GLM.fit_regularized(method='elastic_net', alpha=0.0, start_params=None, refit=False, **kwargs) [source]

Return a regularized fit to a linear regression model.

  • method – Only the elastic_net approach is currently implemented.
  • alpha (scalar or array-like) – The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as params, and contains a penalty weight for each coefficient.
  • start_params (array-like) – Starting values for params.
  • refit (bool) – If True, the model is refit using only the variables that have non-zero coefficients in the regularized fit. The refitted model is not regularized.
Return type:

An array, or a GLMResults object of the same type returned by fit.


The penalty is the elastic net penalty, which is a combination of L1 and L2 penalties.

The function that is minimized is:

\[-loglike/n + alpha*((1-L1\_wt)*|params|_2^2/2 + L1\_wt*|params|_1)\]

where \(|*|_1\) and \(|*|_2\) are the L1 and L2 norms.

Post-estimation results are based on the same data used to select variables, hence may be subject to overfitting biases.

The elastic_net method uses the following keyword arguments:

maxiter : int
Maximum number of iterations
L1_wt : float
Must be in [0, 1]. The L1 penalty has weight L1_wt and the L2 penalty has weight 1 - L1_wt.
cnvrg_tol : float
Convergence threshold for line searches
zero_tol : float
Coefficients below this threshold are treated as zero.

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.