Several stochastic models have tried to capture the architecture of food webs. This approach is interesting, but it is limited by the fact that different assumptions can yield similar results. To overcome this limitation, we develop a purely statistical approach. Body size in terms of an optimal ratio between prey and predator is used as explanatory variable. In 12 observed food webs, this model predicts, on average, 20% of interactions. To analyze the unexplained part, we introduce a latent term: each species is described by two latent traits, foraging and vulnerability, that represent nonmeasured characteristics of species once the optimal body size has been accounted for. The model now correctly predicts an average of 73% of links. The key features of our approach are that latent traits quantify the structure that is left unexplained by the explanatory variable and that this quantification allows a test of whether independent biological information, such as microhabitat use, camouflage, or phylogeny, explains this structure. We illustrate this method with phylogeny and find that it is linked to one or both latent traits in nine of 12 food webs. Our approach opens the door to the formulation of more complex models that can be applied to any kind of biological network.