Linked shrinkage to improve estimation of interaction effects in regression models.

Objectives: The addition of two-way interactions is a classic problem in statistics, and comes with the challenge of quadratically increasing dimension. We aim to a) devise an estimation method that can handle this challenge and b) to aid interpretation of the resulting model by developing computational tools for quantifying variable importance.

Methods: Existing strategies typically overcome the dimensionality problem by only allowing interactions between relevant main effects.