Examining the Model Fit of Quantum Random Walk Model on Simulated Reasoning Response Times

The discrete state Quantum Random Walk (QRW) model of confidence accumulation has been widely studied to model the response times of fast decision tasks (Busemeyer et. al., 2019). Also, the Quantum probability-based model of response accuracy has been studied to model the response choices in a reasoning task (Trueblood & Busemeyer, 2012). However, QRW has not been widely studied to model the response times of reasoning tasks, which may range up to tens of seconds. Hence, the current simulation study evaluated the model fit of QRW on simulated reasoning response times. A discrete state discrete time Markov random walk model was utilized to approximate four within-trial confidence accumulation patterns, typically observed in meta-reasoning studies (Ackerman & Thompson, 2017), resulting in fast to slow response times (Malaiya, in press). Then, QRW was implemented using the Python computational package – JAX. Then, for each of the simulated reasoning response time datasets, the MCMC - No-U-Turn sampling method was utilized to sample from the posterior distribution of the drift rate and diffusion rate parameters of QRW. The convergence of MCMC chains was examined using the Gelman-Rubin R metric and Effective Sample Size. Then, to examine the validity of the fitted QRW, response times were sampled, with replacement, from the fitted QRW, weighted by the likelihood calculated using each posterior sample. Then statistics, such as the mean, of these sampled response times were compared with those of the simulated response times (used to fit QRW).