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We apply the cyclic coordinate descent algorithm of Friedman, Hastie andTibshirani (2010) to the fitting of a conditional logistic regression modelwith lasso ($\ell_1$) and elastic net penalties. The sequential strong rules ofTibshirani et al (2012) are also used in the algorithm and it is shown thatthese offer a considerable speed up over the standard coordinate descentalgorithm with warm starts.  Once implemented, the algorithm is used in simulation studies to compare thevariable selection and prediction performance of the conditional logisticregression model against that of its unconditional (standard) counterpart. Wefind that the conditional model performs admirably on datasets drawn from asuitable conditional distribution, outperforming its unconditional counterpartat variable selection. The conditional model is also fit to a small real worlddataset, demonstrating how we obtain regularisation paths for the parameters ofthe model and how we apply cross validation for this method where naturalunconditional prediction rules are hard to come by.

Regularisation Paths for Conditional Logistic Regression: the clogitL1 package