Generalized Symmetry Models for Hypercubic Concordance Tables

Frequency data obtained classifying a sample of ‘units’ by the same categorical variable repeatedly over ‘components’, can be arranged in a hypercubic concordance table (h.c.t.). This kind of data naturally arises in a number of different areas such as longitudinal studies, studies using matched and clustered data, item‐response analysis, agreement analysis. In spite of the substantial diversity of the mechanisms that can generate them, data arranged in a h.c.t. can all be analyzed via models of symmetry and quasi‐symmetry, which exploit the special structure of the h.c.t. The paper extends the definition of such models to any dimension, introducing the class of generalized symmetry models, which provides a unified framework for inference on categorical data that can be represented in a h.c.t., Within this framework it is possible to derive the common structure which underlies these models and clarify their meaning; their usefulness in applied work is illustrated by a re‐analysis of two real examples.