OLS.fit_regularized(method='elastic_net', alpha=0.0, L1_wt=1.0, start_params=None, profile_scale=False, refit=False, **kwargs)[source]

Return a regularized fit to a linear regression model.


method : string

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.

L1_wt: scalar

The fraction of the penalty given to the L1 penalty term. Must be between 0 and 1 (inclusive). If 0, the fit is a ridge fit, if 1 it is a lasso fit.

start_params : array-like

Starting values for params.

profile_scale : bool

If True the penalized fit is computed using the profile (concentrated) log-likelihood for the Gaussian model. Otherwise the fit uses the residual sum of squares.

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.


An array of coefficients, or a RegressionResults object of the

same type returned by fit.


The elastic net approach closely follows that implemented in the glmnet package in R. The penalty is a combination of L1 and L2 penalties.

The function that is minimized is: ..math:

0.5*RSS/n + alpha*((1-L1_wt)*|params|_2^2/2 + L1_wt*|params|_1)

where RSS is the usual regression sum of squares, n is the sample size, and |*|_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
cnvrg_tol : float
Convergence threshold for line searches
zero_tol : float
Coefficients below this threshold are treated as zero.


Friedman, Hastie, Tibshirani (2008). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software 33(1), 1-22 Feb 2010.