Time-dependent Poisson counter models of response latency in simple judgment.

An important class of sequential-sampling models for response time (RT) assumes that evidence for competing response alternatives accrues in parallel and that a response is made when the evidence total for a particular response exceeds a criterion. One member of this class of models is the Poisson counter model, in which evidence accrues in unit increments and the waiting time between increments is exponentially distributed. This paper generalizes the counter model to allow the Poisson event rate to vary with time. General expressions are obtained for the RT distributions for the two- and the m-alternative cases. Closed-form expressions are obtained for response probabilities under a proportional-rates assumption and for mean RT under conditions in which the integrated event rate increases as an arbitrary power of time. An application in the area of early vision is described, in which the Poisson event rates are proportional to the outputs of sustained and transient channels.

How to fit a response time distribution.

Among the most valuable tools in behavioral science is statistically fitting mathematical models of cognition to data--response time distributions, in particular. However, techniques for fitting distributions very widely, and little is known about the efficacy of different techniques. In this article, we assess several fitting techniques by simulating six widely cited models of response time and using the fitting procedures to recover model parameters. The techniques include the maximization of likelihood and least squares fits of the theoretical distributions to different empirical estimates of the simulated distributions. A running example is used to illustrate the different estimation and fitting procedures. The simulation studies reveal that empirical density estimates are biased even for very large sample sizes. Some fitting techniques yield more accurate and less variable parameter estimates than do others. Methods that involve least squares fits to density estimates generally yield very poor parameter estimates.

A comparison of two response time models applied to perceptual matching.

Two models, a Poisson race model and a diffusion model, are fit to data from a perceptual matching task. In each model, information about the similarity or the difference between two stimuli accumulates toward thresholds for either response. Stimulus variables are assumed to influence the rate at which information accumulates, and response variables are assumed to influence the level of the response thresholds. Three experiments were conducted to assess the performance of each model. In Experiment 1, observers performed under different response deadlines; in Experiment 2, response bias was manipulated by changing the relative frequency of same and different stimuli. In Experiment 3, stimulus pairs were presented at three eccentricities: foveal, parafoveal, and peripheral. We examined whether the race and diffusion models could fit the response time and accuracy data through changes only in response parameters (for Experiments 1 and 2) or stimulus parameters (for Experiment 3). Comparisons between the two models suggest that the race model, which has not been studied extensively, can account for perceptual matching data at least as well as the diffusion model. Furthermore, without the constraints on the parameters provided by the experimental conditions, the diffusion and the race models are indistinguishable. This finding emphasizes the importance of fitting models across several conditions and imposing logical psychological constraints on the parameters of models.

ROC curves and confidence judgements in recognition memory.

Most models of recognition memory rely on a strength/familiarity-based signal detection account that assumes that the processes giving rise to a confidence judgment are the same as those giving rise to an old-new decision. Confidence is assumed to be scaled directly from the perceived familiarity of a probe. This assumption was tested in 2 experiments that examine the shape of confidence-based z receiver operating characteristic (zROC) curves under different levels of response bias induced by changing stimulus probabilities (Experiment 1) and payoffs (Experiment 2). Changes in the shape of the zROC curves with bias indicate that confidence is not scaled directly from perceived familiarity or likelihood. A model of information accumulation in recognition memory is proposed that can account for the observed effects.

Connectionist and diffusion models of reaction time.

Two connectionist frameworks, GRAIN (J. L. McClelland, 1993) and brain-state-in-a-box (J. A. Anderson, 1991), and R. Ratcliff's (1978) diffusion model were evaluated using data from a signal detection task. Dependent variables included response probabilities, reaction times for correct and error responses, and shapes of reaction-time distributions. The diffusion model accounted for all aspects of the data, including error reaction times that had previously been a problem for all response-time models. The connectionist models accounted for many aspects of the data adequately, but each failed to a greater or lesser degree in important ways except for one model that was similar to the diffusion model. The findings advance the development of the diffusion model and show that the long tradition of reaction-time research and theory is a fertile domain for development and testing of connectionist assumptions about how decisions are generated over time.

Process dissociation, single-process theories, and recognition memory.

According to the assumptions of L. L. Jacoby's (1991) process dissociation method, performance in recognition memory is determined by the combination of an unconscious familiarity process and a conscious intentional recollection process. The process dissociation method is used to produce estimates of the contributions of the 2 components to recognition performance. This article investigates whether the method provides the correct estimates of components if performance actually depends on only a single process or on 2 processes different from those assumed by the method. The SAM model (G. Gillund & R. M. Shiffrin, 1984) was used to produce simulated data based on a single process. Variants of SAM with 2 processes and R. C. Atkinson and J. F. Juola's (1973) 2-process model were used to produce data based on 2 processes.

Statistical mimicking of reaction time data: Single-process models, parameter variability, and mixtures.

Statistical mimicking issues involving reaction time measures are introduced and discussed in this article. Often, discussions of mimicking have concerned the question of the serial versus parallel processing of inputs to the cognitive system. We will demonstrate that there are several alternative structures that mimic various existing models in the literature. In particular, single-process models have been neglected in this area. When parameter variability is incorporated into single-process models, resulting in discrete or continuous mixtures of reaction time distributions, the observed reaction time distribution alone is no longer as useful in allowing inferences to be made about the architecture of the process that produced it. Many of the issues are raised explicitly in examination of four different case studies of mimicking. Rather than casting a shadow over the use of quantitative methods in testing models of cognitive processes, these examples emphasize the importance of examining reaction time data armed with the tools of quantitative analysis, the importance of collecting data from the context of specific process models, and the importance of expanding the database to include other dependent measures.

Self-terminating versus exhaustive processes in rapid visual and memory search: an evaluative review.

A major issue in elementary cognition and information processing has been whether rapid search of short-term memory or a visual display can terminate when a predesignated target is found or whether it must proceed until all items are examined. This study summarizes past and recent theoretical results on the ability of self-terminating and exhaustive models to predict differences in slopes between positive (target-present) and negative (target-absent) set-size functions, as well as position effects. The empirical literature is reviewed with regard to the presence of slope differences and position effects. Theoretical investigations demonstrate that self-terminating models can readily predict the results often associated with exhaustive processing, but a very broad class of exhaustive models is incapable of predicting position effects and slope differences typically associated with self-termination. Because position effects and slope differences are found throughout the rapid search literature, we conclude that the exhaustive processing hypothesis is not tenable under common experimental conditions.

Stimulus-response compatability for moving stimuli: perception of affordances or directional coding?

Michaels reported a compatibility effect in which responses were fastest at the destination of a moving stimulus; she interpreted this "destination" compatibility effect in terms of catching actions "afforded" by the stimulus motion. The present study evaluated implications of the catching-affordance account and compared them with those of an account based on spatial coding of relative direction. The destination compatibility effect was obtained when the responses were keypresses rather that catching movements of a joystick and regardless of whether the stimulus expanded, contracted, or only changed location. This effect was a function of relative rather than absolute location of the responses. A similar compatibility effect was obtained when destinations were designated by static arrow stimuli. The results are inconsistent with the catching-affordance account and are best explained by the coding of relative direction.

Enhancement of the Simon effect by response precuing.

When stimuli are presented to the left or right of fixation, and stimulus location is irrelevant, responses are faster if the stimulus location coincides with the location of the assigned response. This phenomenon is called the Simon effect. The present study examined the influence on the Simon effect of attentional precues that signaled the likely stimulus location and intentional precues that signaled the likely response. Experiment 1 was a close procedural replication of an experiment by Verfaellie, Bowers, and Heilman (1988); consistent with their findings, the Simon effect was enhanced by the intentional precue and unaffected by the attentional precue. Experiments 2 and 3 demonstrated the importance of the intentional precue with simpler procedures that involved only intentional and attentional precues, respectively. Finally, the intentional precuing enhancement of the Simon effect was obtained when two stimuli were assigned to each response, regardless of whether the hands were uncrossed (experiment 4) or crossed (experiment 5). Overall, the results indicate that response precuing enhances the Simon effect and favor response-selection accounts over those that attribute the effect to stimulus identification.

Same-different judgments of multiletter strings: insensitivity to positional bias and spacing.

Several recent studies of multiletter matching have included pairs of strings that have the same letters in different positions (rearranged pairs). The task can be defined such that these rearranged pairs are correctly classified as different (i.e., subjects respond "same" only if the strings have the same letters in the same positions--the order task) or as same (i.e., subjects respond "same" if the strings have the same letters regardless of their positions--the item task). The order task produces left-to-right serial-position effects, whereas the item task produces U-shaped serial-position effects. Because these differences suggest that subjects may be able to exert strategic control over the comparison process, two sets of experiments were designed to test whether or not subjects can change the relative weightings devoted to the respective serial positions. In Experiments 1 and 2, the probability that a mismatch occurred in the different positions was manipulated. In Experiments 3 and 4, the physical spacing between letters, as well as whether or not the spaces were filled with neutral noise characters, was varied. None of the manipulations had much influence on the serial-position effects. Thus, the distinct serial-position effects for the order and item tasks apparently are mandatory and not due to any voluntary comparison strategy.

Effects of background symmetry on same-different pattern matching: a compromise-criteria account.

Two experiments are reported, which were designed to test predictions of an account of same-different matching that assumes that bilaterally symmetric backgrounds provide extraneous evidence toward same, whereas asymmetric backgrounds provide evidence toward different. When all backgrounds within a block of trials are of the same type, appropriate adjustments of response criteria can be made to accommodate the irrelevant evidence and thus maintain acceptable levels of accuracy. However, when backgrounds of different types are mixed randomly, compromise criteria are adopted. This compromise-criteria account predicts distinctive interaction patterns for reaction times when blocked versus mixed presentations of various background types are compared. The predicted interactions were obtained for asymmetric- and no-noise backgrounds in Experiment 1 and for symmetric-, asymmetric-, and no-noise backgrounds in Experiment 2. The findings support the general view that extraneous display attributes are weighted into the evidence for same and different, with criteria settings used that minimize errors under the noisiest conditions.