Today’s computer vision models achieve human or near-human level performance across a wide variety of vision tasks. However, their architectures, data, and learning algorithms differ in numerous ways from those that give rise to human vision. In this paper, we investigate the factors that affect alignment between the representations learned by neural networks and human concept representations. Human representations are inferred from behavioral responses in an odd-one-out triplet task, where humans were presented with three images and had to select the odd-one-out. We find that model scale and architecture have essentially no effect on alignment with human behavioral responses, whereas the training dataset and objective function have a much larger impact. Using a sparse Bayesian model of human conceptual representations, we partition triplets by the concept that distinguishes the two similar images from the odd-one-out, finding that some concepts such as food and animals are well-represented in neural network representations whereas others such as royal or sports-related objects are not. Overall, although models trained on larger, more diverse datasets achieve better alignment with humans than models trained on ImageNet alone, our results indicate that scaling alone is unlikely to be sufficient to train neural networks with conceptual representations that match those used by humans.