Spatial metrics of integral and separable dimensions

Two experiments were conducted to investigate the relationship between dimensional integrality and the form of the combination rule or spatial metric used in a similarity judgment task. In Experiment 1, two groups of eight subjects judged the dissimilarity of all pairwise combinations of 12 rectangles differing in height and width (integral dimensions) or 12 circles differing in size and diameter orientation (separable dimensions). The dimensional organization and spatial metric of both sets of dimensions were determined. The results showed that differences in height and width contributed independently to judgments of the overall dissimilarity of rectangles and that these dimensions were combined using a Euclidean metric. In contrast, substantial interactions between circle size and diameter orientation were found. Combinations of these dimensions also appeared to violate the triangle inequality implying that no spatial metric was appropriate. In Experiment 2, parallelogram size and tilt were similarly analyzed. Although some degree of dimensional interaction was observed, it was found that on the average these dimensions were combined using a city-block metric. In a subsequent speeded classification task, orthogonal interference was observed, which suggested that size and tilt are integral dimensions. The implications of both experiments for the supposed association between the Euclidean metric and dimensional integrality are discussed.     

The free classification of analyzable and unanalyzable stimuli

The free classification of two-dimensional analyzable and unanalyzable stimuli was investigated. Analyzable stimuli consist of dimensions which are distinct and phenomenally separable (e.g., colored geometric forms); unanalyzable stimuli consist of two dimensions which are not distinct, not phenomenally separable, and which are probably perceived as a unitary dimension (e.g., Munsell colors). In the first experiment, Ss judged the similarity between each stimulus pair for both types of stimuli. The results replicated previous work in showing that the city-block metric was appropriate for the analyzable stimuli and that the euclidean metric was appropriate for unanalyzable stimuli. In the second experiment, Ss classified sets of analyzable and unanalyzable stimuli into two or three groups in any way they wished. For analyzable stimuli, classification was based on the dimensional structure-stimuli which alter the dimensional structure by defining another dimension change classification. For unanalyzable stimuli, classification was based on the similarity structure-stimuli which alter the similarity structure change classification.     

Perceptual separability and spatial models

Highly analyzable two-dimensional color stimuli were generated using stimulus cards such that one part of each card varied only on the first dimension and the other part varied only on the second. Subjects were required to make judgments of similarity between pairs of these analyzable stimuli, between pairs of relatively unanalyzable color stimuli, and between pairs of geometric stimuli. The results support previous findings that the Euclidean combining rule is appropriate for judgments of single color patches but indicate that the city block combining rule may be appropriate for simple stimuli that vary on perceptually distinct dimensions.     

An analysis of generative representation systems

Three ideas are basic to generative theory: (a) Subjects are assumed to attend to the relations among stimuli, extracting the transformations relating pairs of stimuli; (b) the set of abstracted transformations is decomposed or reduced to an elementary set of generators; (c) subjects use the elementary generators as the basis for judging similarity. The purpose of this paper is to illustrate these ideas with an experiment in which subjects were asked to rate the similarity between stimulus pairs. The stimulus materials consisted of the permutations of a 4-item pattern with the properties of a dihedral group which insured the existence of sets of elementary transformations. Three analytic techniques were used to determine the generator set of transformations abstracted by subjects. The first analysis consisted of a monotonic regression between dissimilarity ratings and the number of elementary generators of a given permutation. The residual variance of this monotone regression, suitably normalized, was used as a quantitative goodness-of-fit measure. For the stochastic analysis, cumulative distributions of dissimilarity ratings were obtained for permutations requiring one, two, or three generators. The idea was that permutations requiring fewer generators should be associated with distributions of lower dissimilarity values (higher similarity scores) as compared to permutations predicted to be transformationally more complex. The final analysis, a multidimensional scaling of dissimilarity ratings, converted subjects' ratings into spatial structures to determine whether individual subjects' ratings exhibited the predicted spatial arrangement. The monotone regression and stochastic analyses abstracted similar generator sets for individual subjects, some of which provided perfect fits to the data. Although the scaling analysis yielded similar estimates of generators, for some subjects, transformations with the same number of generators yielded unequal “cognitive” distances resulting in some-what deformed spatial structures for these subjects. It was concluded that the results generally supported a generative model as an approximation to subjects' representations of interstimulus relationships.     

Similarity relations among synesthetic stimuli and their attributes

Four experiments examined the similarity relations that exist among bimodal attributes that correspond synesthetically (e.g., white color and high pitch) and among stimuli formed by combining these attributes either congruently (e.g., white/high, black/low) or incongruently (e.g., white/low, black/high). Previous research suggests two hypotheses: (a) Synesthetic stimuli are compared as wholes on the basis of their overall similarity, and (b) nonidentical congruent stimuli are more dissimilar than nonidentical incongruent stimuli. In these four experiments, similarity among either individual attributes (Experiments 1 and 4) or bimodal stimuli (Experiments 2 and 3) was measured by either ratings or response latencies; similarity judgments were scaled with an individual differences scaling procedure (SINDSCAL). Stimulus comparisons were fit well by a Euclidean but not a city-block metric, supporting the overall similarity hypothesis. However, there was little evidence that subjects perceived congruity/incongruity among stimulus wholes, even though subjects were sensitive to correspondence/noncorrespondence among attributes. These results were replicated in four additional experiments using larger stimulus sets. A two-process account is proposed in which stimulus formation (intersensory processing) occurs independently of the abstraction of cross-sensory meaning (figurative processing).     

Saliency metric for subadditive dissimilarity judgments of rectangles

Previous findings that dissimilarity judgments for rectangles are strongly subadditive, that qualitative individual differences are always present, and that four-parameter psychophysical maps can reproduce the average ratings (Sch?nemann & Lazarte, 1987) are replicated. However, the present study in addition suggests that the metric for bounded response transformation, previously used to restore additivity of responses, has a modest effect on the fits of the psychophysical maps. The differential weighing of the coordinates already incorporates segmental subadditivity predictions into the maps. In fact, the psychophysical maps define a subadditive saliency metric that depends on assigning larger weights to larger coordinates. This constraint on the weights of these maps, together with the response times, allows us to identify a strategy shift when subjects respond to two classes of stimulus pairs: For rectangle-rectangle pairs, subjects center on the shape and size of the rectangles; for square-rectangle pairs, the focus is on height and width.     

Dimensional dominance and stimulus discriminability.

The relationship between the discriminability of scaling stimuli and assessed dimensional dominance was investigated in three studies. Sixty kindergarten children were assessed using a psychophysical scaling method to determine JND values for the size, brightness, and orientation dimensions. Thirty of the same subjects were then assessed for dimensional dominance using stimuli of two levels of known discriminability, based on the obtained JND values. In a third experiment, the remaining 30 subjects were assessed for dimensional dominance using stimuli that systematically emphasized the values of one dimension relative to the other two dimensions, again based on obtained JND values.The results indicated that (1) kindergarten children were able to perform consistently during psychophysical scaling, and there was little variability between children in their judgments of stimuli, (2) the overall level of discriminability affects dimensional dominance scaling behavior, with subjects more likely to exhibit dominance for one dimension when all the values of scaling stimuli are high in discriminability, and (3) some support for the hypothesis that dimensional dominance scaling behavior can be manipulated by manipulating the relative discriminability of scaling stimuli was found, though the trend was not clear.The relative discriminability of scaling stimuli appears to have some effects on dimensional dominance scaling behavior of young children. However, some pre-experimental bias to attend to a particular dimension seems to remain even when the values of all dimensions present are of equal and known discriminability. Dimensional dominance is a function of an interaction between discriminability of scaling stimuli and the experiential bias or perceptual set of the subject.     

Size-distance paradox with accommodative micropsia

Two experiments tested the hypothesis that the paradoxical relative distance judgment associated with the size-distance paradox is due to the visual system’s assuming equal linear size and perceiving a smaller angular size for the closer stimulus equal in visual angle. In Experiment I, two different sized coins were presented successively, and 16 Ss were asked to give ordinal judgments of apparent distance and apparent size. When the two coins depicted the same figures, the closer stimulus was judged to be farther and smaller, more frequently, than when two coins depicted different figures. In Experiment II, 48 Ss were asked to give ratio judgments of apparent distance, apparent linear size, and apparent angular size for two stimuli which were presented successively. When the stimuli were of equal shape, the mean ratios of the far stimulus to the near stimulus were smaller for the apparent distance but larger for the apparent linear size and angular size than when the stimuli were of different shape. The obtained distance judgments were consistent with the hypothesis but the obtained judgments of linear size and angular size were not.     

DIMENSIONAL INTERPRETATION AND CONFIGURATION INVARIANCE IN MULTIDIMENSIONAL SCALING: AN EMPIRICAL STUDY

This paper is concerned with: a ) the invariance of nonmetric multi- dimensional scaling soludions over changes in stimulus domain; and b) pro- cedures for assisting the researcher in interpreting the axes of multidimen- sional scaling configurations. The stimuli consisted of the names of 17 popular brands of automobiles. Similarities and preference judgments were obtained from 37 subjects, divided into two groups of approximately equal size. Each group received 11 of the 17 stimuli. A core set of 6 stimuli was common over both groups. Each group also rated the 11 car models on 20 semantic differential scales. Results of the study suggested that the interpoint distances of bhe core set of 5 stimuli remained stable over subject groups and differences in stimulus set composition. Semantic differential ratings were used to find directions in the configurational space (obtained from overall similarity judg- ments) whose projections were maximally correlated with the outside (property) vectors. Stimulus configurations developed from the semantic differential space were highly congruent with those found by the analysis of direct similarity judgments. However, attempts to develop stimulus configurations by the "unfolding" of preference data alone did not lead to configurations which closely matched those found by the analysis of direct similarities data.     

Both perceptual and conceptual factors influence taste-odor and taste-taste interactions

Observers are often asked to make intensity judgments for a sensory attribute of a stimulus that is embedded in a background of “irrelevant” stimulusdimensions. Under some circumstances, these background dimensions of the stimulus can influence intensity judgments for the target attribute. For example, judgments of sweetness can be influenced by the other taste or-odor qualities of a solution (Frank & Byram, 1988; Kamen et al., 1961). Experiments 1 and 2 assessed the influence of stimulus context, instructional set, and reference stimuli on cross-quality interactions in mixtures of chemosensory stimuli. Experiment 1 demonstrated that odor-induced changes in sweetness judgments were dramatically influenced when subjects rated multiple attributes of the stimulus as compared with when they judged sweetness alone. Several odorants enhanced sweetness when sweetness alone was judged, while sweetness was suppressed for these same stimuli when total-intensity ratings were broken down into ratings for the sweetness, saltiness, sourness, bitterness, and fruitiness of each solution. Experiment 2 demonstrated a similar pattern of results when bitterness was the target taste. In addition, Experiment 2 showed that the instructional effects applied to both taste-odorand taste-taste mixtures. It was concluded that the taste enhancement and suppression observed for taste-odor and taste-taste mixtures are influenced by (1) instructional sets which influence subjects’ concepts of attribute categories, and (2) the perceptual similarities among the quality dimensions of the stimulus.     

Determinants of cumulative successive contrast in saltiness intensity judgments

When all stimuli elicit the same taste quality, solutions preceded by a high concentration level are judged to be significantly less intense than solutions preceded by a low concentration level. After repetitious stimulation with a different tasting stimulus, the intensity of the present stimulus is overestimated. This phenomenon is called “successive contrast.” In the present study, the cumulative effects of three identical stimuli on the saltiness ratings for a test stimulus are investigated. The preceding stimuli are manipulated with regard to taste quality, saltiness intensity, total taste intensity, and complexity. Whether the size of the cumulative contrast effect is associated with the degree of dissimilarity between preceding stimuli and test stimulus, or with the saltiness or total taste intensity of the preceding stimuli, is investigated. The size of the contrast effect depends on the type of preceding stimulus, its intensity, and the type of test stimulus. No association was found with judgments of the degree of dissimilarity between the preceding stimuli and the test stimulus. For nonsalty preceding stimuli, the contrast effects are independent of concentration level. When the preceding stimuli taste at least partly salty, the total intensity appears to determine the size of the contrast for an unmixed salty test stimulus.     

Testing the attentional model of brightness contrast with relative area and figure-ground organization unconfounded

Using gray-white metric patterns, for which figure-ground relationships had been previously determined, several features of an attentional theory of brightness contrast were investigated. Experiment I, involving three subjects and the method of constant stimuli, showed that ground, the unattended area, could be reliably perceived as brighter; responses were affected by both the type of pattern and level of contrast ratio. Experiment II, involving 40 subjects and the method of magnitude estimation, used metric patterns for which attentional factors were not confounded with relative area. The results supported the first study and further indicated the primary involvement of relative area rather than focus of attention in brightness contrast.

     

The joint analysis of direct ratings,pairwise preferences,and dissimilarities

In studies involving judgments of similarity or dissimilarity, a variety of other variables may also be measured. Examples might be direct ratings of the stimuli, pairwise preference judgments, and physical measurements of the stimuli with respect to various properties. In such cases, there are important advantages to joint analyses of the dissimilarity and collateral variables. A variety of models are described for relating these and algorithms described for fitting these to data. A number of hypothesis tests are developed and an example offered.The research reported here was supported by grant number APA 320 to the author by the National Research Council of Canada.     

Cross-modal additive conjoint structures and psychophysical scale convergence

I investigated a variety of issues related to the measurement of the magnitude of psychological experience, especially the magnitude of sensations. Different groups of subjects made pair comparisons, magnitude estimations, and category judgments of the "total sensory magnitude" of light and sound stimuli presented conjointly. Another group judged the dissimilarity of pairs of conjoint stimuli. Various axioms, especially double cancellation, were tested on the resulting rank orders of conjoint stimuli. Judgements of the total magnitude of conjoint combinations of sound and light stimuli formed an additive conjoint structure. Dissimilarity judgments gave rise to a closely related lattice structure. Moreover, various scales of the individual attributes (loudness and brightness) calculated from the two types of judgments of the conjoint stimuli displayed substantial convergence, each scale for a given modality being linear with all other scales for that modality.     

The <Emphasis Type="Italic">K</Emphasis>-INDSCAL Model for Heterogeneous Three-Way Dissimilarity Data

A weighted Euclidean distance model for analyzing three-way dissimilarity data (stimuli by stimuli by subjects) for heterogeneous subjects is proposed. First, it is shown that INDSCAL may fail to identify a common space representative of the observed data structure in presence of heterogeneity. A new model that removes the rotational invariance of the classical multidimensional scaling problem and specifies K common homogeneous spaces is proposed. The model, called mixture INDSCAL in K classes, or briefly K-INDSCAL, still includes individual saliencies. However, the large number of parameters in K-INDSCAL may produce instability of the estimates and therefore a parsimonious model will also be discussed. The parameters of the model are estimated in a least-squares fitting context and an efficient coordinate descent algorithm is given. The usefulness of K-INDSCAL is demonstrated by both artificial and real data analyses.     

Optional processes in similarity judgments.

This research investigates the nature of similarity relations among three pairs of interacting dimensions: (1) the integral dimensions of auditory pitch and loudness, (2) the configural dimensions of paired parentheses, and (3) the cross-modally corresponding dimensions of visual position and auditory pitch. We evaluated the rules by which information from each dimension combines in similarity judgments. Our claim is that, when judging similarity, processes that are obligatory, or what we call mandatory processes, can commingle with processes of choice, or what we call optional processes. By varying instructions, we found strong evidence of optional processing. Instructions to rate overall similarity encouraged subjects to attend to stimuli as wholes and led to a Euclidean rule in similarity scaling. Instructions to focus on dimensions encouraged subjects to consider each stimulus dimension separately and led to a city-block rule. We argue that optional processes may obscure mandatory ones, and so need to be identified before mandatory processes can be understood.     

Perceiving the centroid of configurations on a rolling wheel

Undergraduates observed configurations of point-lights undergoing wheel-generated motions and judged how wheel-like the movement of each stimulus appeared on a 7-point scale. Viewer judgments were predicted by a metric defining the variable parameters for the motion path of each configuration’s geometric center—the centroid. The effects on judgments of eye movement and the stimulus characteristics of rotation, translation, and configuration were explored in six experiments. First, a strain operation on the dynamic stimuli did not affect the ability of the metric to predict perceptual judgments. Second, the predictive strength of the metric did not interact with the type of eye movements used in viewing the stimuli, though judged wheel-likeness was greater under pursuit vision than under static fixation. Third, variations in the extent of translation yielded little, if any, effect on observers’ judgments, nor did translation in a circular path. Finally, for stimuli having two lights extremely close together in the configuration, the metric’s predictive value was slightly lessened but only at the limits of visual acuity. Thus, within a wide range of presentation conditions, and for a wide variety of configurations, a metric that defined the variable parameters for the motion path of the centroid was an accurate predictor of observers’ judgments of goodness of perceived rotary motion.     

A theory of bidirectional judgments

This paper is concerned with a scaling theory for “bidirectional” judgments, for which the order of judgment is reversible, as in fractional and multiple ratio estimation judgments. With the assumption that judgments are mediated by perceived relations of pairs of stimuli, the theory is developed for judgments of comparison stimuli in relation to standards, taking explicit account of the location of the comparison stimulus relative to the standard. The theory of bidirectional judgments, based on a theory of relative judgment by Fagot (1978, 1979), entails a partial nesting of models characterized by a progressive weakening of the constraints placed on the structure of the data. The weakest model, the relative bias/directional standard (RBDS) model, allows each standard to have two biasing effects, depending on the location of the standard above or below the comparison stimulus. Tests of the theory were carried out on the ratio estimation of brightness and weight data of Engen and Levy (1955) and the part-sum estimation data of Goude (1962). Only the RBDS model was found acceptable for all three data sets