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Cognitive neuroscientists sometimes apply formal models to investigate how the brain implements cognitive processes. These models describe behavioral data in terms of underlying, latent variables linked to hypothesized cognitive processes. A goal of model-based cognitive neuroscience is to link these variables to brain measurements, which can advance progress in both cognitive and neuroscientific research. However, the details and the philosophical approach for this linking problem can vary greatly. We propose a continuum of approaches that differ in the degree of tight, quantitative, and explicit hypothesizing. We describe this continuum using four points along it, which we dub qualitative structural, qualitative predictive, quantitative predictive, and single model linking approaches. We further illustrate by providing examples from three research fields (decision making, reinforcement learning, and symbolic …