Collaborative filtering is a general technique for exploiting the preference patterns of a group of users to predict the utility of items for a particular user. Three different components need to be modeled in a collaborative filtering problem: users, items, and ratings. Previous research on applying probabilistic models to collaborative filtering has shown promising results. However, there is a lack of systematic studies of different ways to model each of the three components and their interactions. In this paper, we conduct a broad and systematic study on different mixture models for collaborative filtering. We discuss general issues related to using a mixture model for collaborative filtering, and propose three properties that a graphical model is expected to satisfy. Using these properties, we thoroughly examine five different mixture models, including Bayesian Clustering (BC), Aspect Model (AM), Flexible Mixture Model (FMM), Joint Mixture Model (JMM), and the Decoupled Model (DM)...