Model selection in sparse contingency tables: LASSO penalties vs classical method

We compare improved classical backward elimination and forward selection methods of model selection in sparse contingency tables with methods based on a regularisation approach involving the least absolute shrinkage and selection operator (LASSO) and the Smooth LASSO. The results show that the modified classical methods outperform the regularisation methods, by producing sparser models which are always hierarchical. Curiously, models selected by the regularisation methods often include effects which are known to be inestimable in the classical paradigm. Our findings support the use of classical methodology.