Reduced-rank decompositions provide descriptions of the variation among the
elements of a matrix or array. In such decompositions, the elements of an array
are expressed as products of low-dimensional latent factors. This article
presents a model-based version of such a decomposition, extending the scope of
reduced rank methods to accommodate a variety of data types such as
longitudinal social networks and continuous multivariate data that are
cross-classified by categorical variables.