Multidimensional Scaling Solutions Research Articles

What Do We Really Want?: Mental Models of Ideal Romantic Involvement Explored through Multidimensional Scaling

Three studies extended the comparison level construct by exploring young adults′ mental models of ideal romantic involvement. Studies 1 and 2 were three-phase multidimensional scaling studies. In Phase 1 subjects′ descriptions of ideal involvement were solicited. In Phase 2 subjects judged the dissimilarities among Phase 1 descriptions, and multidimensional scaling solutions were computed in one through six dimensions. In Phase 3 a list of potential labels for the Phase 2 configurations was developed, and trained judges rated each Phase 1 description with respect to each label. These data were used to interpret the Phase 2 configurations. Two dimensions effectively described the derived configurations-Intimate versus Superficial and Romantic-Traditional versus Practical-Nontraditional. These dimensions defined four quadrants, or types of ideal: Picturebook Fantasy, Marital Bliss, Utilitarian Involvement, and Companionship. A third study asked whether these ideals are relevant to the ways in which subjects think about potential or actual relationships. Relationship descriptions were solicited under one of three instructional sets-ideal involvement, realistic standard, or actual relationship. Judges′ ratings of descriptions revealed few substantive differences across instructional sets, either in mean levels of labels or in the structure of relationships among labels. Thus, the issues that are salient when describing ideal romantic involvement do not differ substantively from those that are salient when thinking about realistic standards or actual, ongoing relationships. This work also demonstrated that women′s ideals exhibit greater Intimacy and Romance-Traditionalism than men′s.

Three dimensions mental health professionals emphasize when judging levels of functioning of the severely mentally disabled in the community

Ratings of the level of functioning of severely disabled clients collected from staff of mental health agencies, while attractive as outcome measures, lack specificity and, at times, consistency. Three multidimensional scaling (MDS) studies were conducted to identify the dimensions staff emphasize when they compare clients as to their level of functioning. Analogues of clients were created to serve as stimuli, dissimilarity judgments of pairs of stimuli were collected, and an individual differences MDS model was applied in each study to distinguish client variance from the judges' perspectives. Ratings along specified dimensions also were collected and compared to the MDS solutions. One dimension emerged as pre-eminent, but it corresponded to many of the pre-selected dimensions, such as competence with daily living tasks, clarity of thinking, appearance and manner, and overall functioning. The other two dimensions were belligerence and openness to psychological intervention or distress with one's problems. Differences among judges were sizable; nevertheless, considerable support for emphasizing these three dimensions was found upon reviewing the contents of other assessments of functioning. Concentrating on these three dimensions of functioning may promote greater agreement among raters, highlight where functional improvements occur, and expand the coverage of functional differences without markedly increasing the costs of assessment.

Cognitive representations of functional interactions with objects

Two studies addressed people's knowledge about the movements underlying functional interactions with objects, when the interactions were described by simple verbal labels expressing environmental goals. In Experiment 1, subjects rated each action with respect to six dimensions: which portion of the limb moved, distance moved, forcefulness, effectors involved, size of the contact surface, and resemblance to grasp. Ratings were systematic and fell on two distinct underlying factors related to limb movement and effector (usually the hand) configuration. In Experiment 2, subjects sorted a subset of the actions by similarity of movement. Clustering and multidimensional scaling solutions indicated that the six initial dimensions contributed to similarity judgments, along with additional parameters. The results support the existence of cognitively accessible, but still relatively specific, representations of functional actions, with potential implications for motor and memory performance.

Multidimensional scaling reliability in similarity judgments about environmental sentences

The aim of this research was to analyze the stability of Multidimensional Scaling (MDS). The investigations on this topic include studies related to the assumptions of linearity and monotonicity and to the validity and reliability of MDS procedures. Centered in this last topic, a test of the reliability of MDS procedure was carried out. We employed a set of complex stimuli: 21 sentences related to environmental field. 40 subjects made similarity judgements about both pairs “sentence A — sentence B” and “sentence B — sentence A”, so obtaining one square matrix per subject. Each of these matrices was broken down into two triangular matrices that were scaled separately by INDSCAL. The coordinates of stimuli in both MDS solutions were correlated. The results show a significant correlation between the two solutions.

Identifying High Level Features of Texture Perception

A fundamental issue in texture analysis is that of deciding what textural features are important in texture perception, and how they are used. Experiments on human preattentive vision have identified several low-level features (such as orientation of blobs and size of line segments), which are used in texture perception. However, the question of what higher level features of texture are used has not been adequately addressed. We designed an experiment to help identify the relevant higher order features of texture perceived by humans. We used 20 subjects, who were asked to perform an unsupervised classification of 30 pictures from Brodatz′s album on texture. Each subject was asked to group these pictures into as many classes as desired. Both hierarchical cluster analysis and nonparametric multidimensional scaling (MDS) were applied to the pooled similarity matrix generated from the subjects′ groupings. A surprising outcome is that the MDS solutions fit the data very well. The stress in the two-dimensional case is 0.10, and the stress in the three-dimensional case is 0.045. We rendered the original textures in these coordinate systems, and interpreted the (rotated) axes. It appears that the axes in the 2D case correspond to periodicity versus irregularity, and directionality versus nondirectionality. In the 3D case, the third dimension represents the structural complexity of the texture. Furthermore, the clusters identified by the hierarchical cluster analysis remain virtually intact in the MDS solution. The results of our experiment indicate that people use three high-level features for texture perception. Future studies are needed to determine the appropriateness of these high-level features for computational texture analysis and classification.

Analysis of pattern-reversal visual evoked-potential topography: replicability in normal subjects and comparisons with Alzheimer's disease.

This paper reports two studies using multivariate analysis to aid the interpretation of cross-coherence of multiple electrode sites in evoked potential responses. In the first study, the replicability of principal components and multidimensional scaling was evaluated by applying both methods to pattern-reversal visual evoked potentials recorded from 28 scalp sites in two subgroups of sex- and age-matched healthy subjects, and then comparing the results. Four dimensions replicated in the two initial multidimensional scaling solutions and appeared to reflect differences in: 1) anterior versus posterior scalp areas, 2) laterality, 3) separation of frontal and occipital sites from other scalp regions, and 4) proximal versus distal placements. The initial principal components did not match well in the two groups, but rotation to congruence improved their replicability and ultimately yielded axes similar to those of the multidimensional scaling dimensions. In the second study, Alzheimer's disease and sex- and age-matched control subjects were evaluated. The four axes identified were the same as those described above, but after the solutions were rotated to align them, the group differences appeared negligible. Examination of the components and dimensions from both studies showed some consistent departures from being merely reflectors of site location, and the apparently visual dimension appeared clearly in all four groups. Judged on the basis of initial interpretability and replicability of the solutions, the results suggest that multidimensional scaling, with appropriate transformation, may provide an effective tool for analyzing pattern-reversal visual evoked-potential topography.

Individual differences in voice quality perception.

Sixteen listeners (10 expert, 6 naive) judged the dissimilarity of pairs of voices drawn from pathological and normal populations. Separate nonmetric multidimensional scaling solutions were calculated for each listener and voice set. The correlations between individual listeners' dissimilarity ratings were low. However, scaling solutions indicated that each subject judged the voices in a reliable, meaningful way. Listeners differed more from one another in their judgments of the pathological voices (which varied widely on a number of acoustic parameters) than they did for the normal voices (which formed a much more homogeneous set acoustically). The acoustic features listeners used to judge dissimilarity were predictable from the characteristics of the stimulus sets: only parameters that showed substantial variability were perceptually salient across listeners. These results are consistent with prototype models of voice perception. They suggest that traditional means of assessing listener reliability in voice perception tasks may not be appropriate, and highlight the importance of using explicit comparisons between stimuli when studying voice quality perception.

Seriation and Multidimensional Scaling: A Data Analysis Approach to Scaling Asymmetric Proximity Matrices

A number of model-based scaling methods have been developed that apply to asymmetric proximity matrices. A flexible data analysis approach is pro posed that combines two psychometric procedures— seriation and multidimensional scaling (MDS). The method uses seriation to define an empirical order ing of the stimuli, and then uses MDS to scale the two separate triangles of the proximity matrix defined by this ordering. The MDS solution con tains directed distances, which define an "extra" dimension that would not otherwise be portrayed, because the dimension comes from relations between the two triangles rather than within triangles. The method is particularly appropriate for the analysis of proximities containing temporal information. A major difficulty is the computa tional intensity of existing seriation algorithms, which is handled by defining a nonmetric seriation algorithm that requires only one complete itera tion. The procedure is illustrated using a matrix of co-citations between recent presidents of the Psychometric Society.

Similarity-scaling studies of dot-pattern classification and recognition.

Classification performance in the dot-pattern, prototype-distortion paradigm (e.g., Posner & Keele, 1968) was modeled within a multidimensional scaling (MDS) framework. MDS solutions were derived for sets of dot patterns that were generated from prototypes. These MDS solutions were then used in conjunction with exemplar, prototype, and combined models to predict classification and recognition performance. Across 3 experiments, an MDS-based exemplar model accounted for the effects of several fundamental learning variables, including level of distortion of the patterns, category size, delay of transfer phase, and item frequency. Most important, the model quantitatively predicted classification probabilities for individual dot patterns in the sets, not simply general trends of performance. There was little evidence for the existence of a prototype-abstraction process that operated above and beyond pure exemplar-based generalization.

Principal components and multidimensional scaling of auditory and visual event-related potential topography.

Principal components analysis and metric multidimensional scaling were used to assess auditory and visual event-related potential topography in healthy late-middle-aged and elderly adults (n = 20). Binaurally elicited auditory evoked potentials and full-field checkerboard pattern reversal visual event-related potentials were recorded from 28 scalp sites. The zero-lag, cross-correlations of all waveforms for 300 msec post-stimulus epochs were obtained and separate analyses of the auditory and visual data were performed. Ultimately, three of the four dimensions identified in the principal components and multidimensional scaling solutions were similar and represented electrode site differences in (1) the anterior-posterior plane; (2) laterality; and, (3) the proximal-distal relation to midline. The remaining multidimensional scaling axis appeared to reflect effects specific to the modality of stimulation. Under auditory stimulation, the temporal and central-parietal sites were distinct from other scalp regions, whereas under visual stimulation, the occipital and frontal sites were distinctive. Although the results of the principal component analyses were conceptually similar to the multidimensional scaling outcomes, there were consistent differences between them. The findings provide empirical support for the validity of these multivariate methods in topographic analysis.

The Structure of Student Interest in Computers and Information Technology: An Application of Facet Theory and Multidimensional Scaling.

The present study addressed the question of whether computers and information technology constitute a uniform attitude object which can influence the study interests of students. Based on a facet design, an interest questionnaire with 72 university course descriptions was constructed in which computers and information technology was embedded as one of four item-design facets (Weinsier & Leutner, 1988). One hundred students from each of two universities responded to the questionnaire. The multidimensional interest structures of the two samples were nearly identical. The design facets constituted uniform attitude objects and the multidimensional scaling solution of the inter-item correlation matrix could be partitioned almost perfectly according to regional hypotheses derived from the facet design. Next to the discipline facet (i.e., academic discipline), computers and information technology constituted the most relevant facet of student interest. An analysis of variance supported the conclusions drawn from the multidimensional scalings.

Multidimensional Scaling Analysis of Dysphonia in Two Speaker Groups

The objective of this research was to identify perceptually relevant features of 30 dysphonic female voices. The perceptual dimensions used by listeners in judging the similarity of the dysphonic voices were derived in two multidimensional scaling (MDS) procedures using ALSCAL. Three dimensions were extracted in each MDS solution and accounted for approximately 60% of the total variance in the judgments. The three dimensions were related to measures of intensity, frequency, and perturbation. The results are discussed in relation to how clinicians use perceptual judgments in evaluating dysphonic voices.

Tests of an exemplar model for relating perceptual classification and recognition memory.

Experiments were conducted in which Ss made classification, recognition, and similarity judgments for 34 schematic faces. A multidimensional scaling (MDS) solution for the faces was derived on the basis of the similarity judgments. This MDS solution was then used in conjunction with an exemplar-similarity model to accurately predict Ss' classification and recognition judgments. Evidence was provided that Ss allocated attention to the psychological dimensions differentially for classification and recognition. The distribution of attention came close to the ideal-observer distribution for classification, and some tendencies in that direction were observed for recognition. Evidence was also provided for interactive effects of individual exemplar frequencies and similarities on classification and recognition, in accord with the predictions of the exemplar model. Unexpectedly, however, the frequency effects appeared to be larger for classification than for recognition.

Multidimensional scaling and factor models of test and item responses.

This article discusses 2 alternatives to the factor model for test or item responses. From the two alternative models, proximity measures are derived so that the proximity measures are within an additive constant of squared euclidean distances between item or test parameters. Hence, multidimensional scaling (MDS) can be used to estimate the item parameters in the alternative models. Solutions that are based on the models are compared. In light of the response models, interpretation and appropriateness of factor and MDS solutions are discussed

Further tests of an exemplar-similarity approach to relating identification and categorization.

Further tests were provided of an exemplar-similarity model for relating the identification and categorization of separable-dimension stimuli (Nosofsky, 1986). On the basis of confusion errors in an identification paradigm, a multidimensional scaling (MDS) solution was derived for a set of 16 separable-dimension stimuli. This MDS solution was then used in conjunction with the exemplar-similarity model to accurately predict performance in four separate categorization paradigms with the same stimuli. A key to achieving the accurate quantitative fits was the assumption that a selective attention process systematically modifies similarities among exemplars across different category structures. The tests reported go well beyond earlier ones (Nosofsky, 1986) in demonstrating the generalizability and utility of the theoretical approach. Implications of the results for alternative quantitative models of classification performance, including Ashby and Perrin's (1988) general recognition theory, were also considered.

Trait anxiety and the cognitive representation of significant life events: Some correlates of situation-specific traits

Abstract This paper describes an exploratory investigation of Endler's person X situation model of trait anxiety using multidimensional scaling and related methods. The aim was to discover whether individual differences in “situation-specific” trait anxiety were related to differences in the way individuals cognitively represent significant life events. Thirty-four respondents provided brief descriptions of important personal experiences. These events were used as items in a pair-wise matching task to generate individual multidimensional scaling (MDS) solutions, and descriptive constructs for event similarity and dissimilarity. The dimensions and descriptors emerging from these analyses were correlated with five dimensions of trait anxiety, interpersonal, physical danger, ambiguous/novel, daily routines, and death. The findings provided some limited evidence for concordance between situation-specific traits and cognitive organisation. The ambiguous and physical danger scales were associated with affective...

Acquiescence in Components Analysis and Multidimensional Scaling of Self-Rating Items

Earlier work has shown that when multidimensional scaling (MDS) is applied to item intercorrelations, met ric MDS implicitly subtracts the standardized person mean (SPM) from responses. As a result, when a met ric or nonmetric MDS solution is compared to a com ponents solution, the components solution often con tains one component with no counterpart among the scaling dimensions. If self-report items form a bal anced scale and negatively worded items are not re verse scored, the SPM is closely related to several con cepts of acquiescence and disacquiescence. In this paper, MDS and components solutions are compared using two balanced self-report item sets. In the Likert self-report attitude item set, the MDS and components solutions were essentially the same. In a set of affec tive well-being items, the components solution con tained a general component with no counterpart among the scaling dimensions. Scores along the general com ponent were substantially correlated with measures of acquiescence and disacquiescence. Results in the sec ond dataset suggest that when the self-report items are balanced and the negatively worded items have not been reverse scored, MDS and components solutions can differ largely with respect to a component closely associated with certain measures of acquiescence. In dex terms: acquiescence, attitude measurement, factor analysis, multidimensional scaling, personality mea surement, response bias, self-report items.

Listener experience and perception of voice quality

This study examines the role of listener experience with populations of voices in the perception of vocal quality. Prototype models suggest that the strategy that naive listeners use to evaluate abnormal vocal qualities will differ significantly from that of listeners experienced with dysphonic populations. Listener groups should not differ in perceptual strategy for normal voices, where their experience is equal. The nature of differences in strategy is also examined: as listeners gain experience with populations of voices, do they hear them in more complicated ways, resulting in higher dimensional multidimensional scaling solutions and/or lower r2 values for these solutions? Alternatively, does experience increase the efficiency with which listeners utilize a relatively constant set of perceptual parameters? Six naive and six experienced listeners judged the similarity of 17 dysphonic and 17 normal voices. Separate MDS solutions were found for each listener group for each voice set, and regressions compared the solutions. The relative complexity and efficiency of individual perceptual strategies are also discussed.

How Do People Think About Intelligence?

Two studies are reported concerning implicit theories of intelligence. The first study replicated procedures employed by Sternberg, Conway, Ketron, and Bernstein (1981). Factor analysis of importance ratings of intelligent and unintelligent behaviors suggested a simpler model of implicit theories than suggested by Sternberg et al. However, the use of importance ratings for examining implicit theories was challenged because the results proved ambiguous. The second study used a sorting procedure to produce similarity data. Multidimensional and tree scaling solutions indicated that the primary distinction in implicit theories was between intelligent and unintelligent behaviors and that important distinctions were not made among intelligent behaviors. In general, the data suggested that implicit theories of intelligence are much simpler than most formal theories used in psychology.

A simple procedure for finding a composite of several multidimensional scaling solutions

One of the better known procedures for finding a representative composite of several different MDS solutions is based on Carroll’s generalized canonical correlation model (Carroll 1968). However, the program for implementing the fitting of this model has not received wide distribution. The present paper provides a simple computational method for implementing Carroll’s approach and shows its relationship to ordinary principal components analysis. In addition, we provide an algorithm for computing the parameters of Carroll’xs model in the presence of missing data. Each method is illustrated with data sets drawn from a marketing research study.