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Statistical Models for Multiway Array Data

Social science datasets are often in the form of matrices or arrays, potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as well as correlation among the variables. Social networks and other relational datasets may exhibit correlation among the senders and receivers of relationships. In this talk I will discuss a class of statistical models for the analysis of such array-valued data. Specifically, I will extend the matrix normal model for matrix-valued data to a class of array normal distributions having separable covariance structure. We relate this model to the higher-order SVD for analysis of array data, and show how the model can be motivated in terms of a latent variable representation. Model fitting and parameter estimation for array-normal distributions will be illustrated in the analysis of several examples, including international trade networks, imputation for nation specific life-tables, and estimation of high-order interactions in ANOVA models.