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

The Lévy Flight Model (LFM; Voss et al., 2019) modifies the Diffusion Decision Model (DDM; Ratcliff, 1978) by integrating a heavy-tailed noise distribution into evidence accumulation. Initial results suggest that the LFM may offer a more accurate representation of the true cognitive process. 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 from an LFM are analyzed with the DDM. To this end, 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 a notable underestimation of boundary separation and non-decision time when fitted to LFM data. The full DDM significantly overestimated inter-trial variabilities in starting point and non-decision time, while it still underestimating boundary separation. In conclusion, our results suggest that DDM-based analyses may lead to biased results when the true data-generating process is more accurately captured by a LFM. Implications for previous findings are discussed.