statsmodels.regression.mixed_linear_model.MixedLM.fit_regularized

MixedLM.fit_regularized(start_params=None, method='l1', alpha=0, ceps=0.0001, ptol=1e-06, maxit=200, **fit_kwargs)

Fit a model in which the fixed effects parameters are penalized. The dependence parameters are held fixed at their estimated values in the unpenalized model.

Parameters:

start_paramsarray_like, optional

Starting values for the optimization.

methodstr of Penalty object

Method for regularization. If a string, must be ‘l1’.

alphaarray_like

Scalar or vector of penalty weights. If a scalar, the same weight is applied to all coefficients; if a vector, it contains a weight for each coefficient. If method is a Penalty object, the weights are scaled by alpha. For L1 regularization, the weights are used directly.

cepspositive real scalar

Fixed effects parameters smaller than this value in magnitude are treated as being zero.

ptolpositive real scalar

Convergence occurs when the sup norm difference between successive values of fe_params is less than ptol.

maxitint

The maximum number of iterations.

**fit_kwargs

Additional keyword arguments passed to fit.

Returns:

MixedLMResults

The model instance containing the fitted results.

Notes

The covariance structure is not updated as the fixed effects parameters are varied.

The algorithm used here for L1 regularization is a “shooting” or cyclic coordinate descent algorithm.

If method is ‘l1’, then fe_pen and cov_pen are used to obtain the covariance structure, but are ignored during the L1-penalized fitting.

References

Friedman, J. H., Hastie, T. and Tibshirani, R. Regularized Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, 33(1) (2008) http://www.jstatsoft.org/v33/i01/paper

http://statweb.stanford.edu/~tibs/stat315a/Supplements/fuse.pdf