Chapter 27 - Use of Biplots to Diagnose Independence Models in Three-Way Contingency Tables

Abstract

This chapter discusses the use of biplots for the diagnosis of independence models in three-way contingency tables. An essential part of the analysis of contingency tables is the testing for independence of classifications. In three-way tables, there are many possible independence hypotheses, each of which may be tested, but consistent inferences must take into account the implication relations among them. Analyses of three-way contingency tables are therefore often difficult to interpret, especially because they produce too many acceptable models. This difficulty creates a need for methods that simplify the appraisal of the data and reduce the profusion of acceptable models. The chapter proposes the rules for visual diagnosis of independence that are based on patterns of biplots. Ideally, the rules allow diagnosis of one model for an entire table but in practice they often indicate models for subtables. The chapter concludes with a discussion of concepts related to diagnosis in two-way tables and three-way tables.