<p>Over the past several decades, decision-making research has been dominated by the study of binary choice tasks, with key models assuming that people remain equally cautious regardless of how long they have spent on the choice problem. Recent research has begun to place a greater focus on studying tasks with a continuous-response scale, as well as models that allow for decreases in caution over decision time; however, these research topics have remained separate from one another. For instance, proposed models of continuous-response scales have assumed constant caution over time, and studies investigating whether caution decreases over time have focused on binary choice tasks. One reason for this separation is the lack of methodology for estimating the parameters of the decision models with time-dependent parameters for continuous responses. This paper aims to provide a stable and efficient parameter estimation technique for hyper-spherical diffusion models with a time-dependent threshold. Here, we propose an integral equation method for estimating the first-passage time distribution of hyper-spherical diffusion models. We assessed the robustness of our method through parameter recovery studies for constant and time-dependent threshold models, with our results demonstrating efficient and precise estimates for the parameters in both situations.</p>