A MULTIDIMENSIONAL SCALING APPROACH TO THE PERCEPTION OF ART. I

G oude G. A multidimensional scaling approach to the perception of art. I. Scand. J. Psyckol ., 1972, 1 3 , 258–271.—-Five experiments with similarity estimation and ratio estimation of experiences of art (paintings) were used for testing a similarity model for multidimensional scaling. A multidimensional analysis gave five interpreted factors. Graphical estimations were compared with numerical estimations. Results from naive observers were related to results from a specialist group.     

Similarity judgments of line length

Nine Ss judged similarity of pairs of lines on a scale from 0 to 100, and 14 Ss made magnitude estimations of similarity of pairs of lines. The two scales of similarity were linearly related. Scale values for subjective length were obtained in one dimension using a nonmetric multidimensional analysis. Subjective length was found to be logarithmically related to objective length, and similarity was found to be an exponential     

Speeded old-new recognition of multidimensional perceptual stimuli: modeling performance at the individual-participant and individual-item levels

Observers made speeded old-new recognition judgments of color stimuli embedded in a multidimensional similarity space. The paradigm used multiple lists but with the underlying similarity structures repeated across lists, to allow for quantitative modeling of the data at the individual-participant and individual-item levels. Correct-rejection response times (RTs) got systematically faster as the similarity of foils to the old study items decreased. There were also intricate patterns of speed-accuracy trade-offs that varied across individual items and participants. An exemplar-based random-walk model provided a good overall quantitative account of the recognition choice probabilities, mean correct RTs, and mean error RTs associated with the individual items on the basis of their positions in multidimensional similarity space. However, the model failed to predict the very long RTs associated with correct rejections of a prototype foil.     

Cognitive processing of multidimensional stimuli in schizophrenia: formal modeling of judgment speed and content

This article presents a formal, mathematical account of relations between response times on simple cognitive tasks and content of complex judgments involving multiple stimulus dimensions for people with schizophrenia. Changes in multidimensional judgments were viewed as the result of interference from increased stages of encoding with respect to the individual dimensions. Information on dimensional properties encoded earlier in a judgment trial was considered to be more susceptible to loss over the rest of the trial, because of a larger number of encoding stages applied to the remaining dimensional properties. Model predictions were tested with samples of paranoid and nonparanoid schizophrenic participants and controls. Unidimensional encoding speed was assessed by reaction times in an explicit similarity ratings task, and multidimensional judgment content was assessed by the relative importance of different stimulus dimensions to participants' ratings in an implicit similarity ratings task. Results support validity of the model.     

ON THE DANGERS OF AVERAGING ACROSS SUBJECTS WHEN USING MULTIDIMENSIONAL SCALING OR THE SIMILARITY-CHOICE MODEL

Abstract— When ratings of judged similarity or frequencies of stimulus identification are averaged across subjects, the psychological structure of the data is fundamentally changed. Regardless of the structure of the individual-subject data, the averaged similarity data will likely be well fit by a standard multidimensional scaling model, and the averaged identification data will likely be well fit by the similarity-choice model. In fact, both models often provide excellent fits to averaged data, even if they fail to fit the data of each individual subject. Thus, a good fit of either model to averaged data cannot be taken as evidence that the model describes the psychological structure that characterizes individual subjects. We hypothesize that these effects are due to the increased symmetry that is a mathematical consequence of the averaging operation.     

A theoretical framework for testing the additive difference model for dissimilarities data: Representing gambles as multidimensional stimuli

Implicit within the acceptance of most multidimensional scaling models as accurate representations of an individual's cognitive structure for a set of complex stimuli, is the acceptance of the more general Additive Difference Model (ADM). A theoretical framework for testing the ordinal properties of the ADM for dissimilarities data is presented and is illustrated for a set of three-outcome gambles. Paired comparison dissimilarity judgments were obtained for two sets of gambles. Judgments from one set were first analyzed using the ALSCAL individual differences scaling model. Based on four highly interpretable dimensions derived from this analysis, a predicted set of dimensions were obtained for each subject for the second set of gambles. The ordinal properties of the ADM necessary for interdimensional additivity and intradimensional subtractivity were then tested for each subject's second set of data via a new computer-based algorithm, ADDIMOD. The tests indicated that the ADM was rejected. Although violations of the axioms were significantly less than what would be expected by chance, for only one subject was the model clearly supported. It is argued that while multidimensional scaling models may be useful as data reduction techniques, they do not reflect the perceptual processes used by individuals to form judgments of similarity. Implications for further study of multidimensional scaling models are offered and discussed.     

Modeling individual differences in cognition

Many evaluations of cognitive models rely on data that have been averaged or aggregated across all experimental subjects, and so fail to consider the possibility of important individual differences between subjects. Other evaluations are done at the single-subject level, and so fail to benefit from the reduction of noise that data averaging or aggregation potentially provides. To overcome these weaknesses, we have developed a general approach to modeling individual differences using families of cognitive models in which different groups of subjects are identified as having different psychological behavior. Separate models with separate parameterizations are applied to each group of subjects, and Bayesian model selection is used to determine the appropriate number of groups. We evaluate this individual differences approach in a simulation study and show that it is superior in terms of the key modeling goals of prediction and understanding. We also provide two practical demonstrations of the approach, one using the ALCOVE model of category learning with data from four previously analyzed category learning experiments, the other using multidimensional scaling representational models with previously analyzed similarity data for colors. In both demonstrations, meaningful individual differences are found and the psychological models are able to account for this variation through interpretable differences in parameterization. The results highlight the potential of extending cognitive models to consider individual differences.     

Bilingualism and the perception of professional concepts

A selected set of professional concepts was subjected to analysis through two separate multidimensional scaling techniques, the INDSCAL and TORSCA models, to evaluate the intergroup perceptual differences of four experimental groups, made up of unilingual French, unilingual English and bilingual students. The linguistic relativism thesis provided the research hypotheses on the relationship between language access and usage and concept perception. The multidimensional scaling techniques were applied to the matrix of subjects' similarity judgments on pairs of concepts, thus enabling the identification of three dimensions. The dimensions were labelled as conjunctive, relational and disjunctive, and were assumed to be related to the criteria employed by the subjects in their similarity rankings. An analysis of variance of the individual saliences on each dimension provided evidence of linguistic relativism for both the relational and disjunctive dimensions. These findings support the contention that unilingual speakers of separate languages differ from each other and from bilingual speakers in their perception of professional concepts.     

A COMPARATIVE STUDY OF SOME MULTIDIMENSIONAL VECTOR MODELS FOR SUBJECTIVE SIMILARITY

E kehammar B. A comparative study of some multidimensional vector models for subjective similarity. Scand. J. Psychol ., 1972, 1 3 , 190–197.—h this report, two theoretical vector models for subjective similarity were deduced from a "content" definition of subjective similarity. One of the derived similarity equations proved in empirical model testing to describe the similarity principle in perception of form better than earlier, similar models. Deviations between observed similarity estimates and values expected according to the model are discussed, among other things, in terms of the heterogeneity of the stimulus set.     

MULTIDIMENSIONAL RATIO SCALING AND MULTIDIMENSIONAL SIMILARITY OF SIMPLE GEOMETRIC FIGURES

The special case of purely qualitative multidimensional similarity was studied in four experiments concerned with simple geometric figures. A previously proposed equation did not describe the relation between subjective similarity and angular separation of the percept vectors. Factor analyses indicate that in the 'homogeneous' experiments (with parallelogram figures) there were two pairs of inversely related subjective attributes which vary as a function of the difference between the horizontal and vertical axes of the parallelogram, and that in the 'heterogeneous' experiments (different figures) there were four main independent subjective attributes.     

Spatial,non-spatial and hybrid models for scaling

In this paper, hierarchical and non-hierarchical tree structures are proposed as models of similarity data. Trees are viewed as intermediate between multidimensional scaling and simple clustering. Procedures are discussed for fitting both types of trees to data. The concept of multiple tree structures shows great promise for analyzing more complex data. Hybrid models in which multiple trees and other discrete structures are combined with continuous dimensions are discussed. Examples of the use of multiple tree structures and hybrid models are given. Extensions to the analysis of individual differences are suggested.1976 Psychometric Society Presidential Address.While people too numerous to list here have contributed ideas, inspiration, and other help, I particularly wish to acknowledge the contributions of Sandra Pruzansky, without whom this paper could not have been written. I would also like to acknowledge the past contributions of my long-time colleague Jih-Jie Chang, without whose help I probably would not have beenasked to write it.     

Multidimensional letter similarity derived from recognition errors

In order to provide a reliable measure of the similarity of uppercase English letters, a confusion matrix based on 1,200 presentations of each letter was established. To facilitate an analysis of the perceived structural characteristics, the confusion matrix was decomposed according to Luce’s choice model into a symmetrical similarity matrix and a response bias vector. The underlying structure of the similarity matrix was assessed with both a hierarchical clustering and a multidimensional scaling procedure. This data is offered to investigators of visual information processing as a valuable tool for controlling not only the overall similarity of the letters in a study, but also their similarity on individual feature dimensions.     

An investigation of race and sex similarity effects in interviews: a multilevel approach to relational demography

This research studied the effects of race and sex similarity on ratings in one-on-one highly structured college recruiting interviews (N = 708 interviewers and 12203 applicants for 7 different job families). A series of hierarchical linear models provided no evidence for similarity effects, although the commonly used D-score and analysis-of-variance-based interaction approaches conducted at the individual level of analysis yielded different results. The disparate results demonstrate the importance of attending to nested data structures and levels of analysis issues more broadly. Practically, the results suggest that organizations using carefully administered highly structured interviews may not need to be concerned about bias due to the mismatch between interviewer and applicant race or sex.     

Classification in well-defined and ill-defined categories: evidence for common processing strategies

Early work in perceptual and conceptual categorization assumed that categories had criterial features and that category membership could be determined by logical rules for the combination of features. More recent theories have assumed that categories have an ill-defined structure and have prosposed probabilistic or global similarity models for the verification of category membership. In the experiments reported here, several models of categorization were compared, using one set of categories having criterial features and another set having an ill-defined structure. Schematic faces were used as exemplars in both cases. Because many models depend on distance in a multidimensional space for their predictions, in Experiment 1 a multidimensional scaling study was performed using the faces of both sets as stimuli, In Experiment 2, subjects learned the category membership of faces for the categories having criterial features. After learning, reaction times for category verification and typicality judgments were obtained. Subjects also judged the similarity of pairs of faces. Since these categories had characteristic as well as defining features, it was possible to test the predictions of the feature comparison model (Smith et al.), which asserts that reaction times and typicalities are affected by characteristic features. Only weak support for this model was obtained. Instead, it appeared that subjects developed logical rules for the classification of faces. A characteristic feature affected reaction times only when it was part of the rule system devised by the subject. The procedure for Experiment 3 was like that for Experiment 2, but with ill-defined rather than well-defined categories. The obtained reaction times had high correlations with some of the models for ill-defined categories. However, subjects' performance could best be described as one of feature testing based on a logical rule system for classification. These experiments indicate that whether or not categories have criterial features, subjects attempt to develop a set of feature tests that allow for exemplar classification. Previous evidence supporting probabilistic or similarity models may be interpreted as resulting from subjects' use of the most efficient rules for classification and the averaging of responses for subjects using different sets of rules.     

Similarity and categorization of environmental sounds

Four experiments investigated the acoustical correlates of similarity and categorization judgments of environmental sounds. In Experiment 1, similarity ratings were obtained from pairwise comparisons of recordings of 50 environmental sounds. A three-dimensional multidimensional scaling (MDS) solution showed three distinct clusterings of the sounds, which included harmonic sounds, discrete impact sounds, and continuous sounds. Furthermore, sounds from similar sources tended to be in close proximity to each other in the MDS space. The orderings of the sounds on the individual dimensions of the solution were well predicted by linear combinations of acoustic variables, such as harmonicity, amount of silence, and modulation depth. The orderings of sounds also correlated significantly with MDS solutions for similarity ratings of imagined sounds and for imagined sources of sounds, obtained in Experiments 2 and 3--as was the case for free categorization of the 50 sounds (Experiment 4)--although the categorization data were less well predicted by acoustic features than were the similarity data.     

Predicting similarity and categorization from identification.

In this article, the relation between the identification, similarity judgment, and categorization of multidimensional perceptual stimuli is studied. The theoretical analysis focused on general recognition theory (GRT), which is a multidimensional generalization of signal detection theory. In one application, 2 Ss first identified a set of confusable stimuli and then made judgments of their pairwise similarity. The second application was to Nosofsky's (1985b, 1986) identification-categorization experiment. In both applications, a GRT model accounted for the identification data better than Luce's (1963) biased-choice model. The identification results were then used to predict performance in the similarity judgment and categorization conditions. The GRT identification model accurately predicted the similarity judgments under the assumption that Ss allocated attention to the 2 stimulus dimensions differently in the 2 tasks. The categorization data were predicted successfully without appealing to the notion of selective attention. Instead, a simpler GRT model that emphasized the different decision rules used in identification and categorization was adequate.     

A simple multivariate probabilistic model for preferential and triadic choices

Multidimensional probabilistic models of behavior following similarity and choice judgements have proven to be useful in representing multidimensional percepts in Euclidean and non-Euclidean spaces. With few exceptions, these models are generally computationally intense because they often require numerical work with multiple integrals. This paper focuses attention on a particularly general triad and preferential choice model previously requiring the numerical evaluation of a 2n-fold integral, wheren is the number of elements in the vectors representing the psychological magnitudes. Transforming this model to an indefinite quadratic form leads to a single integral. The significance of this form to multidimensional scaling and computational efficiency is discussed.The authors would like to thank Jean-Claude Falmagne and Norman Johnson for suggestions and advice concerning quadratic forms.     

Multidimensional analysis of twenty-one odors

Berglund, B., Berglund, U., Engen, T., & Ekman, G.¹ Multidimensional analysis of twenty-one odors. Scand. J. Psychol., 1973, 14, 131–137.-The present paper reports an experiment on the application of multidimensional scaling to the sense of smell for the purpose of revealing basic psychophysical dimensions of odorants matched in perceived intensity and varying only in perceived quality. The results showed clear evidence for the existence of individual odor spaces, but in apparent contradiction to related studies in the literature individual differences were too large to establish a representative odor space for the whole group. For nearly all individual subjects one of the factors extracted seemed to represent a unique hedonic dimension apparently unrelated to the physical attributes of the odorants. It is suggested that such psychological factors may be as important a basis for the judgment of the similarity of odors as the physical attributes of the odorants. Both the interpretation of multidimensional analysis and the extent to which the sense of smell is analytic or synthetic depend on an understanding of this problem.     

Multidimensionality and Asymmetry in Religious Switching Behavior1

Rokeach proposed that switching between denominations is governed by their perceived similarity on a unidimensional continuum. Resulting research has been based on unidimensional methods assuming symmetric interdenominational exchanges. Both assumptions are questionable. We use two data sources, a local survey accounting for ministers' perceptions of similarity between religions and the General Social Surveys accounting for actual switching behavior. Analytic methods, including multidimensional scaling, seriation, and nearest neighbor analysis, were chosen for their ability to account for multidimensionality and asymmetry. Results support a relationship between multidimensional similarity and gaining members but less to losing members. We conclude that religious switching is best understood as a multidimensional asymmetric process. Applied examples are presented.     

Lure similarity affects visual episodic recognition: Detailed tests of a noisy exemplar model

Summed-similarity models of visual episodic recognition memory successfully predict the variation in false alarm rates across different test items. With data averaged across subjects, Kahana and Sekuler demonstrated that subjects' performance appears to change along with the mean similarity among study items; with high interstimulus similarity, subjects were less likely to commit false alarms to similar lures. We examined this effect in detail by systematically varying the coordinates of study and test items along a critical stimulus dimension and measuring memory performance at each point. To reduce uncontrolled variance associated with individual differences in vision, the coordinates of study and test items were scaled according to each subject's discrimination threshold. Fitting each of four summed-similarity models to the individual subjects' data demonstrated a clear superiority for models that take account of interitem similarity on a trialwise basis.