Determining the Dimensionality of Multidimensional Scaling Representations for Cognitive Modeling

Multidimensional scaling models of stimulus domains are widely used as a representational basis for cognitive modeling. These representations associate stimuli with points in a coordinate space that has some predetermined number of dimensions. Although the choice of dimensionality can significantly influence cognitive modeling, it is often made on the basis of unsatisfactory heuristics. To address this problem, a Bayesian approach to dimensionality determination, based on the Bayesian Information Criterion (BIC), is developed using a probabilistic formulation of multidimensional scaling. The BIC approach formalizes the trade-off between data-fit and model complexity implicit in the problem of dimensionality determination and allows for the explicit introduction of information regarding data precision. Monte Carlo simulations are presented that indicate, by using this approach, the determined dimensionality is likely to be accurate if either a significant number of stimuli are considered or a reasonable estimate of precision is available. The approach is demonstrated using an established data set involving the judged pairwise similarities between a set of geometric stimuli. Copyright 2001 Academic Press.     

A marginalization model for the multidimensional unfolding analysis of ranking data

A marginalization model for the multidimensional unfolding analysis of ranking data is presented. A subject samples one of a number of random points that are multivariate normally distributed. The subject perceives the distances from the point to all the stimulus points fixed in the same multidimensional space. The distances are error perturbed in this perception process. He/she produces a ranking dependent on these error-perturbed distances. The marginal probability of a ranking is obtained according to this ranking model and by integrating out the subject (ideal point) parameters, assuming the above distribution. One advantage of the model is that the individual differences are captured using the posterior probabilities of subject points. Three sets of ranking data are analyzed by the model.     

Mathematical Studies of the Information in the Stimulus-Response Matrix

This paper considers the information transmitted in absolute judgments as encoded in a stimulus-response matrix (e.g., see Garner and Hake, 1951). When transmitted information is plotted against the number of stimulus categories in the matrix, one obtains a curve that increases monotonically toward a plateau, which is the maximum information transmittable per stimulus for the particular range of stimuli employed. We demonstrate that although the maximum information transmitted is an attribute of the stimulus continuum itself, the shape of the curve is an empirical property of the stimulus-response matrix, which is determined, in part, by maintaining a constant stimulus category width. Therefore, in principle, each curve of information transmitted vs number of stimulus categories can be determined by a single point: the rightmost point on the graph. Copyright 2001 Academic Press.     

非预想刺激的运动速率对无意视盲的影响

无意视盲是指由于对某些事物的专注而导致的眼前对象被忽视的现象。它受到诸如非预想刺激的位置、大小、颜色; 非预想刺激与注意刺激之间的关系; 被试的年龄、专业知识、加工能力等诸多因素的影响。本文通过改进的MR范式考察了“等时”和“等距”条件下非预想刺激的运动速率对无意视盲的影响。实验结果显示: (1)非预想刺激的运动速率和其呈现时间对无意视盲的比率有显著影响; (2)在一定的呈现时间范围内, 视盲率随运动速率的升高而降低, 但当维持相等的运动距离时, 视盲率没有显著变化; (3)当呈现时间超出一定范围时, 运动速率对无意视盲的影响急剧减小, 即呈现时间制约着运动速率对无意视盲的影响, 两者间呈倒U型曲线关系。文末就实验结果进行了详细分析和讨论。     

The effect of set on the two-point tactual threshold

This experiment studies the influence of set on the two-point tactual threshold. The two-point limen (critical stimulus) was determined along the mid-longitudinal line of both volar and dorsal surfaces of the right forearms of seven university students. Test-stimuli were selected at 3 mm. steps both up and down from each of the critical stimuli. Each of these test-stimuli was presented separately, the critical stimulus being interpolated 30 times in each test of the series. The proportions of two-point and one-point responses to the critical stimulus were then determined again in a control series. It was found that, as the test-stimulus deviated in the positive direction from the critical stimulus, the proportion of two-point responses to the critical stimulus increased, reached a maximum and then began to decline. A similar rise and fall in one-point responses were found in the opposite direction. The results were explained by Adaptation Level Theory.     

Tell me, what did you see? The stimulus on computers

Most psychology experiments start with a stimulus, and, for an increasing number of studies, the stimulus is presented on a computer monitor. Usually, that monitor is a CRT, although other technologies are becoming available. The monitor is a sampling device; the sampling occurs in four dimensions: spatial, temporal, luminance, and chromatic. This paper reviews some of the important issues in each of these sampling dimensions and gives some recommendations for how to use the monitor effectively to present the stimulus. In general, the position is taken that to understand what the stimulus actually is requires a clear specification of the physical properties of the stimulus, since the actual experience of the stimulus is determined both by the physical variables and by the psychophysical variables of how the stimulus is handled by our sensory systems.     

Use of a computer-controlled firearms training simulator in perception response time experiments

This paper describes the use of a custom-configured computer-controlled firearms training simulator to measure perception response (reaction) time (RT) to a stimulus in which the degree of threat presented is a manipulable variable across trials. The computer records the number of frames of videotape traversed between the point of presentation of the threat in the video stimulus and the point at which the subject responds by drawing the firearm. For the purposes of data analysis, these frame-count measures are converted to RT measurements. Example data are presented that capture perception RT at both thedraw-stimulus and thefire-stimulus points in situations for which either only one threat or more than one threat exists. Other elements, such as degree of threat and accuracy of response, provide additional data.     

Short-term memory for event duration: Modality specificity and goal dependency

Time perception is involved in various cognitive functions. This study investigated the characteristics of short-term memory for event duration by examining how the length of the retention period affects inter- and intramodal duration judgment. On each trial, a sample stimulus was followed by a comparison stimulus, after a variable delay period (0.5?C5?s). The sample and comparison stimuli were presented in the visual or auditory modality. The participants determined whether the comparison stimulus was longer or shorter than the sample stimulus. The distortion pattern of subjective duration during the delay period depended on the sensory modality of the comparison stimulus but was not affected by that of the sample stimulus. When the comparison stimulus was visually presented, the retained duration of the sample stimulus was shortened as the delay period increased. Contrarily, when the comparison stimulus was presented in the auditory modality, the delay period had little to no effect on the retained duration. Furthermore, whenever the participants did not know the sensory modality of the comparison stimulus beforehand, the effect of the delay period disappeared. These results suggest that the memory process for event duration is specific to sensory modality and that its performance is determined depending on the sensory modality in which the retained duration will be used subsequently.     

Evaluating the importance of the convex hull in solving the Euclidean version of the traveling salesperson problem: reply to Lee and Vickers (2000)

Lee and Vickers (2000) suggest that the results of MacGregor and Ormerod (1996), showing that the response uncertainty to traveling salesperson problems (TSPs) increases with increasing numbers of nonboundary points, may have resulted as an artifact of constraints imposed in the construction of stimuli. The fact that similar patterns of results have been obtained for our "constrained" stimuli, for a stimulus constructed under different constraints, for 13 randomly generated stimuli, and for random and patterned 48-point problems provides empirical evidence that the results are not artifactual. Lee and Vickers further suggest that, even if not artifactual, the results are in principle limited to arrays of fewer than 50 points and that, beyond this, the total number of points and number of nonboundary points are "diagnostically equivalent." This claim seems to us incorrect, since arrays of any size can be constructed that will permit experimental tests of whether problem difficulty is influenced by the number of nonboundary points, or the total number of points, or both. We present a reanalysis of our original data using hierarchical regression analysis which indicates that both factors may influence problem complexity.     

Stimulus uncertainty does not impair stereopsis

The effect of stimulus uncertainty on the stereoscopic resolution of letters was examined for two classes of letters: (1) letters presented stereoscopically as random-element stereograms, and (2) letters presented as two-dimensional physical contours. The variables of stimulus discriminability (stereoscopic vs. physical contours) and stimulus uncertainty (number of alternative letter targets) were combined factorially. Stereoscopically presented letters were more difficult to resolve, but stimulus uncertainty had the same effect for both stereoscopic and physically defined letters. The additivity of these two variables suggests that the perception of stereoscopic forms is an automatic process not impaired by uncertainty about the form to be resolved.     

Discrimination of spatial and temporal intervals defined by three light flashes: Effects of spacing on temporal judgments and of timing on spatial judgments

Observers were presented stimulus patterns consisting of a sequence of three laterally displaced light flashes, which defined two spatial intervals and two temporal intervals. The position and time of the second flash were varied factorially, and observers were asked to make relative judgments of either the two spatial intervals or the two temporal intervals. “Induction” effects of stimulus timing on spatial judgments and of stimulus spacing on temporal judgments were both found; however, the directionality of these effects differed between subjects. The results are inconsistent with the hypothesis, derived from previous findings, that such effects are determined primarily by a tendency toward perceiving constant velocity of apparent motion; it is proposed that the directionality of the induction effects is determined largely by the strategy adopted by the observer for combining spatial and temporal stimulus information.     

Peripheral and foveal segmentation of angle textures

Studies of the effects of retinal eccentricity on the visual segmentation of textures are presented. The textures used in these studies were composed of angle elements. These were presented tachistoscopically to college students in three different experiments. Results showed that there were different relationships between segmentation performance and eccentricity, depending on the width of the angles used in the background and target texture. One major difference was that peak performance was found in the fovea in some conditions, and in peripheral areas in other conditions. Performance in the fovea and the periphery seemed to be determined by qualitatively different features. It was assumed that an appropriate explanation is that the system-internal representation of a specific stimulus within the early visual system differs as a function of the retinal location at which it is projected. Thus, the critical features discriminating between target and background texture have to be sought in the system-internal representation of the stimulus instead of in the stimulus itself. The data show that a relatively exact system-internal representation of the stimulus is present in the fovea, where performance is determined by angle width. In the periphery, in contrast, angles seem to be represented as “blobs,” and performance is determined by the orientation of the blobs’ main axes.     

Face preference at birth: the role of an orienting mechanism

It has been proposed that newborns’ preferential orienting to faces is solely controlled by a subcortically mediated orienting mechanism (i.e. Conspec). In contrast, preferential‐looking tasks show that face preference at birth manifests itself also with measures that index fixation duration. It is possible, however, that orienting and fixation duration are confounded and only orienting matters. The present study used a revised version of the preferential‐looking technique, in which the same stimulus (i.e. a facelike or a non‐facelike pattern) was simultaneously presented to both sides of the visual field. Results showed that longer total fixation times on the facelike stimuli resulted from the sum of a greater number of brief fixations, rather than from the sum of a small number of long fixations. These findings support the hypothesis that, for facelike patterns, the duration of infant’s fixation on the stimulus is determined by the nature of the pattern that impinges on the periphery of the visual field, more than by the nature of the pattern that is being looked at.     

The role of the adjacency between background cues and objects in visual localization during ocular pursuit

Subjects used eye movements to pursue a light target that moved from left to right with a velocity of 15 deg s-1. The stimulus was a sudden five-fold decrease in target intensity during the movement. The subject's task was to localize the stimulus relative to either a single stationary background point or the midpoint between two points (28 deg apart) placed 0.5 deg above the target path. The stimulus was usually mislocated in the direction of eye movement; the mislocation was affected by the spatial adjacency between background and stimulus. When an auditory, rather than a visual, stimulus was presented during tracking, target position at the time of stimulus presentation was visually mislocated in the direction opposite to that of eye movement. The effect of adjacency between background and target remained the same. The involvement of processes of subject-relative and object-relative visual perception is discussed.     

Attentional sampling of multiple wagon wheels

Attending to a periodic motion stimulus can induce illusory reversals of the direction of motion. This continuous wagon wheel illusion (c-WWI) has been taken to reflect discrete sampling of motion information by visual attention. An alternative view is that it is caused by adaptation. Here, we attempt to discriminate between these two interpretations by asking participants to attend to multiple periodic motion stimuli: The discrete attentional sampling account, but not the adaptation account, predicts a decrease of c-WWI temporal-frequency tuning with set size (with a single periodic motion stimulus the c-WWI is tuned to a temporal frequency of 10 Hz). We presented one to four rotating gratings that occasionally reversed direction while participants counted reversals. We considered reversal overestimations as manifestations of the c-WWI and determined the temporal-frequency tuning of the illusion for each set size. Optimal temporal frequency decreased with increasing set size. This outcome favors the discrete attentional sampling interpretation of the c-WWI, with a sampling rate for each individual stimulus dependent on the number of stimuli attended.     

Bias in proportion judgments: the cyclical power model

When participants make part-whole proportion judgments, systematic bias is commonly observed. In some studies, small proportions are overestimated and large proportions underestimated; in other studies, the reverse pattern occurs. Sometimes the bias pattern repeats cyclically with a higher frequency (e.g., overestimation of proportions less than .25 and between .5 and .75; underestimation otherwise). To account for the various bias patterns, a cyclical power model was derived from Stevens' power law. The model proposes that the amplitude of the bias pattern is determined by the Stevens exponent, beta (i.e., the stimulus continuum being judged), and that the frequency of the pattern is determined by a choice of intermediate reference points in the stimulus. When beta < 1, an over-then-under pattern is predicted; when beta > 1, the under-then-over pattern is predicted. Two experiments confirming the model's assumptions are described. A mixed-cycle version of the model is also proposed that predicts observed asymmetries in bias patterns when the set of reference points varies across trials.     

Feature analyzers for the phonetic dimensionstop vs. continuant

Perception of sounds along the phonetic dimensionstop vs. continuant was studied by means of a selective adaptation procedure. Subjects first identified a series of synthetic consonant-vowel syllables whose formant transitions varied in duration, slope, and amplitude characteristics. They were perceived as either [ba] or [wa]. After the initial identification test, an adapting stimulus was presented repeatedly, and then the subjects again identified the original test series. Adapting with a stop (either [ba] or [da]) led to a decrease in the number of test stimuli identified as [ba], whereas adapting with the continuant sound [wa] led to an increase in the number of [ba] identification responses. Removing the vowel portion of an adapting stimulus greatly reduced the identification shift only when the resulting stimulus was no longer perceived as speech-like. A reduction in the number of [ba] identifications occurred even when a nonspeech “stop” (the sound of a plucked string) was used as the adapting stimulus, suggesting that phonetic processing is not a necessary condition for an adaptation effect.     

Experimental note on fading of briefly flashed lines

A peripheral uniform stimulus on a uniform background tends to fade when a ring enclosing the stimulus is flashed briefly, indicating that neural signals external to the stimulus such as those from the ring or those from the background tend to inhibit the onset-response or after-discharge of the stimulus. In this study, a peripheral achromatic line was flashed briefly on an achromatic background while the subject was steadily fixating on a point on the background. It was predicted that the stimulus line would fade due to background inhibition of the onset-response or afterdischarge of the stimulus. On a reference line, subjects indicated two points delimiting the part of the stimulus line which looked uniform in intensity of color. These points converged toward the center of the reference line as the luminance of the stimulus line approached that of the background. Compared to the central uniform part, the nonuniform parts near the endpoints of the stimulus line looked more faded. These results support the idea that the background surrounding a stimulus tends to inhibit the onset-response of after-discharge of the stimulus.     

Backward and forward masking associated with saccadic eye movement

Visual masking effects on test flash thresholds were measured under real and simulated eye movement conditions to determine whether visual masking is primarily responsible for elevations in threshold that are sometimes associated with saccadic eye movements. Brief luminous flashes presented to the central retina before, during, and after saccades were masked by stimuli presented either pre- or postsaccadically. The amount and time course of masking were quantitatively dependent on stimulus parameters of intensity and temporal separation and were unaffected by eye movement parameters (amplitude, velocity, direction) as long as retinal stimulus conditions were constant. The duration of forward masking was longer than that of backward masking. When retinal conditions during saccades were mimicked while the eyes were held steady, masking interactions were identical to those obtained during real saccades. These results indicate that masking effects during saccades in ordinary environments are determined solely by the stimulus situation at the retina. Putative nonvisual, centrally originating saccadic suppression suggested by other authors is evidently not additive with visually determined masking during saccades.     

The effect of an after-coming random pattern on the perception of brief visual stimuli

The perception of briefly exposed visual forms is shown to be masked by an after- coming random pattern stimulus of approximately equal intensity. This effect occurs only under certain well defined conditions; it is limited by the minimum stimulus exposure time in excess of threshold which overcomes masking (critical stimulus duration) as well as by the minimum interval between presentation of the two stimuli which permits evasion of the masking action (critical interval). Over the range of stimulus duration in which masking occurs, critical interval varied with stimulus duration in such a way that the interval multiplied by the stimulus duration equals a constant. Critical stimulus duration and critical interval at threshold are shown to vary little under a variety of conditions. The effect of the random pattern stimulus is limited to the part of the visual field to which it is presented.