog : array-like
1-d endogenous response variable. The dependent variable.
exog : array-like
A nobs x k array where
nobs
is the number of observations andk
is the number of regressors. An intercept is not included by default and should be added by the user. Seestatsmodels.tools.add_constant
.M : statsmodels.robust.norms.RobustNorm, optional
The robust criterion function for downweighting outliers. The current options are LeastSquares, HuberT, RamsayE, AndrewWave, TrimmedMean, Hampel, and TukeyBiweight. The default is HuberT(). See statsmodels.robust.norms for more information.
missing : str
Available options are ?none?, ?drop?, and ?raise?. If ?none?, no nan checking is done. If ?drop?, any observations with nans are dropped. If ?raise?, an error is raised. Default is ?none.?
Notes
Attributes
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df_model : float
- The degrees of freedom of the model. The number of regressors p less one for the intercept. Note that the reported model degrees of freedom does not count the intercept as a regressor, though the model is assumed to have an intercept.
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df_resid : float
- The residual degrees of freedom. The number of observations n less the number of regressors p. Note that here p does include the intercept as using a degree of freedom.
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endog : array
- See above. Note that endog is a reference to the data so that if data is already an array and it is changed, then
endog
changes as well. -
exog : array
- See above. Note that endog is a reference to the data so that if data is already an array and it is changed, then
endog
changes as well. -
M : statsmodels.robust.norms.RobustNorm
- See above. Robust estimator instance instantiated.
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nobs : float
- The number of observations n
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pinv_wexog : array
- The pseudoinverse of the design / exogenous data array. Note that RLM has no whiten method, so this is just the pseudo inverse of the design.
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normalized_cov_params : array
- The p x p normalized covariance of the design / exogenous data. This is approximately equal to (X.T X)^(-1)
Examples
>>> import statsmodels.api as sm >>> data = sm.datasets.stackloss.load() >>> data.exog = sm.add_constant(data.exog) >>> rlm_model = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())
>>> rlm_results = rlm_model.fit() >>> rlm_results.params array([ 0.82938433, 0.92606597, -0.12784672, -41.02649835]) >>> rlm_results.bse array([ 0.11100521, 0.30293016, 0.12864961, 9.79189854]) >>> rlm_results_HC2 = rlm_model.fit(cov="H2") >>> rlm_results_HC2.params array([ 0.82938433, 0.92606597, -0.12784672, -41.02649835]) >>> rlm_results_HC2.bse array([ 0.11945975, 0.32235497, 0.11796313, 9.08950419]) >>> >>> rlm_hamp_hub = sm.RLM(data.endog, data.exog, M=sm.robust.norms.Hampel()).fit( sm.robust.scale.HuberScale())
>>> rlm_hamp_hub.params array([ 0.73175452, 1.25082038, -0.14794399, -40.27122257])
Methods
deviance
(tmp_results)Returns the (unnormalized) log-likelihood from the M estimator. fit
([maxiter, tol, scale_est, init, cov, ...])Fits the model using iteratively reweighted least squares. from_formula
(formula, data[, subset])Create a Model from a formula and dataframe. hessian
(params)The Hessian matrix of the model information
(params)initialize
()Initialize (possibly re-initialize) a Model instance. loglike
(params)predict
(params[, exog])Return linear predicted values from a design matrix. score
(params)Attributes
endog_names
exog_names
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