A key requirement in studies of endemic vector-borne or zoonotic disease is an estimate of the spatial variation in vector or reservoir host abundance. For many vector species, multiple indices of abundance are available, but current approaches to choosing between or combining these indices do not fully exploit the potential inferential benefits that might accrue from modelling their joint spatial distribution. Here, we develop a class of multivariate generalized linear geostatistical models for multiple indices of abundance. We illustrate this novel methodology with a case study on Norway rats in a low-income urban Brazilian community, where rat abundance is a likely risk factor for human leptospirosis. We combine three indices of rat abundance to draw predictive inferences on a spatially continuous latent process, rattiness, that acts as a proxy for abundance. We show how to explore the association between rattiness and spatially varying environmental factors, evaluate the relative importance of each of the three contributing indices and assess the presence of residual, unexplained spatial variation, and identify rattiness hotspots. The proposed methodology is applicable more generally as a tool for understanding the role of vector or reservoir host abundance in predicting spatial variation in the risk of human disease.