Efficient interaction selection for clustered data via stagewise generalized estimating equations.

Model selection in the presence of interaction terms is challenging as the final model must maintain a hierarchy between main effects and interaction terms. This work presents two stagewise estimation approaches to appropriately select models with interaction terms that can utilize generalized estimating equations to model clustered data. The first proposed technique is a hierarchical lasso stagewise estimating equations approach, which is shown to directly correspond to the hierarchical lasso penalized regression. The second is a stagewise active set approach, which enforces the variable hierarchy by conforming the selection to a properly growing active set in each stagewise estimation step. The effectiveness in interaction selection and the superior computational efficiency of the proposed techniques are assessed in simulation studies. The new methods are applied to a study of hospitalization rates attributed to suicide attempts among 15 to 19 year old at the school district level in Connecticut.