statsmodels.gam.generalized_additive_model.GLMGam.fit_regularized¶
- GLMGam.fit_regularized(method='elastic_net', alpha=0.0, start_params=None, refit=False, opt_method='bfgs', **kwargs)¶
Return a regularized fit to a linear regression model.
- Parameters
- method{‘elastic_net’}
Only the elastic_net approach is currently implemented.
- alphascalar 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_paramsarray_like
Starting values for params.
- refitbool
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.
- opt_method
str
The method used for numerical optimization.
- **kwargs
Additional keyword arguments used when fitting the model.
- Returns
GLMResults
An array or a GLMResults object, 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:
- maxiterint
Maximum number of iterations
- L1_wtfloat
Must be in [0, 1]. The L1 penalty has weight L1_wt and the L2 penalty has weight 1 - L1_wt.
- cnvrg_tolfloat
Convergence threshold for maximum parameter change after one sweep through all coefficients.
- zero_tolfloat
Coefficients below this threshold are treated as zero.