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

Area of Science:

• Cognitive Psychology
• Computational Neuroscience
• Decision Science

Background:

• The Lévy-flight model (LFM) enhances the diffusion decision model (DDM) by incorporating heavy-tailed noise in evidence accumulation.
• Previous research suggests the LFM may more accurately represent binary decision-making processes than the standard DDM.
• Analyzing data generated by the LFM using the classical DDM could lead to misinterpretations of underlying cognitive mechanisms.

Purpose of the Study:

• To investigate estimation biases when analyzing Lévy-flight model (LFM) data with the diffusion decision model (DDM).
• To compare the performance of neural network-based inference and Markov chain Monte Carlo (MCMC) for parameter estimation.
• To evaluate model performance on experimental data with manipulated speed and accuracy demands.

Main Methods:

• Extensive simulations were conducted using both basic and full versions of the DDM and LFM.
• Cross-fitting via simulation-based inference with neural networks (BayesFlow framework) was employed.
• A Markov chain Monte Carlo (MCMC) approach served as a benchmark for neural network estimates.

Main Results:

• Neural networks and MCMC showed comparable estimation performance for the basic DDM.
• The basic DDM systematically overestimated boundary separation and underestimated non-decision time for LFM-generated data.
• The full DDM exhibited overestimation of boundary separation and inter-trial variabilities in starting point and non-decision time.

Conclusions:

• DDM analyses can introduce significant biases when the underlying data-generating process is better described by the LFM.
• Despite simulation biases, both DDM and LFM provided convergent interpretations when applied to experimental data.
• The stability parameter ($\alpha$) in the LFM showed condition-specific differences in the experimental task.