Extending TVA With Trial-to-Trial Variability in Processing Speed: A Monte Carlo Simulation Study

Abstract The Theory of Visual Attention (TVA) typically treats processing speed as fixed within the modelled condition structure. This assumption may be too restrictive when effective processing speed varies from trial to trial. We introduce a variability-augmented extension of a behavioural TVA count model in which trial-to-trial fluctuations in processing speed are represented explicitly through a gamma-distributed speed parameter, while preserving the classical interpretation of processing speed ( C ), visual short-term memory capacity ( K ), and perceptual threshold ( $$t_0$$ ). A Monte Carlo simulation study evaluated both models, together with the trial-to-trial $$t_0$$ -variability model of Dyrholm et al. (2011), across whole-report scenarios with negligible, mild, moderate, and strong trial-to-trial variability in processing speed, and with variability in $$t_0$$ . The extended model improved model selection and parameter recovery under strong variability, with the advantage emerging when variability was large enough to induce systematic bias in the fixed-speed model’s estimates of C and $$t_0$$ ; under moderate variability the evidence was transitional, and with fewer trials per dataset the precision lost to the additional parameter could outweigh the bias it removed. The two forms of variability left different traces in the data and the two variability models were distinguishable: the $$t_0$$ -variability model did not register speed variability and left the bias in C in place, whereas the extended model absorbed only part of the threshold variability. These findings suggest that the proposed extension is best understood as a conditional complement to standard behavioural TVA, appropriate when notable trial-to-trial variability in processing speed is present, rather than as a universal replacement.