A hierarchical bayesian statistical framework for response time distributions

This paper provides a statistical framework for estimating higher-order characteristics of the response time distribution, such as the scale (variability) and shape. Consideration of these higher order characteristics often provides for more rigorous theory development in cognitive and perceptual psychology (e.g., Luce, 1986). RT distribution for a single participant depends on certain participant characteristics, which in turn can be thought of as arising from a distribution of latent variables. The present work focuses on the three-parameter Weibull distribution, with parameters for shape, scale, and shift (initial value). Bayesian estimation in a hierarchical framework is conceptually straightforward. Parameter estimates, both for participant quantities and population parameters, are obtained through Markov Chain Monte Carlo methods. The methods are illustrated with an application to response time data in an absolute identification task. The behavior of the Bayes estimates are compared to maximum likelihood (ML) estimates through Monte Carlo simulations. For small sample size, there is an occasional tendency for the ML estimates to be unreasonably extreme. In contrast, by borrowing strength across participants, Bayes estimation shrinks extreme estimates. The results are that the Bayes estimators are more accurate than the corresponding ML estimators.We are grateful to Michael Stadler who allowed us use of his data. This research is supported by (a) National Science Foundation Grant SES-0095919 to J. Rouder, D. Sun, and P. Speckman, (b) University of Missouri Research Board Grant 00-77 to J. Rouder, (c) National Science Foundation grant DMS-9972598 to Sun and Speckman, and (d) a grant from the Missouri Department of Conservation to D. Sun.     

Display size effects in visual search: Analyses of reaction time distributions as mixtures

In a reanalysis of data from Cousineau and Shiffrin (2004) and two new visual search experiments, we used a likelihood ratio test to examine the full distributions of reaction time (RT) for evidence that the display size effect is a mixture-type effect that occurs on only a proportion of trials, leaving RT in the remaining trials unaffected, as is predicted by serial self-terminating search models. Experiment 1 was a reanalysis of Cousineau and Shiffrin's data, for which a mixture effect had previously been established by a bimodal distribution of RTs, and the results confirmed that the likelihood ratio test could also detect this mixture. Experiment 2 applied the likelihood ratio test within a more standard visual search task with a relatively easy target/distractor discrimination, and Experiment 3 applied it within a target identification search task within the same types of stimuli. Neither of these experiments provided any evidence for the mixture-type display size effect predicted by serial self-terminating search models. Overall, these results suggest that serial self-terminating search models may generally be applicable only with relatively difficult target/distractor discriminations, and then only for some participants. In addition, they further illustrate the utility of analysing full RT distributions in addition to mean RT.     

Estimation of parameters for the Grice theory of simple reaction time

The variable-criterion theory of simple reaction times proposed by G. R. Grice is briefly summarized. Grice's method of parameter estimation is described, and it is shown how these procedures can be converted to a least-squares estimation. Finally, the likelihood function is derived from the theory, thereby permitting use of the method of maximum likelihood for estimating the Grice parameters in experiments of simple reaction times.     

A reaction time paradigm to assess (implicit) complaint-specific dysfunctional beliefs

We investigated whether an implicit association test (IAT) can be used to assess dysfunctional beliefs in the realm of psychopathology. As a first exploration we therefore constructed a IAT that was designed to differentiate between high and low social anxious individuals. Social situation and neutral words were the targets (e.g. date vs hall), and positive and negative outcomes (e.g. compliment vs rejection) the associated attributes. High social anxious women (N=32) showed the predicted deterioration of task performance if the required responses switched from compatible to incompatible with the idea that social situations are related to negative outcomes and vice versa, whereas the opposite was true for low anxious women (N=32). Thus a modified IAT seems a useful and highly flexible tool to implicitly assess complaint-specific dysfunctional associations and may be a valuable addition to the usual (explicit) self-report measures of patients' beliefs.     

A standard conceptual framework for the study of subjective time

Research on the mental representation of time (‘subjective time’) has provided broad insights into the nature of time perception and temporal processing. As the field comprises different scientific disciplines, such as psychology, philosophy, and neuroscience, studies differ with regard to the basic terms and concepts used. For this reason, research on subjective time lacks a coherent conceptual system. We argue that research in the field of subjective time should aim at establishing such a system, i.e., a more standardized terminology, in order to strengthen its theoretical basis and to support an efficient communication of results. Based on key empirical findings and concepts that are commonly (but inconsistently) used in the literature, we argue for a conceptual framework for the study of subjective time that differentiates between three types of mental representations of time: basic temporal processing, time perception in terms of passage, and time perception in terms of duration.     

A fast numerical algorithm for the estimation of diffusion model parameters

In this paper, we describe a new algorithmic approach for parameter estimation in Ratcliff's [(1978). A theory of memory retrieval. Psychological Review, 85 (2), 59-108] diffusion model. This problem, especially if inter-trial variabilities of parameters are included in the model, is computationally very expensive; the parameter estimation procedure often takes a long time even with today's high-speed computers. The algorithm described here makes the calculation of the cumulative distribution functions for predicted process durations computationally much less expensive. This improvement is achieved by solving the Kolmogorov backward equation numerically instead of employing the previously used closed form solution. Additionally, the algorithm can determine the optimum fit for one of the model parameters (the starting point z) directly, thereby reducing the dimension of the parameter search space by one. The resulting method is shown to be notably faster than the standard (closed-form solution) method for parameter estimation.     

Measuring reaction time without measuring movement time: A modification of the Hormann and Allen millisecond timer for the Commodore 64 or 128

It is frequently desirable to measure reaction time independently of movement time. The Hormann and Allen (1987) millisecond timer for the Commodore 64 or 128 can be modified to allow the measurement of reaction time with minimal movement time. A BASIC loader is provided for a keyboard version and an external switch version of the modified timer. Machine language code is provided for use with MONITOR, the machine language utility built into the Commodore 128.     

A comparison of sequential sampling models for two-choice reaction time

The authors evaluated 4 sequential sampling models for 2-choice decisions--the Wiener diffusion, Ornstein-Uhlenbeck (OU) diffusion, accumulator, and Poisson counter models--by fitting them to the response time (RT) distributions and accuracy data from 3 experiments. Each of the models was augmented with assumptions of variability across trials in the rate of accumulation of evidence from stimuli, the values of response criteria, and the value of base RT across trials. Although there was substantial model mimicry, empirical conditions were identified under which the models make discriminably different predictions. The best accounts of the data were provided by the Wiener diffusion model, the OU model with small-to-moderate decay, and the accumulator model with long-tailed (exponential) distributions of criteria, although the last was unable to produce error RTs shorter than correct RTs. The relationship between these models and 3 recent, neurally inspired models was also examined.     

A critical comparison of two random-walk models for two-choice reaction time

Two random-walk models for two-choice reaction time, being the sequential probability ratio test model initially suggested by Stone and the relative judgment theory recently proposed by Link, are here compared. The comparison shows the precise mathematical relation between the models, the predictions they have in common, and two points at which they differ. Three experiments concerned with the effect of stimulus probability on two-choice reaction time are examined with respect to three predictions from the models. In this three-way comparison the two models are more like each other than either is to the data; a greater variety of phenomena is revealed than either model can at present accommodate.     

Musicians outperform nonmusicians in magnitude estimation: Evidence of a common processing mechanism for time,space and numbers

It has been proposed that time, space, and numbers may be computed by a common magnitude system. Even though several behavioural and neuroanatomical studies have focused on this topic, the debate is still open. To date, nobody has used the individual differences for one of these domains to investigate the existence of a shared cognitive system. Musicians are known to outperform nonmusicians in temporal discrimination tasks. We therefore observed professional musicians and nonmusicians undertaking three different tasks: temporal (participants were required to estimate which of two tones lasted longer), spatial (which line was longer), and numerical discrimination (which group of dots was more numerous). If time, space, and numbers are processed by the same mechanism, it is expected that musicians will have a greater ability, even in nontemporal dimensions. As expected, musicians were more accurate with regard to temporal discrimination. They also gave better performances in both the spatial and the numerical tasks, but only outside the subitizing range. Our data are in accordance with the existence of a common magnitude system. We suggest, however, that this mechanism may not involve the whole numerical range.     

A clock pulse generator (CPG) for behavioral time research

A device is described which (1) generates very accurate time calibration tones suitable for tape recording along with experimental behaviors, and (2) creates from such a recorded tone an easy-to-read structured pulse train for oscillographic tracings. Calibration tones at 1-, 5-, and 10-kHz pulse rates are derived from a crystal oscillator module and are made available for tape recording at one output of the device. The second output produces a four-level structured pulse train in which there is one pulse for each cycle of the calibration tone (every 10th is a little larger, every 100th a little larger yet, and every 1,000th larger still). An example of the use of this device in speech, timing research is given.     

RTSYS: A DOS application for the analysis of reaction time data

RTSYS is a menu-driven DOS application for the manipulation, analysis, and graphical display of reaction time data. It can be used either in a single-task environment under DOS, with access to a set operating system commands, or as an application under Windows. All functions have context-sensitive help. RTSYS fits the ex-Gaussian distribution to reaction time data without the difficulties usually associated with numerical parameter estimation. Distribution fitting and flexible censoring and rescaling options allow RTSYS to address the problems of reaction time distribution skew and outlying responses with reasonable sample sizes. RTSYS can automatically process multiple input files from experiments with arbitrary designs and produce formatted output of statistics for further processing by graphical and inferential statistical packages. The present article reviews and explains techniques used by RTSYS and provides an overview of the operation of the program.     

A diffusion model explanation of the worst performance rule for reaction time and IQ

The worst performance rule for cognitive tasks [Coyle, T.R. (2003). IQ, the worst performance rule, and Spearman's law: A reanalysis and extension. Intelligence, 31, 567-587] in which reaction time is measured is the result that IQ scores correlate better with longer (i.e., 0.7 and 0.9 quantile) reaction times than shorter (i.e., 0.1 and 0.3 quantile) reaction times. We show that this pattern of correlations can be predicted by the diffusion model [Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59-108], in two ways: either assuming that the rate of accumulation of information toward a decision is higher for higher IQ subjects or assuming that the criterial amounts of information they require before a decision are lower. Importantly, the model explains both reaction times and accuracy, so the two possibilities can be distinguished.     

A simple framework (ASF) for behavioral and neuroimaging experiments based on the psychophysics toolbox for MATLAB

The cognitive neurosciences combine behavioral experiments with acquiring physiological data from different modalities, such as electroencephalography, magnetoencephalography, transcranial magnetic stimulation, and functional magnetic resonance imaging, all of which require excellent timing. A simple framework is proposed in which uni- and multimodal experiments can be conducted with minimal adjustments when one switches between modalities. The framework allows the beginner to quickly become productive and the expert to be flexible and not constrained by the tool by building on existing software such as MATLAB and the Psychophysics Toolbox, which already are serving a large community. The framework allows running standard experiments but also supports and facilitates exciting new possibilities for real-time neuroimaging and state-dependent stimulation.     

A new method for the estimation of the onset of the lateralized readiness potential (LRP)

The aim of this work was to develop a new method for the estimation of the onset of the lateralized readiness potential (LRP). In contrast to the known methods that use only restricted data segments for estimation, the proposed segmented regression (SR) method employs the LRP trace from the stimulus onset to the LRP peak. Comparison of the SR with two other methods, done with both simulated and real data, shows that the SR method yields a relatively unbiased absolute onset time that is not affected by different LRP gradients before and after the onset. Moreover, the SR estimator proved to be quite sensitive to subtle onset differences across conditions.     

The effect of movement amplitude and target diameter on reaction time: comments on Siegel (1977)

Siegel's (1977) interpretation that his reaction time results were solely a function of response factors (movement amplitude and target diameter) was discussed and criticized. It was argued that Siegel's interpretation was inappropriate because stimulus factors (eccentric and visual angle) and response factors were confounded. It was also argued that the surprising U-shaped relation between reaction time and movement amplitude was probably the result of the confounding between stimulus and response factors.