Comparing fixed and collapsing boundary versions of the diffusion model

Abstract

Optimality studies and studies of decision-making in monkeys have been used to support a model in which the decision boundaries used to evaluate evidence collapse over time. This article investigates whether a diffusion model with collapsing boundaries provides a better account of human data than a model with fixed boundaries. We compared the models using data from four new numerosity discrimination experiments and two previously published motion discrimination experiments. When model selection was based on BIC values, the fixed boundary model was preferred over the collapsing boundary model for all of the experiments. When model selection was carried out using a parametric bootstrap cross-fitting method (PBCM), which takes into account the flexibility of the alternative models and the ability of one model to account for data from another model, data from 5 of 6 experiments favored either fixed boundaries or boundaries with only negligible collapse. We found that the collapsing boundary model produces response times distributions with the same shape as those produced by the fixed boundary model and that its parameters were not well-identified and were difficult to recover from data. Furthermore, the estimated boundaries of the best-fitting collapsing boundary model were relatively flat and very similar to those of the fixed-boundary model. Overall, a diffusion model with decision boundaries that converge over time does not provide an improvement over the standard diffusion model for our tasks with human data.

Global gain modulation generates time-dependent urgency during perceptual choice in humans

“…Recent studies that applied quantitative model comparison techniques to multiple behavioural datasets provided some support for the presence of a time-dependent influence on the decision process of highly-trained monkeys, but little evidence for time-dependency in mostly naïve human subjects1531. By contrast, we observed clear support for model variants with strong time-dependency in humans that, aside from brief initial training sessions, had no prior experience with the imperative task.…”

“…While these findings have illuminated the mechanistic basis of SAT regulation in non-human primates, time-invariance remains a dominant assumption in the human decision-making literature10 and recent empirical and model comparison reports have reinforced this stance15293031. Moreover, even in non-human primates, little is known about the neurophysiological source of urgency.…”

Multifaceted adaptation of the neural decision process with prior knowledge of time constraints and stimulus probability

“…Such a collapsing-bound scheme has been established in theoretical work to be optimal when sensory discriminability varies across trials (Malhotra et al 2018;Moran 2015), when there is a cost to continued accumulation (Drugowitsch et al 2012;Boehm et al 2019), or when missed deadlines are penalised (Frazier and Yu 2008). Yet, behavioral modelling evidence is extremely mixed as to whether human subjects actually collapse their decision bounds in practice (Malhotra et al 2017;Evans and Hawkins 2019;Palestro et al 2018), with several recent studies that performed formal model comparisons clearly favouring standard constant-bound models (Hawkins et al 2015;Voskuilen et al 2016). In fact, definitively establishing the role of collapsing bounds based solely on behavioural modelling is highly challenging because one of its primary qualitative expressions -increased error rates on trials with longer RTs -can be alternatively produced with increased between-trial drift rate variability , and many collapsing bound models suffer from identifiability issues due to a lack of constraints .…”

An overcomplete approach to fitting drift-diffusion decision models to trial-by-trial data

“…Fitting DDMs to trial-by-trial RT data (JD, 07-2019) Recall that recent extensions of vanilla DDMs include e.g., collapsing bounds (Hawkins et al, 2015;Voskuilen et al, 2016) or nonlinear transformations of the state-space (Tajima et al, 2016). Although we did not consider these variants of the DDM model, we would argue that most of these effectively reduce to a simple modification of the self-consistency equation.…”