Diffusion models are widely-used and successful accounts of the time course of two-choice decision making. Most diffusion models assume constant boundaries, which are the threshold levels of evidence that must be sampled from a stimulus to reach a decision. We summarize theoretical results from statistics that relate distributions of decisions and response times to diffusion models with time-varying boundaries. We then develop a computational method for finding time-varying boundaries from empirical data, and apply our new method to two problems. The (...) first problem involves finding the time-varying boundaries that make diffusion models equivalent to the alternative sequential sampling class of accumulator models. The second problem involves finding the time-varying boundaries, at the individual level, that best fit empirical data for perceptual stimuli that provide equal evidence for both decision alternatives. We discuss the theoretical and modeling implications of using time-varying boundaries in diffusion models, as well as the limitations and potential of our approach to their inference. (shrink)

I provide a personal perspective on metastudies and emphasize lesser-known benefits. I stress the need for integrative theories to establish commensurability between experiments. I argue that mathematical social scientists should be engaged to develop integrative theories, and that likelihood functions provide a common mathematical framework across experiments. The development of quantitative theories promotes commensurability engineering on a larger scale.