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Cognitive neuroscientists use a variety of methodologies to answer difficult questions about cognitive processes. Each of these methodologies have distinctive strengths and limitations. In order to develop a comprehensive theory of a cognitive process, often disjointed findings must be integrated. Joint modeling (Palestro et al., 2018) is a framework with which these distinct modalities can be mathematically linked. Here, we propose a framework to formally specify neurally-based theories via a type of joint model called an integrative model. We use response inhibition, measured via the stop-signal task (Logan, Cowan, & Davis, 1984), as a case study, because of the extensive literature across a variety of behavioral and neural domains. Our goal is to specify a formal theory of the neural dynamics of stopping using an integrative model to test the ability of this model to reproduce major findings in the stop-signal literature. First, we provide a review of the stop-signal literature and explain how these findings inform our model. Second, we introduce two open-access stop-signal datasets, including an fMRI study (Aron & Poldrack, 2006) and an EEG study (Castiglione, Wagner, Anderson, & Aron, 2019), which provide the stimuli for our simulations. Additionally, we use the neural data to define our regions of interest. Third, we specify our integrative model and describe how a single dynamical latent state model can be used to simultaneously predict both EEG and fMRI data. Fourth, we present results from simulation studies showing the dynamics of the underlying state space, and compare the simulated results using the stimuli from both experiments to expected findings based on the literature and the observed findings of the specific experiments. We find that the simulated models are capable of capturing multiple neural signatures of successful stopping, particularly in the inferior frontal gyrus. We conclude by discussing how this framework could be improved by allowing further constraint, such as through behavior or structural data. In conclusion, integrative modeling provides a systematic way to fuse findings from distinct modalities to formally specify a unifying theory.