Vector-space models of semantics represent words as continuously-valued vectors and measure similarity based on the distance or angle between those vectors. Such representations have become increasingly popular due to the recent development of methods that allow them to be efficiently estimated from very large amounts of data. However, the idea of relating similarity to distance in a spatial representation has been criticized by cognitive scientists, as human similarity judgments have many properties that are inconsistent with the geometric constraints that a distance metric must obey. We show that two popular vector-space models, Word2Vec and GloVe, are unable to capture certain critical aspects of human word association data as a consequence of these constraints. However, a probabilistic topic model estimated from a relatively small curated corpus qualitatively reproduces the asymmetric patterns seen in the human data. We also demonstrate that a simple co-occurrence frequency performs similarly to reduced-dimensionality vector-space models on medium-size corpora, at least for relatively frequent words.