Hierarchical subspace models for contingency tables

TL;DR

This paper introduces hierarchical subspace models for multiway contingency tables, enabling more parsimonious models that maintain key independence structures, with improved estimation and testing methods demonstrated on real datasets.

Contribution

It proposes a novel hierarchical subspace modeling approach that reduces model complexity while preserving essential independence structures in contingency tables.

Findings

Models with fewer degrees of freedom outperform traditional hierarchical models

The approach maintains key conditional independence structures

Empirical results demonstrate the effectiveness of the proposed models

Abstract

For 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 conditional independence structures in the hierarchical model. We discuss estimation and exacts tests of the proposed model and illustrate the advantage of the proposed modeling with some data sets.