Visualizing, Summarizing, and Comparing Odds Ratio Structures

The odds ratio is one of the main measures of association in 2× 2 tables. For larger tables, summary measures of association have been proposed as well as modeling strategies, where the odds ratios can be deduced from the parameters of a model. We propose a computationally simple scaling methodology, which gives a summary measure of association and a visualization of the odds ratio structure. Different variants of the methodology are discussed and compared, both theoretically and empirically. The methodology is also generalized to multiple tables, where not only the structure of each table is important, but also comparisons among tables.