1. Recent studies on plant-pollinator networks have focused on explaining network structure through linkage rules, including spatio-temporal overlap, and phenotypic trait or phylogenetic signal complementarity. Few studies, however, have quantified the extent to which functional traits affect the probability of plants and pollinators interacting with each other. 2. Dirichlet-multinomial (DM) regression is a consumer-resource model for the interaction probabilities in a mutualistic network. This flexible model accommodates network heterogeneity through random effects and overdispersion and can estimate the contribution of species-level traits to plant-pollinator interactions. 3. Using artificial networks based on linkage rules and neutrality, we evaluate the performance of DM regression and explore the model's parameter space. We also analyse an empirical network in which the interaction probabilities are modelled by species characteristics. 4. Study results show that such random effects models can provide good fits to observed data. The characteristics pollinators seek in plant species may be better anticipated if species interactions are modelled by the functional traits that drive them.