The Remote Associates Test (RAT) is a word association retrieval task that consists of a series of problems, each with three seemingly unrelated prompt words. The subject is asked to produce a single word that is related to all three prompt words. In this paper, we provide support for a theory in which the RAT assesses a person's ability to retrieve relevant word associations from long-term memory. We present a computational model of humans solving the RAT and investigate how prior knowledge and memory retrieval mechanisms influence the model's ability to match human behavior. We expand prior modeling attempts by investigating multiple large knowledge bases and by creating a cognitive process model that uses long-term memory spreading activation retrieval processes inspired by ACT-R and implemented in Soar. We evaluate multiple model variants for their ability to model human problem difficulty, including the incorporation of noise and base-level activation into memory retrieval. We conclude that the main factors affecting human difficulty are the existence of associations between prompt words and solutions, the relative strengths and directions of those associations compared to associations to other words, and the ability to perform multiple retrievals.