Discrete mixed membership modeling and continuous latent factor modeling (also known as matrix factorization) are two popular, complementary approaches to dyadic data analysis. In this work, we develop a fully Bayesian framework for integrating the two approaches into unified Mixed Membership Matrix Factorization (M3F) models.  We introduce two M3F models, derive Gibbs sampling inference procedures, and validate our methods on the EachMovie, MovieLens, and Netflix Prize collaborative filtering datasets.  We find that, even when fitting fewer parameters, the M3F models outperform state-of-the-art latent factor approaches on all benchmarks, yielding the greatest gains in accuracy on sparsely-rated, high-variance items.

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