Multivariate categorical data are common in many fields. We are motivated byelection polls studies assessing evidence of changes in voters opinions withtheir candidates preferences in the 2016 United States Presidential primariesor caucuses. Similar goals arise routinely in several applications, but currentliterature lacks a general methodology which combines flexibility, efficiency,and tractability in testing for group differences in multivariate categoricaldata at different---potentially complex---scales. We address this goal byleveraging a Bayesian representation which factorizes the joint probabilitymass function for the group variable and the multivariate categorical data asthe product of the marginal probabilities for the groups, and the conditionalprobability mass function of the multivariate categorical data, given the groupmembership. To enhance flexibility, we define the conditional probability massfunction of the multivariate categorical data via a group-dependent mixture oftensor factorizations, thus facilitating dimensionality reduction and borrowingof information, while providing tractable procedures for computation, andaccurate tests assessing global and local group differences. We compare ourmethods with popular competitors, and discuss improved performance insimulations and in American election polls studies.
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