Lévy Versus Wiener: Assessing the Effects of Model Misspecification on Diffusion Model Parameters

The Lévy-flight model (LFM; Voss et al., Psychonomic Bulletin & Review, 26, 813-832, 2019) modifies the diffusion decision model (DDM; Ratcliff, Psychological Review, 85(2), 59, 1978) by integrating a heavy-tailed noise distribution into evidence accumulation. Initial studies suggest that the LFM can competitively fit human response time distributions. Consequently, they argued that the LFM may reflect the binary decision process more faithfully. If this is the case, analyzing data with a classical DDM may misrepresent the underlying latent processes. In the present study, we explore the estimation biases that arise when data conforming to an LFM are analyzed with the DDM. We conducted extensive simulations using both basic and full versions of the DDM and the LFM, employing cross-fitting through simulation-based inference with neural networks as implemented in the BayesFlow framework. Given the susceptibility of neural networks to misspecification, we additionally employ a Markov chain Monte Carlo (MCMC) approach as a benchmark for the neural estimates. Our results demonstrate that neural networks and MCMC exhibited nearly identical estimation performance for the basic DDM. Importantly, the basic DDM showed notable overestimation of boundary separation and underestimation of non-decision time when fitted to data generated by the LFM. The full DDM significantly overestimated inter-trial variabilities in starting point and non-decision time, while still overestimating boundary separation. Subsequently, we applied the models to experimental data from a task incorporating speed and accuracy manipulations. Both models reflected the expected effects of the experimental manipulation on boundary separation and non-decision time, additionally, the stability parameter $\alpha$ differed between conditions in the LFM. In conclusion, while our simulations indicate that DDM-based analyses may introduce biases when the true data-generating process aligns more closely with the LFM, applying both models to experimental data led to convergent interpretations.