Inference involving diversity gradients typically is gathered by mechanistic tests involving single dimensions of biodiversity such as species richness. Nonetheless, because traits such as geographic range size, trophic status or phenotypic characteristics are tied to a particular species, mechanistic effects driving broad diversity patterns should manifest across numerous dimensions of biodiversity. We develop an approach of stronger inference based on numerous dimensions of biodiversity and apply it to evaluate one such putative mechanism: the mid-domain effect (MDE). Species composition of 10,000-km2 grid cells was determined by overlaying geographic range maps of 133 noctilionoid bat taxa. We determined empirical diversity gradients in the Neotropics by calculating species richness and three indices each of phylogenetic, functional and phenetic diversity for each grid cell. We also created 1,000 simulated gradients of each examined metric of biodiversity based on a MDE model to estimate patterns expected if species distributions were randomly placed within the Neotropics. For each simulation run, we regressed the observed gradient onto the MDE-expected gradient. If a MDE drives empirical gradients, then coefficients of determination from such an analysis should be high, the intercept no different from zero and the slope no different than unity. Species richness gradients predicted by the MDE fit empirical patterns. The MDE produced strong spatially structured gradients of taxonomic, phylogenetic, functional and phenetic diversity. Nonetheless, expected values generated from the MDE for most dimensions of biodiversity exhibited poor fit to most empirical patterns. The MDE cannot account for most empirical patterns of biodiversity. Fuller understanding of latitudinal gradients will come from simultaneous examination of relative effects of random, environmental and historical mechanisms to better understand distribution and abundance of the current biota.