Investigating the potential psychological significance of the alpha parameter in the Lévy flight model of decision making: A reliability analysis approach

This study critically examines the cognitive and theoretical foundations of the alpha parameter within the Lévy flight model (LFM), an extension of the diffusion decision model (DDM) that incorporates heavy-tailed noise distributions. The alpha parameter, which modulates the tail of these distributions, is assessed for its test-retest reliability - an essential criterion for its classification as a cognitive style measure. Utilizing data from three previous studies, we observed that alpha demonstrates consistent reliability across tasks and time points, supporting its role as a trait-like characteristic. Our observation regarding the interrelations between LFM parameters showed that although most parameters exhibited weak correlations, reflecting their representation of distinct aspects of data, moderate correlations were observed between alpha and both threshold and non-decision time. Furthermore, investigating practice effects, we observed consistent reductions in non-decision time, threshold, and often alpha across sessions, accompanied by a corresponding increase in drift rate in demanding tasks. Notably, alpha showed a strong relationship with the mean reaction time of error responses, indicating its critical role in explaining fast error responses. Additionally, our examination of the predicted decision-time distribution found that lower alpha values correspond to shorter response times in the first quartile of both correct and error responses, highlighting its impact on capturing the dynamics of fast decision-making. Employing the BayesFlow framework for parameter estimation, we evaluated its precision across varying trial counts. These findings offer insights for future research on LFM and similar models.