Collaborative Filtering (CF) aims at finding patterns in a sparse matrix of contingency. It can be used for example to mine the ratings given by users on a set of items. In this paper, we introduce a new model for CF based on the Generalized Linear Models formalism. Interestingly, it shares specificities of the model-based and the factorization approaches. The model is simple, and yet it performs very well on the popular MovieLens and Jester datasets.