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.