statsmodels.robust.robust_linear_model.RLM

class statsmodels.robust.robust_linear_model.RLM(endog, exog, M=<statsmodels.robust.norms.HuberT object>, missing='none', **kwargs)

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 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.’

Notes

Attributes

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)

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])
>>> mod = sm.RLM(data.endog, data.exog, M=sm.robust.norms.Hampel())
>>> rlm_hamp_hub = mod.fit(scale_est=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, drop_cols])	Create a Model from a formula and dataframe.
hessian(params)	The Hessian matrix of the model
information(params)	Fisher information matrix of model
initialize()	Initialize (possibly re-initialize) a Model instance.
loglike(params)	Log-likelihood of model.
predict(params[, exog])	Return linear predicted values from a design matrix.
score(params)	Score vector of model.

Attributes

endog_names	Names of endogenous variables
exog_names	Names of exogenous variables