Sequential sampling models without random between-trial variability: the racing diffusion model of speeded decision making

Abstract

Most current sequential sampling models have random between-trial variability in their parameters. These sources of variability make the models more complex in order to fit response time data, do not provide any further explanation to how the data were generated, and have recently been criticised for allowing infinite flexibility in the models. To explore and test the need of between-trial variability parameters we develop a simple sequential sampling model of N-choice speeded decision making: the racing diffusion model. The model makes speeded decisions from a race of evidence accumulators that integrate information in a noisy fashion within a trial. The racing diffusion does not assume that any evidence accumulation process varies between trial, and so, the model provides alternative explanations of key response time phenomena, such as fast and slow error response times relative to correct response times. Overall, our paper gives good reason to rethink including between-trial variability parameters in sequential sampling models Keywords Response time • Sequential sampling models • Decision making Evidence accumulation is arguably the most dominant theory of how people make speeded decisions (see Donkin & Brown, 2018, for a review), and it is typically instantiated in sequential sampling models (e.g., Ratcliff, 1978;Usher & McClelland, 2001;. These models provide an accurate account of correct and error response time (RT) distributions as well as the corresponding accuracy rates in speeded decision making tasks. The models also allow researchers to translate the data into the meaningful psychological parameters that generate the data.Sequential sampling models assume a simple cognitive architecture consisting of stimulus encoding, response selection, and overt response execution. To make a

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“…Even considering only model-free (as opposed to model-based (Daw and Dayan, 2014)) reinforcement learning, there exists a variety of learning rules (e.g., Palminteri et al, 2015; Rescorla and Wagner, 1972; Rummery and Niranjan, 1994; Sutton, Richard, 1988), as well as the possibility of multiple learning rates for positive and negative prediction errors (Christakou et al, 2013; Daw et al, 2002; Frank et al, 2009; Gershman, 2015; Haughey et al, 2007; Niv et al, 2012), and many additional concepts, such as eligibility traces to allow for updating of previously visited states (Barto et al, 1981; Bogacz et al, 2007). Similarly, in the decision-making literature, there exists a wide range of evidence-accumulation models, including most prominently the diffusion decision model (DDM; Ratcliff, 1978; Ratcliff et al, 2016) and race models such as the linear ballistic accumulator model (LBA; Brown and Heathcote, 2008) and racing diffusion (RD) models (Boucher et al, 2007; Hawkins and Heathcote, 2020; Leite and Ratcliff, 2010; Logan et al, 2014; Purcell et al, 2010; Ratcliff et al, 2011; Tillman et al, 2020).…”

How do recall requirements affect decision-making in free recall initiation? A linear ballistic accumulator approach

“…Recently, Osth and Farrell (2019) jointly modeled serial position and complete RT distributions with two different evidence accumulation models: the LBA and racing diffusion model (Tillman, Van Zandt, & Logan, 2020) to provide novel insights into primacy and recency effects in free recall initiation. Not only did this work account for both response probabilities and latency distributions, the modeling led to several novel insights.…”

An Empirical Exploration of Fast and Slow Errors at Group and Subject Levels in Speeded Decision-making

“…Response time (RT) distributions are right skewed despite many researchers treating the data as normal. The relative speed of correct and error responses are not equal (Laming, 1968;Ratcliff, 1978;Ratcliff & Rouder, 1998;Tillman, Van Zandt, & Logan, 2020), where the error RT is either faster than the correct RT on average (i.e., fast errors) or slower than the correct RT on average (i.e., slow errors). Slow errors occur when the choice is difficult or accuracy is emphasized and fast errors occur when the choice is easy or there is pressure to decide quickly (Swensson, 1972).…”

“…The second component is between-trial starting point variability, which allows the model to predict fast errors (Laming, 1968;Smith & Vickers, 1988;Ratcliff & Rouder, 1998;Ratcliff, Van Zandt, & McKoon, 1999). Tillman et al (2020) argued that there are several issues that arise when adding in additional sources of variability. First, sequential sampling models have become increasingly complex in order to fit RT data and adding in the variability parameters involves two numerical integrations that can be computationally demanding.…”

“…Second, the between-trial variability assumptions are not part of the process model that explains how the RT data are generated. Tillman et al (2020) noted that the inclusion of between-trial variability in starting points or drift rates depended on the existence and magnitude of fast and slow errors. Yet, the exact magnitudes of fast and slow errors are rarely reported by researchers because they are usually not the focus of the experiment.…”