Simple reaction time and statistical facilitation: A parallel grains model☆
Introduction
Ample neurophysiological data indicate that the feed-forward coding of incoming sensory information (e.g., Delorme, Richard, & Fabre-Thorpe, 2000; Fabre-Thorpe, Delorme, Marlot, & Thorpe, 2001) is massively parallel. For one thing, largely separate neural systems simultaneously code auditory, visual, and tactile stimuli (e.g., Martin, 1991). In addition, parallel subsystems code different attributes within each sensory modality, as exemplified by the separate coding of form, color, and motion within the visual system (e.g., Kandel, 1991). Finally, parallel processing is the rule even within specific neural subsystems; even a small visual stimulus, for example, influences the activities of many neurons in primary visual cortex (e.g., [Hubel and Wiesel, 1959], [Hubel and Wiesel, 1962]; Wässle, Grunert, Rohrenbeck, & Boygott, 1990), and analogous effects seem to be present in the auditory system (Rauschecker, 1998).
Neurophysiological data also suggest that the parallel representation of sensory information may be maintained even to the level at which sensorimotor connections are made. The motor cortical areas accept inputs in parallel from a variety of areas that are themselves driven by sensory systems (e.g., thalamus; Ghez, 1991). Indeed, the primary motor cortex may even accept inputs directly from various sensory areas, because the activity of some of its neurons is time-locked better to stimulus onset than to motor responding (Requin, Riehle, & Seal, 1992).
The possibility of parallel pathways from the sensory systems to the motor system has important implications for modeling of simple reaction time (RT) tasks. When the observer must initiate the response as quickly as possible following the detection of any stimulus onset, the reaction process may be conceived of as a race between different parallel sensory inputs to the motor system, with response latency determined by the fastest racer or perhaps the fastest group of racers.
Raab, 1962b was the first to propose a race model for simple RT, suggesting that a race could explain the redundant signals effect (RSE) observed in divided-attention tasks. When the observer must make the same speeded response to either a visual signal or an auditory one, for example, mean RT is less when both signals are presented (redundant signals) than when only one is presented. In Raab’s model, the decision to respond was made when either the visual or the auditory signal was detected, so a single racer was assumed to include all of the information from a single stimulus. The latencies of the visual and auditory detection processes were random variables with overlapping probability distributions. Responses to redundant signals were especially fast because the decision was determined by the winner of a race between the two separate detection processes. With overlapping distributions of finishing times, the laws of probability dictate that the faster of two racers finishes in less time, on average, than either of the individual racers.1 Thus, Raab suggested the label “statistical facilitation” for this explanation of the RSE.
Raab’s, 1962b analysis of statistical facilitation has been extremely influential in the study of the RSE. As is discussed further later, there has been considerable work aimed at deriving and testing quantitative predictions of Raab’s model (e.g., [Colonius, 1986], [Colonius, 1987], [Colonius, 1988]; Diederich, 1992; Miller, 1982b; Mordkoff & Yantis, 1991; Townsend & Nozawa, 1995; Ulrich & Giray, 1986; Ulrich & Miller, 1997). In addition, there have been attempts to modify the race model so that it can be reconciled with contradictory findings (e.g., Mordkoff & Yantis, 1991). For the present purposes, however, there are two important limitations of Raab’s model. First, it has been applied only to the RSE observed in divided-attention tasks. The available physiological evidence for parallel coding suggests that the concept of statistical facilitation could be applied much more widely than this. Second, each stimulus is represented by a single racer, as noted earlier.2 The assumption of a single racer per stimulus simplifies the mathematical analysis and it has also been made in other race models of sensory and perceptual detection processes (e.g., [Bundesen, 1987], [Bundesen, 1990]). Nonetheless, it seems inconsistent with evidence that each stimulus activates multiple parallel codes. The purpose of the present article is to propose a more general race model for simple RT with neither of these limitations; we show that the race mechanism could explain a number of phenomena within simple RT, given the reasonable assumption that each stimulus activates a number of codes in parallel.
In view of the massively parallel nature of sensory processing, it is perhaps surprising that models of simple RT have not given more emphasis to race processes and statistical facilitation. In choice RT tasks, these concepts have been used to model not only perceptual processes (e.g., Bundesen, 1987; Van der Heijden, 1981), but also cognitive processes (e.g., Kounios, Osman, & Meyer, 1987; Logan & Cowan, 1984; Meyer, Irwin, Osman, & Kounios, 1988; Ruthruff, 1996), memory processes (e.g., Logan, 1988; Townsend & Ashby, 1983; Vorberg & Ulrich, 1987), and motor processes (e.g., Osman, Kornblum, & Meyer, 1986; Ulrich & Wing, 1991). In the literature on simple RT, however, most models of sensory detection latencies have postulated a single channel within which evidence accumulates (but see Burbeck & Luce, 1982; Rouder, 2000, and Smith, 1995, for two-channel models).
The present article develops a general framework for the analysis of simple RT tasks, emphasizing the concepts of race processes and statistical facilitation. This framework borrows from previous detection latency models the basic idea of a noisy evidence accumulation process. The framework departs from earlier approaches, however, in that it allows each stimulus to activate multiple codes or grains in parallel, and it views the detection process as a race between these grains. Each grain is assumed to represent the concerted activity of a large number of neurons, as does a unit in a neural network model (e.g., Rumelhart & McClelland, 1982). Thus, different grains can be regarded either as qualitatively different information codes (e.g., [Miller, 1982a], [Miller, 1988]; Treisman, 1988), as detectors of different types of stimulus features (e.g., Burbeck & Luce, 1982; Estes, 1950), or as separate packets of activation (e.g., Anderson, 1977; McClelland, 1979).
Within this framework, we develop a specific model that can explain various detection latency phenomena previously modeled in isolation from one another, if at all. For example, it is well established that simple RT decreases with increases in the size, brightness, or duration of a visual stimulus. We will show that a relatively simple set of core assumptions involving race processes provides a framework within which statistical facilitation can provide a unified explanation of these and other phenomena.
Section snippets
The Parallel Grains Model (PGM)
In this section, we describe the assumptions of PGM and develop it as a framework within which to explain various simple RT phenomena in later sections. The primary goal of this section is to derive the predicted mean RT. This derivation proceeds in three steps: (a) present the assumptions of the model; (b) analyze the distribution of each grain’s arrival time at a decision center; (c) show how the mean RT can be obtained from the joint effects of all grains.
Effects of stimulus area
In simple RT tasks, participants respond faster to large visual stimuli than to small ones. This effect of stimulus area on mean RT was first noted by Froeberg, 1907 (discussed in Woodworth & Schlosberg, 1954). Within PGM, the area effect is easily explained in terms of statistical facilitation. Given what is known about the spatiotopic mapping within the visual system (e.g., Cowey, 1979; Daniel & Whitteridge, 1961), it is quite natural to suppose that a larger stimulus can potentially activate
Effects of stimulus duration
Just as people respond faster to larger stimuli, they respond faster to stimuli of longer durations (Froeberg, 1907, discussed in Woodworth & Schlosberg, 1954), with simple RT decreasing to an asymptote at durations of approximately 50 ms or even less ([Hildreth, 1973], [Hildreth, 1979]; Mansfield, 1973; Raab, 1962a; Ulrich, Rinkenauer, & Miller, 1998). As was true of the area effect, PGM can again account for the duration effect in terms of statistical facilitation. Within the model, an
Criterion effects
So far, we have shown how PGM can account for effects of stimulus variables (i.e., area, intensity, and duration) on simple RT. In all of these cases, the experimental manipulation would be expected to affect the process of activating grains within PGM, and the phenomena seem fully explained by statistical facilitation. In addition, however, the literature on simple RT provides ample evidence for instructional effects that are not attributable to stimulus-driven processes (e.g., Henderson, 1970
The redundant signals effect
PGM also offers a simple framework within which to account for a somewhat more complicated simple RT phenomenon called the “redundant signals effect” (RSE). The RSE is observed in divided-attention tasks; in bimodal versions of these tasks, for example, participants are asked to make a speeded response to either an auditory signal, a visual signal, or both. In single-signal trials, only one signal is presented, whereas on redundant-signals trials both are presented at the same or nearly the
Differential effects of stimulus intensity on perceptual latency and RT
Several researchers have found that stimulus intensity has larger effects on simple RT than on measures of perceptual latency obtained in temporal-order judgment tasks (Menendez & Lit, 1983; Roufs, 1974; Sanford, 1974). For example, Sanford, 1974 measured perceptual latencies to tones of varying intensities. Participants watched a pointer revolving around a clock face and reported the location of the pointer at the perceived onset of the tone. The latency of tone perception (PL) was estimated
Reaction time distributions
Having established that PGM can account for a range of experimental effects observed in simple RT tasks, in this section we examine the model in more detail to see whether its predicted RT distributions are generally consistent with known properties of observed RT distributions.
To be regarded as plausible, any model of simple RT must reproduce two main properties found in virtually all analyses of RT distributions. First, the standard deviations of observed RT distributions always increase with
General discussion
The basic framework of PGM involves a set of parallel grains, each of which can potentially be activated by a stimulus and contribute its activation toward the response. The latencies associated with each individual grain are quite noisy, with random fluctuations in both the time required for it to become active and the time required for its activation to reach the decision center responsible for initiating the response. In fact, with brief stimuli an available grain may not become active at
Conclusions
In this article we have developed a model in which stimuli activate a number of parallel grains, and detection occurs when a sufficient number of these grains reach a decision center. Within this framework, we have shown how Raab’s, 1962b principle of statistical facilitation can explain various phenomena of simple RTs, including effects and interactions of stimulus intensity, duration, and area, and coactivation effects. Statistical facilitation provides a coherent conceptual account of these
Acknowledgements
This work was supported by cooperative research funds from the Deutsche Raum- und Luftfahrtgesellschaft e.V. and the New Zealand Ministry of Research, Science, and Technology. We thank Claude Bonnet for providing the observed median RTs in Fig. 4, Gordon Logan, Philip L. Smith, Marius Usher, and two anonymous reviewers for helpful comments on earlier versions of the manuscript, and Allen Osman for helpful discussions.
References (154)
- et al.
Response time distributions in memory scanning
Journal of Mathematical Psychology
(1993) - et al.
Effects of spatial configuration on contrast detection
Vision Research
(1998) - et al.
Parallel versus serial processing: New vistas on the distributed organization of the visual system
Current Opinion in Neurobiology
(1995) Possibly dependent probability summation of reaction time
Journal of Mathematical Psychology
(1990)- et al.
Ultra-rapid categorisation of natural scenes does not rely on colour cues: A study in monkeys and humans
Vision Research
(2000) Intersensory facilitation of reaction time: Evaluation of counter and diffusion coactivation models
Journal of Mathematical Psychology
(1995)- et al.
The functional area for summation to threshold for sinusoidal gratings
Vision Research
(1978) The relative judgment theory of two choice response time
Journal of Mathematical Psychology
(1975)Latency functions in human vision
Vision Research
(1973)- et al.
Implicit redundant-targets effect in visual extinction
Neuropsychologia
(1996)
Spatial summation across the vertical meridian in hemianopics: A test of blindsight
Neuropsychologia
The general-gamma distribution and reaction times
Journal of Mathematical Psychology
The motor system in simple reaction time experiments
Acta Psychologica
Divided attention: Evidence for coactivation with redundant signals
Cognitive Psychology
Discrete and continuous models of human information processing: Theoretical distinctions and empirical results
Acta Psychologica
Visuo-spatial neural response interactions in early cortical processing during a simple reaction time task: A high-density electrical mapping study
Neuropsychologia
Neural models with cognitive implications
Spatial summation properties of directionally selective mechanisms in human vision
Journal of the Optical Society of America
Input–output relations in simple reaction time experiments
Quarterly Journal of Experimental Psychology
Deriving exact predictions from the cascade model
Psychological Review
Subitizing: Magical numbers or mere superstition
Psychological Research
Statistical theory of reliability and life testing: Probability models
Reaction time studies of sensory magnitude and perceptual processing
Psychologica
Reaction time and visual area: Searching for the determinants
Bulletin of the Psychonomic Society
Implications of sustained and transient channels for theories of visual pattern masking, saccadic suppression, and information processing
Psychological Review
Visual attention: Race models for selection from multielement displays
Psychological Research
A theory of visual attention
Psychological Review
Scientific research I: The search for system
Evidence from auditory simple reaction times for both change and level detectors
Perception & Psychophysics
Measuring channel dependence in separate activation models
Perception & Psychophysics
Modeling dependent processing in reaction time analysis
Modeling the redundant signals effect by specifying the hazard function
Perception & Psychophysics
Activation-state representation of models for the redundant-signals-effect
Interhemispheric neural summation in the absence of the corpus callosum
Brain
Cortical maps and visual perception: The Grindley Memorial Lecture
Quarterly Journal of Experimental Psychology
The representation of the visual field on the cerebral cortex of the monkey
Journal of Physiology
Intersensory facilitation
Intersensory facilitation in the motor component? A reaction time analysis
Psychological Research
Grice-representability of response time distribution families
Psychometrika
Toward a statistical theory of learning
Psychological Review
Finite mixture distributions
A limit to the speed of processing in ultra-rapid visual categorization of novel natural scenes
Journal of Cognitive Neuroscience
The relation between magnitude of the stimulus and the time of the reaction
Archives of Psychology NY
Voluntary movement
On the nature of intersensory facilitation of reaction time
Perception & Psychophysics
Motor coactivation revealed by response force in divided and focused attention
Journal of Experimental Psychology: Human Perception and Performance
Pre- and post-stimulus activation of response channels: A psychophysiological analysis
Journal of Experimental Psychology: Human Perception and Performance
Introduction to matrices with applications in statistics
Speed-accuracy trade off in auditory detection
Cited by (0)
- ☆
The order of authorship was decided by a coin toss.