statsmodels.genmod.generalized_linear_model.GLM.fit_regularized¶
-
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.
Parameters: - 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.
Returns: Return type: An array, or a GLMResults object of the same type returned by fit.
Notes
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.