Purpose: Agent-based models are typically “simple-agent” models, in which agents behave according to simple rules, or “complex-agent” models which incorporate complex models of cognitive processes. I argue that there is also an important role for agent-based computer models in which agents incorporate cognitive models of moderate complexity. In particular, I argue that such models have the potential to bring insights from the humanistic study of culture into population-level modeling of cultural change. Methods: I motivate my proposal in part by describing an agent-based modeling framework, POPCO, in which agents’ communication of their simulated beliefs depends on a model of analogy processing implemented by artificial neural networks within each agent. I use POPCO to model a hypothesis about causal relations between cultural patterns proposed by Peggy Sanday. Results: In model 1, empirical patterns like those reported by Sanday emerge from the influence of analogies on agents’ communication with each other. Model 2 extends model 1 by allowing the components of a new analogy to diffuse through the population for reasons unrelated to later effects of the analogy. This illustrates a process by which novel cultural features might arise. Conclusions: The inclusion of relatively simple cognitive models in agents allows modeling population-level effects of inferential and cultural coherence relations, including symbolic cultural relationships. I argue that such models of moderate complexity can illuminate various causal relationships involving cultural patterns and cognitive processes.