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’, ‘l1_slsqp’}, optional

‘elastic_net’ uses coordinate descent and supports the full elastic net penalty. ‘l1_slsqp’ solves a smooth constrained reformulation of the L1 problem with slsqp, an interior point style method, and only supports the lasso penalty (L1_wt must be 1).

alphascalar or array_like, optional

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, optional

Starting values for params.

refitbool, optional

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_methodstr, optional

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.

The l1_slsqp method uses the following keyword arguments:

maxiterint

Maximum number of iterations (default 1000).

trim_mode{‘auto’, ‘size’, ‘off’}

If not ‘off’, trim (set to zero) parameters that would have been zero if the solver reached the theoretical minimum. If ‘auto’, trim params using the theoretical optimality conditions. If ‘size’, trim params if they have very small absolute value.

size_trim_tolfloat

Tolerance used when trim_mode is ‘size’.

auto_trim_tolfloat

Tolerance used when trim_mode is ‘auto’.

qc_tolfloat

Print warning and do not allow auto trim when the optimality conditions are violated by this much.

qc_verbosebool

If True, print out a full QC report upon failure.

accfloat

Requested accuracy as used by slsqp (default 1e-10).