Prose Representation: A Multidimensional Scaling Approach

Multidimensional scaling was employed to study the comprehension of prose. Subjects rated the similarity between pairs of 20 nouns before reading. After reading a passage containing the nouns, the subjects re-rated the words with respect to similarity within the passage. Subjects then recalled the passage. The similarity ratings were analyzed by multidimensional scaling. The results indicated that the scaling analysis provided an effective, valid indicator of prose representation. The multidimensional structural characteristics of dimension interpretation, clustering, and centrality were interpreted in terms of the theme, episodes, and central organizing feature of the story, respectively. Theoretically, the analysis indicated that comprehension was a function of the passage organization mapping onto the existing memory structure superimposed upon and suppressing the prior conceptual structure.     

Multidimensional Scaling in Counseling Research and Practice

The authors briefly describe the use of multidimensional scaling (MDS) in counseling. They discuss types of data that have been analyzed using MDS, kinds of MDS analyses, and the interpretation of MDS results and review MDS research relevant to vocational, family, group, and individual counseling. They also briefly discuss potential applications in counseling practice.     

Goodness-of-Fit Assessment in Multidimensional Scaling and Unfolding

Judging goodness of fit in multidimensional scaling requires a comprehensive set of diagnostic tools instead of relying on stress rules of thumb. This article elaborates on corresponding strategies and gives practical guidelines for researchers to obtain a clear picture of the goodness of fit of a solution. Special emphasis will be placed on the use of permutation tests. The second part of the article focuses on goodness-of-fit assessment of an important variant of multidimensional scaling called unfolding, which can be applied to a broad range of psychological data settings. Two real-life data sets are presented in order to walk the reader through the entire set of diagnostic measures, tests, and plots. R code is provided as supplementary information that makes the whole goodness-of-fit assessment workflow, as presented in this article, fully reproducible.     

A Counseling Practitioner's Primer to the Use of Multidimensional Scaling

Applications of multidimensional scaling (MDS) to counseling practice are discussed, and the author's use of MDS as a tool in a counseling training group is described.     

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.     

The Dimensions Underlying Loneliness Counseling Interventions: A Multidimensional Scaling Solution

The purpose of this study was to investigate major dimensions affecting the acceptability of loneliness counseling interventions from the potential client's perspective and to compare the results with dimensions posited by theoretical models of treatment acceptability. Data were collected from 241 university students who were asked to sort loneliness counseling interventions on the basis of their similarities. Multidimensional scaling analyses revealed 4 dimensions underlying the acceptability of loneliness counseling interventions: the type of activity required by the intervention, the counselor-client relationship, the difficulty of the intervention, and the fit of the intervention to the problem.     

The Circumplexity of Leary's Interpersonal Circle: A Multidimensional Scaling Perspective

To investigate the circulant structure of the 16 scales comprising the Interpersonal Checklist (ICL; Laforge & Suczek, 1955), intercorrelation matrices for mate and female undergraduate ICL scores were subjected to multidimentional scaling analysis. Results showed the following: (a) while the 16 ICL scales fall in a rough circular array, measurement gaps exist in the friendly-dominant and hostile-submissive quadrants; (b) sixteenths A-B-P and L-M-N were misarranged; (c) stress coefficients for a three-dimensional solution were in an acceptable range. Implications of these findings for future research and anchoring of the ICL to Kiesler's (1983) "1982 Interpersonal Circle" are discussed.     

Confirmatory Factor Analysis and Profile Analysis via Multidimensional Scaling

This paper describes the Confirmatory Factor Analysis (CFA) parameterization of the Profile Analysis via Multidimensional Scaling (PAMS) model to demonstrate validation of profile pattern hypotheses derived from multidimensional scaling (MDS). Profile Analysis via Multidimensional Scaling (PAMS) is an exploratory method for identifying major profiles in a multi-subtest test battery. Major profile patterns are represented as dimensions extracted from a MDS analysis. PAMS represents an individual observed score as a linear combination of dimensions where the dimensions are the most typical profile patterns present in a population. While the PAMS approach was initially developed for exploratory purposes, its results can later be confirmed in a different sample by CFA. Since CFA is often used to verify results from an exploratory factor analysis, the present paper makes the connection between a factor model and the PAMS model, and then illustrates CFA with a simulated example (that was generated by the PAMS model) and at the same time with a real example. The real example demonstrates confirmation of PAMS exploratory results by using a different sample. Fit indexes can be used to indicate whether the CFA reparameterization as a confirmatory approach works for the PAMS exploratory results.     

Confirmatory Factor Analysis and Multidimensional Scaling for Construct Validation of Cognitive Abilities

Although factor analysis is the most commonly-used method for examining the structure of cognitive variable interrelations, multidimensional scaling (MDS) can provide visual representations highlighting the continuous nature of interrelations among variables. Using data (N = 8,813; ages 17-97 years) aggregated across 38 separate studies, MDS was applied to 16 cognitive variables representative of five well-established cognitive abilities. Parallel to confirmatory factor analytic solutions, and consistent with past MDS applications, the results for young (18-39 years), middle (40-65 years), and old (66-97 years) adult age groups consistently revealed a two-dimensional radex disk, with variables from fluid reasoning tests located at the center. Using a new method, target measures hypothesized to reflect three aspects of cognitive control (updating, storage-plus-processing, and executive functioning) were projected onto the radex disk. Parallel to factor analytic results, these variables were also found to be centrally located in the cognitive ability space. The advantages and limitations of the radex representation are discussed.     

Hierarchical Bayesian parameter estimation for cumulative prospect theory

Cumulative prospect theory (CPT Tversky & Kahneman, 1992) has provided one of the most influential accounts of how people make decisions under risk. CPT is a formal model with parameters that quantify psychological processes such as loss aversion, subjective values of gains and losses, and subjective probabilities. In practical applications of CPT, the model’s parameters are usually estimated using a single-participant maximum likelihood approach. The present study shows the advantages of an alternative, hierarchical Bayesian parameter estimation procedure. Performance of the procedure is illustrated with a parameter recovery study and application to a real data set. The work reveals that without particular constraints on the parameter space, CPT can produce loss aversion without the parameter that has traditionally been associated with loss aversion. In general, the results illustrate that inferences about people’s decision processes can crucially depend on the method used to estimate model parameters.     

Group And Individual Regularities In Trait Inference: A Multidimensional Scaling Analysis

This study concerned regularities in trait inference, the manner in which limited information about another person is used to form a consistent total impression. An individual differences model for multidimensional scaling was appraised as a method for faithfully strong both broad culturally- determined standards, and differently-structured points of view. Judgments of likelihood of joint occurrence of trait pairs and measures of cognition were obtained from 139 subjects. Scaling analyses resulted in two points of view, the largest of which yielded dimensions of interpersonal affectivity, harmfulness, and charitableness. S e w a t e analyses of randomly divided groups yielded indices of dimension stability ranging up to .99. The results support the view that the multidimensional scaling model can serve well to explain and order trait inference data.     

A Multidimensional Scaling Analysis of Perceptions of Academic Dishonesty Among Fifth-Grade Students

A study was conducted to investigate the perceptions of academic dishonesty in fifth-grade students. Two methods were used to gather data: a sorting task, which was used to indirectly assess the students' perceptions, and a rating scale task, which was used to externally validate the results of the sorting task. Results of the multidimensional scaling analysis yielded two dimensions, the first being tests/homework and papers, and the second, more ambiguous appearing to differentiate based on seriousness.     

Hierarchical Bayesian estimation and hypothesis testing for delay discounting tasks

A state-of-the-art data analysis procedure is presented to conduct hierarchical Bayesian inference and hypothesis testing on delay discounting data. The delay discounting task is a key experimental paradigm used across a wide range of disciplines from economics, cognitive science, and neuroscience, all of which seek to understand how humans or animals trade off the immediacy verses the magnitude of a reward. Bayesian estimation allows rich inferences to be drawn, along with measures of confidence, based upon limited and noisy behavioural data. Hierarchical modelling allows more precise inferences to be made, thus using sometimes expensive or difficult to obtain data in the most efficient way. The proposed probabilistic generative model describes how participants compare the present subjective value of reward choices on a trial-to-trial basis, estimates participant- and group-level parameters. We infer discount rate as a function of reward size, allowing the magnitude effect to be measured. Demonstrations are provided to show how this analysis approach can aid hypothesis testing. The analysis is demonstrated on data from the popular 27-item monetary choice questionnaire (Kirby, Psychonomic Bulletin & Review, 16(3), 457–462 2009), but will accept data from a range of protocols, including adaptive procedures. The software is made freely available to researchers.     

The Rokeach Value Survey: Underlying Structure and Multidimensional Scaling

Studies have demonstrated that the ordinal, ipsative data provided by the Rokeach Value Survey (RVS; Rokeach 1973) are not suited to factor analysis. In this study, nonmetric multidimensional scaling (MDS) was used with a sorting task to identify the underlying subset of values. American college students were the participants, and the results indicate that individualism-achievement and collectivism-affiliation are the underlying dimensions of the RVS for both the terminal and the instrumental values. Observed variation in the use of MDS space was predicted, based on participants' developmental differences as measured by the Maslowian Assessment Survey (Williams & Page, 1989). Gender differences in the use of MDS space by participants were not observed. Analysis of angular variance was used to test both hypotheses.     

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types—continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.     

The Effects of Theistic and Atheistic Counselor Values on Client Trust: A Multidimensional Scaling Analysis

Using Multidimensional Scaling (MDS), we investigated how theistic or atheistic values of an analogue counselor influenced trust of the counselor by 49 religious psychotherapy clients and 51 religious leaders.     

The Multidimensional Scaling Of A Set Of Artistic Drawings : Perceived Structure And Scale Correlates

Product-centered research on creativity approaches the criterion problem of what is to be the referent for creativity through the analysis of tangible products such as a r t objects, writing, or scientific achievements. The present research is concerned with the evaluation and study of artist drawings contributed by sophomore students a t the Rhode Island School of Design. Multi-dimensional scaling methods were applied to similarity judgments obtained from art experts on two separate sets of 26 drawings. Three similarity dimensions accounted for the interstimulus distances for each set of drawings. Although no statistical test was available, the dimensions from the two seta appeared to correspond. Scale values of 4 drawings common to the two sets were consistent, and the dimensions appeared to define very similar stimulus characteristics. It was concluded that multidimensional scaling procedures provided a means for differentiating among a set of complex, esthetic products. Scale values of drawings on the three dimensions also correlated differentially with cognitive and achievement measures available on the students, suggesting that product dimensions identified via similarity judgments were related to characteristics of individuals producing the products. Hypotheses were developed as to the psychological meaning of the three product dimensions.     

Bayesian Hierarchical Multivariate Formulation with Factor Analysis for Nested Ordinal Data

This article devises a Bayesian multivariate formulation for analysis of ordinal data that records teacher classroom performance along multiple dimensions to assess aspects characterizing good instruction. Study designs for scoring teachers seek to measure instructional performance over multiple classroom measurement event sessions at varied occasions using disjoint intervals within each session and employment of multiple ratings on intervals scored by different raters; a design which instantiates a nesting structure with each level contributing a source of variation in recorded scores. We generally possess little a priori knowledge of the existence or form of a sparse generating structure for the multivariate dimensions at any level in the nesting that would permit collapsing over dimensions as is done under univariate modeling. Our approach composes a Bayesian data augmentation scheme that introduces a latent continuous multivariate response linked to the observed ordinal scores with the latent response mean constructed as an additive multivariate decomposition of nested level means that permits the extraction of de-noised continuous teacher-level scores and the associated correlation matrix. A semi-parametric extension facilitates inference for teacher-level dependence among the dimensions of classroom performance under multi-modality induced by sub-groupings of rater perspectives. We next replace an inverse Wishart prior specified for the teacher covariance matrix over dimensions of instruction with a factor analytic structure to allow the simultaneous assessment of an underlying sparse generating structure. Our formulation for Bayesian factor analysis employs parameter expansion with an accompanying post-processing sign re-labeling step of factor loadings that together reduce posterior correlations among sampled parameters to improve parameter mixing in our Markov chain Monte Carlo (MCMC) scheme. We evaluate the performance of our formulation on simulated data and make an application for the assessment of the teacher covariance structure with a dataset derived from a study of middle and high school algebra teachers.     

Multidimensional Fechnerian Scaling: Pairwise Comparisons, Regular Minimality, and Nonconstant Self-Similarity

Stimuli presented pairwise for same-different judgments belong to two distinct observation areas (different time intervals and/or locations). To reflect this fact the underlying assumptions of multidimensional Fechnerian scaling (MDFS) have to be modified, the most important modification being the inclusion of the requirement that the discrimination probability functions possess regular minima. This means that the probability with which a fixed stimulus in one observation area (a reference) is discriminated from stimuli belonging to another observation area reaches its minimum when the two stimuli are identical (following, if necessary, an appropriate transformation of the stimulus measurements in one of the two observation areas). The remaining modifications of the underlying assumptions are rather straightforward, their main outcome being that each of the two observation areas has its own Fechnerian metric induced by a metric function obtained in accordance with the regular variation version of MDFS. It turns out that the regular minimality requirement, when combined with the empirical fact of nonconstant self-similarity (which means that the minimum level of the discrimination probability function for a fixed reference stimulus is generally different for different reference stimuli), imposes rigid constraints on the interdependence between discrimination probabilities and metric functions within each of the observation areas and on the interdependence between Fechnerian metrics and metric functions belonging to different observation areas. In particular, it turns out that the psychometric order of the stimulus space cannot exceed 1.