Hierarchical multilinear models for multiway data

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 is cross-classified by categorical variables. The proposed model-based approach is hierarchical, in that the latent factors corresponding to a given dimension of the array are not a priori independent, but exchangeable. Such a hierarchical approach allows more flexibility in the types of patterns that can be represented. Some key words: Bayesian, multiplicative model, PARAFAC, regularization, shrinkage.

• Type: Journal
• Year: 2011
• Where: CSDA
• Authors: Peter D. Hoff
• Keywords: CSDA 2011, Latent Factors, Longitudinal Social Networks, Low-dimensional Latent Factors, Social Sciences