LASSO penalised likelihood in high-dimensional contingency tables

We consider several least absolute shrinkage and selection operator (LASSO) penalized likelihood approaches in high dimensional contingency tables and with hierarchical log-linear models. These include the proposal of a parametric, analytic, convex, approximation to the LASSO. We compare them with "classical" stepwise search algorithms. The results show that both backwards elimination and forward selection algorithms select more parsimonious (i.e. sparser) models which are always hierarchical, unlike the competing LASSO techniques.