Generalized symmetry models for hypercubic concordance tables

Frequency data obtained classifying a sample of 'units' by the same categor ical 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 th e substantial diversity of the mechanisms that can generate them, data arra nged in a h.c.t. can ail be analyzed via models of symmetry and quasi-symme try, which exploit the special structure of the h.c.t. The paper extends th e definition of such models to any dimension, introducing the class of gene ralized symmetry models, which provides a unified framework for inference o n categorical data that can be represented in a h.c.t.. Within this framewo rk it is possible to derive the common structure which underlies these mode ls and clarify their meaning;their usefulness in applied work is illustrate d by a re-analysis of two real examples.