Hierarchical subspace models for contingency tables

For the statistical analysis of multiway contingency tables, we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom than the usual hierarchical model, while preserving the localization property of the inference in the hierarchical model. This approach also enables us to evaluate the localization property of a given log-affine model. We discuss estimation and exact tests of the proposed model and illustrate the advantage of the proposed modeling with some data sets.

► We introduce the hierarchical subspace models (HSMs) for contingency tables.
► HSM is a classification of log-affine models in terms of decomposability.
► HSM enables us to evaluate the decomposability of a given log-affine model.
► By the decomposability, the inference of the model is localized to smaller submodels.