Algebraic Descriptions of Nominal Multivariate Discrete Data

Traditionally, multivariate discrete data are analyzed by means of log-linear models. In this paper we show how an algebraic approach leads naturally to alternative models, parametrized in terms of the moments of the distribution. Moreover we derive a complete characterization of all meaningful transformations of the components and show how transformations affect the moments of a distribution. It turns out that our models provide the necessary formal description of longitudinal data; moreover in the classical case, they can be considered as an analysis tool, complementary to log-linear models.