Gap-acceptance at roundabout entries is a safety-critical driver behavior with direct implications for intersection capacity analysis, microscopic traffic simulation, and the development of autonomous driving systems. Existing models either treat the decision as a static threshold comparison, limiting their ability to capture behavioral heterogeneity and context dependence, or rely on data-driven methods that achieve strong predictive performance at the cost of interpretability and mechanistic insight. This study proposes a unified behavioral framework that couples cumulative prospect theory (CPT) with the drift diffusion model (DDM) for gap-acceptance decisions at roundabout entries. The CPT module translates observable traffic states into a time-varying subjective value difference between entering and waiting, capturing loss aversion and probability distortion as systematic features of driver risk perception. This value difference drives the drift rate of the DDM module, in which entry commitment accumulates stochastically over time until accumulated evidence reaches the decision boundary. A simulation-based maximum likelihood (SML) estimator combined with a differential evolution (DE) optimizer jointly identifies all five model parameters from naturalistic trajectory data, with gaps that expire without entry treated as right-censored observations from a survival perspective. The framework is evaluated on the Citysim trajectory dataset against five baseline models spanning four established modelling paradigms. Results show that the proposed framework achieves superior performance in both gap decision behavior prediction and entry timing prediction across all distance windows, with an accuracy of 87.83% and a Hit@1.0s of 88.0% at the full 30–0 m window. The estimated parameters reveal that drivers at roundabout entries exhibit substantially higher loss aversion and stronger probability distortion than general behavioral economics benchmarks, and the framework reproduces the hesitation-then-commit kinematic signature observed in naturalistic driving data, providing mechanistic insights that purely predictive models cannot offer.