On Model Selection Algorithms in Multi-dimensional Contingency Tables

We present a review focussed on model selection in log-linear models and contingency tables. The concepts of sparsity and high-dimensionality have become more important nowadays, for example, in the context of high-throughput genetic data. In particular, we describe recently developed automatic search algorithms for finding optimal hierarchical log-linear models (HLLMs) in sparse multi-dimensional contingency tables in R and some LASSO-type penalized likelihood model selection approaches. The methods rely, in part, on a new result which identifies and thus permits the rapid elimination of non-existent maximum likelihood estimators in high-dimensional tables.