Modeling reaction time and accuracy of multiple-alternative decisions by ProQuest


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									Attention, Perception, & Psychophysics
2010, 72 (1), 246-273

                           Modeling reaction time and accuracy
                            of multiple-alternative decisions
                                                             Fábio P. Leite
                                                    Ohio State University, Lima, Ohio

                                                           RogeR RatcLiFF
                                                 Ohio State University, Columbus, Ohio

                Several sequential­sampling models using racing diffusion processes for multiple­alternative decisions were
             evaluated, using data from two perceptual discrimination experiments. The structures of the models differed on
             a number of dimensions, including whether there was lateral inhibition between accumulators, whether there
             was decay in evidence, whether evidence could be negative, and whether there was variability in starting points.
             Data were collected from a letter discrimination task in which stimulus difficulty and probability of the response
             alternatives were varied along with number of response alternatives. Model­fitting results ruled out a large
             number of model classes in favor of a smaller number of specific models, most of which showed a moderate to
             high degree of mimicking. The best­fitting models had zero to moderate values of decay, had no inhibition, and
             assumed that the addition of alternatives affected the subprocesses contributing to the nondecisional time, the
             degree of caution, or the quality of evidence extracted from stimuli.

   Perceptual decision making is an area of research that               Two variants of this general class are the Wiener diffusion
has received a great deal of attention over the last 10 years           process model (Ratcliff, 1978, 2002; Ratcliff & McKoon,
or so. In psychology, it has been investigated with a range             2008; Ratcliff & Rouder, 2000) and the multiple racing
of approaches, from experimental to theoretical (Bogacz,                diffusion processes model (Ratcliff, 2006; P. L. Smith,
Usher, Zhang, & McClelland, 2007; Ratcliff & Rouder,                    2000; Usher & McClelland, 2001). In the standard diffu­
1998; Ratcliff, Van Zandt, & McKoon, 1999; P. L. Smith,                 sion process, evidence is accumulated in a single variable
1995; P. L. Smith & Ratcliff, 2009; P. L. Smith, Ratcliff,              toward one of two decision criteria. This model is diffi­
& Wolfgang, 2004; Usher & McClelland, 2001), and it                     cult to extend to multiple alternatives, although Laming
has been studied with combined theoretical and empirical                (1968) and Pike (1966), for example, have offered quali­
approaches in neuroscience (Gold & Shadlen, 2000; New­                  tative suggestions. The model that seems most natural for
some, Britten, & Movshon, 1989; Salzman & Newsome,                      the multiple­alternative paradigm assumes that evidence
1994; Shadlen & Newsome, 2001; Supèr, Spekreijse, &                     is accumulated in separate accumulators, corresponding
Lamme, 2001). In most research to date, the focus has                   to the different alternatives. In particular, the model that
been on the two­choice experimental paradigm (e.g., Rat­                best exemplifies the set of features we wish to test is the
cliff & Rouder, 1998). There has also been an accumulat­                leaky competing accumulator (LCA; Usher & McClel­
ing body of research that has taken models of processing                land, 2001). This model assumes that stochastic accumu­
and extended them to multiple­choice paradigms (Bogacz                  lation of information occurs continuously over time, with
et al., 2007; McMillen & Holmes, 2006; Usher & Mc­                      leakage (decay) and lateral inhibition (competition among
Clelland, 2004; Usher, Olami, & McClelland, 2002). But                  accumulators), with the possibility of variability in both
to this point in time, there have been relatively few com­              starting point and the drift rates driving the accumulation
bined experimental and theoretical studies of multiple­                 process. The LCA model, however, has been fit to rela­
alternative perceptual decision making. Our aim in this                 tively few experimental data sets.
article is to address the lack of such studies by presenting               The general evidence accumulation model has been
an experiment and comprehensive theoretical analyses.1                  applied to a number of domains, from neurophysiologi­
   The growing consensus in the perceptual­decision­                    cal data to cognitive tasks such as memory, lexical pro­
making domain is that only models that assume that evi­                 cessing, and absolute identification, to aging and im­
dence is gradually accumulated over time can account for                paired processing, and to consumer decision making
the full range of experimental data—namely, accuracy and                (Boucher, Palmeri, Logan, & Schall, 2007; Brown &
both correct and error reaction time (RT) distributions.                Heathcote, 2005; Brown, Marley, Donkin, & Heathcote,

                                                        F. P. Leite,

© 2010 The Psychonomic Society, Inc.                                246
                                                                       Comparison of multiChoiCe rt models                247

2008; Busemeyer & Townsend, 1993; Ditterich, 2006;              responses jointly and, so, identify the different sources
Gomez, Perea, & Ratcliff, 2007; Mazurek, Roitman, Dit­          of noise.
terich, & Shadlen, 2003; Niwa & Ditterich, 2008; Rat­              Evidence accumulation models have also been related
cliff, Cherian, & Segraves, 2003; Ratcliff, Gomez, &            to physiological measures in humans, using both func­
McKoon, 2004; Ratcliff, Hasegawa, Hasegawa, Smith, &            tional magnetic resonance imaging (f MRI) and elec­
Segraves, 2007; Ratcliff & Smith, 2004; Ratcliff, Thapar,       troencephalography (EEG). Heekeren et al. (2006), for
& McKoon, 2006; Ratcliff, Thapar, Smith, & McKoon,              example, found evidence for a decision variable existing
2005; Ratcliff & Van Dongen, 2009; Roe, Busemeyer,              independently of motor planning and execution. They had
& Townsend, 2001). One of the features of models in             participants express their decision about direction of mo­
the evidence accumulation class is that in order for them       tion using two independent motor systems, oculomotor
to successfully account for the full range of experimen­        and manual, and found that four brain regions showed an
tal data, they need to assume that various components           increased BOLD signal to high coherence (relative to low
of processing vary from trial to trial (Laming, 1968;           coherence), independent of the motor system used to ex­
Ratcliff, 1978; Ratcliff & Rouder, 1998; Ratcliff et al.,       press the decision. Philiastides, Ratcliff, and Sajda (2006),
1999). These models can be contrasted with signal de­           using a single­trial analysis of EEG data from a face–car
tection theory (SDT; Swets, Tanner, & Birdsall, 1961),          discrimination task with human participants, found sup­
in which all sources of noise are combined into a single        port for a time separation between perceptual processing
source—namely, variability in perceptual strength. For          and decision­making processing. This separation suggests
example, in the class of diffusion process models, the          that cortical networks could dynamically allocate addi­
decision process is assumed to be variable, within a            tional processing time for difficult decisions.
trial (within­trial noise) and across trials, in perceptual        In behavioral research in psychology, perceptual deci­
strength (drift rate) and starting points.                      sion making has been studied using models that make
   In neuroscience, Hanes and Schall (1996) were the first      a great deal of contact between theory and data. In par­
to convincingly argue that it is possible to relate evidence    ticular, the sequential sampling framework has been
accumulation models to single­cell recording data. They         successful in accounting for both RT and accuracy, as
suggested that rhesus monkeys’ saccadic movements were          well as speed–accuracy trade­off effects (for reviews,
initiated if and only if the neural activity in frontal eye     see Luce, 1986; Ratcliff & Smith, 2004; Vickers, Cau­
field cells surpassed a (constant) threshold and that RT        drey, & Willson, 197
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