ABSTRACT
The task of figuring out what variables to use, variable selection, is an important aspect in the construction of both predictive and inferential models. Hand-constructed stepwise regression can lead to erroneous conclusions if hypothesis tests from the final model are presented without correcting for the post hoc variable selection step. This chapter analyses derive a specific approach that is particularly adept at solving this particular task. There are several approaches to understanding why l1-penalized regression leads to a parsimonious regression vector. Coordinate descent is a general purpose convex optimization algorithm particularly well-suited to solving the elastic net equation. Coordinate descent successively minimizes the objective function along each variable. The implementation of the generalized elastic net looks similar to the linear elastic net but includes a sample weighting that depends on the link function and exponential family used in the model.
