class statsmodels.robust.robust_linear_model.RLM(endog, exog, M=<statsmodels.robust.norms.HuberT object at 0x63d8d50>, missing='none', **kwargs)[source]

Robust Linear Models

Estimate a robust linear model via iteratively reweighted least squares given a robust criterion estimator.


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 and k is the number of regressors. An intercept is not included by default and should be added by the user. See statsmodels.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.’



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.
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.
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.
nobs : float
The number of observations n
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.
normalized_cov_params : array
The p x p normalized covariance of the design / exogenous data. This is approximately equal to (X.T X)^(-1)


>>> 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,
>>> 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,
>>> rlm_hamp_hub.params
array([  0.73175452,   1.25082038,  -0.14794399, -40.27122257])


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
initialize() Initialize (possibly re-initialize) a Model instance.
predict(params[, exog]) Return linear predicted values from a design matrix.



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