Modeling reaction time and accuracy of multiple-alternative decisions

Abstract

246Perceptual decision making is an area of research that has received a great deal of attention over the last 10 years or so. In psychology, it has been investigated with a range of approaches, from experimental to theoretical (Bogacz, Usher, Zhang, & McClelland, 2007;Ratcliff & Rouder, 1998;Ratcliff, Van Zandt, & McKoon, 1999;P. L. Smith, 1995;P. L. Smith & Ratcliff, 2009;P. L. Smith, Ratcliff, & Wolfgang, 2004;Usher & McClelland, 2001), and it has been studied with combined theoretical and empirical approaches in neuroscience (Gold & Shadlen, 2000;Newsome, Britten, & Movshon, 1989;Salzman & Newsome, 1994;Shadlen & Newsome, 2001;Supèr, Spekreijse, & Lamme, 2001). In most research to date, the focus has been on the two-choice experimental paradigm (e.g., Ratcliff & Rouder, 1998). There has also been an accumulating body of research that has taken models of processing and extended them to multiple-choice paradigms (Bogacz et al., 2007;McMillen & Holmes, 2006;Usher & McClelland, 2004;Usher, Olami, & McClelland, 2002). But to this point in time, there have been relatively few combined experimental and theoretical studies of multiplealternative perceptual decision making. Our aim in this article is to address the lack of such studies by presenting an experiment and comprehensive theoretical analyses. 1 The growing consensus in the perceptual-decisionmaking domain is that only models that assume that evidence is gradually accumulated over time can account for the full range of experimental data-namely, accuracy and both correct and error reaction time (RT) distributions.Two variants of this general class are the Wiener diffusion process model (Ratcliff, 1978(Ratcliff, , 2002Ratcliff & McKoon, 2008;Ratcliff & Rouder, 2000) and the multiple racing diffusion processes model (Ratcliff, 2006;P. L. Smith, 2000;Usher & McClelland, 2001). In the standard diffusion process, evidence is accumulated in a single variable toward one of two decision criteria. This model is difficult to extend to multiple alternatives, although Laming (1968) and Pike (1966), for example, have offered qualitative suggestions. The model that seems most natural for the multiple-alternative paradigm assumes that evidence is accumulated in separate accumulators, corresponding to the different alternatives. In particular, the model that best exemplifies the set of features we wish to test is the leaky competing accumulator (LCA; Usher & McClelland, 2001). This model assumes that stochastic accumulation of information occurs continuously over time, with leakage (decay) and lateral inhibition (competition among accumulators), with the possibility of variability in both starting point and the drift rates driving the accumulation process. The LCA model, however, has been fit to relatively few experimental data sets.The general evidence accumulation model has been applied to a number of domains, from neurophysiological data to cognitive tasks such as memory, lexical processing, and absolute identification, to aging and impaired processing, and to consumer de...

Multialternative drift-diffusion model predicts the relationship between visual fixations and choice in value-based decisions

“…This gives rise to a large number of possible model permutations, and thus to a difficult problem of model comparison (5,27). From this viewpoint, it is remarkable that a simple extension of the binary case without the additional mechanisms was able to account for the experimental data with good quantitative accuracy using the previously identified parameters.…”

“…Even in the binary choice case, there are many variations to the DDM that have been proposed in the literature (9,17,27,42). This gives rise to a large number of possible model permutations, and thus to a difficult problem of model comparison (5,27).…”

“…The DDM has also been shown to provide highly accurate descriptions of accuracy and response times in domains such as memory retrieval and decision-making, where the stimuli are not explicitly stochastic (17,19,20,(22)(23)(24)(25)(26)(27)(28); this suggests that these decisions might be made using a similar process of random information accumulation and integration. To see why, consider the case of binary value-based choice.…”

“…The question is difficult because a large number of possible extensions with significantly different behavioral and neurobiological properties are possible (5,27,(30)(31)(32)(33)(34). Furthermore, the optimal statistical test associated with the case of multiple alternatives is unknown, and only approximations have been proposed (32,33).…”

A comparison of two diffusion process models in accounting for payoff and stimulus frequency manipulations

“…They show that the diffusion model and the two-stage model performed similarly well in capturing the data pattern, especially for correct responses. This type of mimicking between competitive models has been reported and discussed elsewhere (e.g., Ashby & Townsend, 1980;Leite & Ratcliff, 2010;Ratcliff & Smith, 2004), although the models I tested did not mimic one another in all instances, particularly not among error responses or at the extreme ends of the correct-RT distributions (i.e., .1 and .9 quantiles).…”