Ordinal Mixed Membership Models

We present a novel class of mixed membership models for joint distributions of groups of observations that co-occur with ordinal response variables for each group for learning statistical associations between the ordinal response variables and the observation groups. The class of proposed models addresses a requirement for predictive and diagnostic methods in a wide range of practical contemporary applications. In this work, by way of illustration, we apply the models to a collection of consumer-generated reviews of mobile software applications, where each review contains unstructured text data accompanied with an ordinal rating, and demonstrate that the models infer useful and meaningful recurring patterns of consumer feedback. We also compare the developed models to relevant existing works, which rely on improper statistical assumptions for ordinal variables, showing significant improvements both in predictive ability and knowledge extraction.