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.     

Client Perceptions of and Preferences for University-Based Career Services

One hundred thirty-three students who were actively seeking career services reported on their perceptions of the similarity among, and their preferences for, 17 different types of career assistance by way of a paired comparison task. Multidimensional scaling (MDS) and multidimensional preference modeling procedures were used to map these data into spatial representations. Ethnicity, international/domestic student status, tendency to foreclose (TTFS; Blustein, Ellis, & Devenis, 1989), and previous experience with an interest inventory each accounted for differences in perceptions. All participants preferred career assistance involving direct interaction with employed individuals, but class level, occupational status, previous participation in a career development class, and previous experience with career counseling accounted for differences in preferences.     

Distance stability analysis in multidimensional scaling using the jackknife method

Stability or sensitivity analysis is an important topic in data analysis that has received little attention in the application of multidimensional scaling (MDS), for which the only available approaches are given in terms of a coordinate‐based analytical jackknife methodology. Although in MDS the prime interest is in assessing the stability of the points in the configuration, this methodology may be influenced by imprecisions resulting from the inherently necessary Procrustes method. This paper proposes an analytical distance‐based jackknife procedure to study stability and cross‐validation in MDS in terms of the jackknife distances, which is not influenced by the Procrustes method. For each object, the corresponding jackknife estimated points are considered as naturally clustered points, and stability and cross‐validation are analysed in terms of the MDS distances arising from the jackknife procedure, on the basis of a weighted cluster‐MDS algorithm. A jackknife‐relevant configuration is also proposed for cross‐validation in terms of coordinates, in a cluster‐MDS framework.     

Dissimilarities as indices of individual perceptual structure

The generality of dissimilarity judgments and of configurations obtained by multidimensional scaling (MDS) as indices of perceptual structure was examined. The Ss made magnitude estimates of dissimilarity of pairs of photos, and MDS configurations were constructed separately for each S. The compatability of dissimilarities (judgments or distances in MDS configurations) with two other tasks Ss performed was then examined. These additional tasks, an “encoding” and a “decoding” task, required the S to first construct a message by making use of a set of four photos and, a week later, to decode the messages. Results obtained were interpreted as indicating a degree of generality of the dissimilarities and supporting a hypothesis of individual differences in perceptual structure for the stimulus set. A “data-purification” hypothesis for MDS was discussed and examined.

     

Avoiding the dangers of averaging across subjects when using multidimensional scaling

Ashby, Maddox and Lee (Psychological Science, 5 (3) 144) argue that it can be inappropriate to fit multidimensional scaling (MDS) models to similarity or dissimilarity data that have been averaged across subjects. They demonstrate that the averaging process tends to make dissimilarity data more amenable to metric representations, and conduct a simulation study showing that noisy data generated using one distance metric, when averaged, may be better fit using a different distance metric. This paper argues that a Bayesian measure of MDS models has the potential to address these difficulties, because it takes into account data-fit, the number of dimensions used by an MDS representation, and the precision of the data. A method of analysis based on the Bayesian measure is demonstrated through two simulation studies with accompanying theoretical analysis. In the first study, it is shown that the Bayesian analysis rejects those MDS models showing better fit to averaged data using the incorrect distance metric, while accepting those that use the correct metric. In the second study, different groups of simulated ‘subjects’ are assumed to use different underlying configurations. In this case, the Bayesian analysis rejects MDS representations where a significant proportion of subjects use different configurations, or when their dissimilarity judgments contain significant amounts of noise. It is concluded that the Bayesian analysis provides a simple and principled means for systematically accepting and rejecting MDS models derived from averaged data.     

Scale properties of the Holtzman inkblots

Scaling techniques were presently applied to perceptions of inkblots, to empirically delineate the relationship between their stimulus properties and the nature of verbal associations elicited in projective testing. The Holtzman Inkblot Technique (HIT) was administered in group form to a relatively diverse group of college students. Subjects also individually rated the similarity of pairs of the HIT inkblots. Similarity judgments were analyzed via a multidimensional scaling (MDS) approach which recovered dimensions of variations among blots. The MDS procedures also captured variation across subjects in their utilization of blot stimulus properties. MDS solutions generally reflected differences among the blots along dimensions of physical characteristics of the blots. Differences in responsiveness of subjects to these characteristics appeared to reliably reflect meaningful substantive distinctions among subjects, many of which were not captured by traditional HIT variables. Implications were discussed in terms of further MDS applications and possible re-evaluation of HIT variables or procedures.     

Scaling techniques for modeling directional knowledge

A common way for researchers to model or graphically portray spatial knowledge of a large environment is by applying multidimensional scaling (MDS) to a set of pairwise distance estimations. We introduce two MDS-like techniques that incorporate people’s knowledge of directions instead of (or in addition to) their knowledge of distances. Maps of a familiar environment derived from these procedures were more accurate and were rated by participants as being more accurate than those derived from nonmetric MDS. By incorporating people’s relatively accurate knowledge of directions, these methods offer spatial cognition researchers and behavioral geographers a sharper analytical tool than MDS for studying cognitive maps.     

Determining the significance of scale values from multidimensional scaling profile analysis using a resampling method

Although multidimensional scaling (MDS) profile analysis is widely used to study individual differences, there is no objective way to evaluate the statistical significance of the estimated scale values. In the present study, a resampling technique (bootstrapping) was used to construct confidence limits for scale values estimated from MDS profile analysis. These bootstrap confidence limits were used, in turn, to evaluate the significance of marker variables of the profiles. The results from analyses of both simulation data and real data suggest that the bootstrap method may be valid and may be used to evaluate hypotheses about the statistical significance of marker variables of MDS profiles.     

流式细胞术在骨髓增生异常综合征及再生障碍性贫血诊断中的应用

为探讨骨髓增生异常综合征患者与再生障碍性贫血患者骨髓髓系细胞的免疫表型变化,用流式细胞术检测骨髓增生异常综合征、再生障碍性贫血及正常对照髓系细胞的表面抗原。结果显示骨髓增生异常综合征组髓系细胞较正常对照组及再生障碍性贫血组表面抗原表达明显不同。因此,流式细胞术有助于二者的诊断及鉴别诊断。     

Mapping the similarity space of paintings: Image statistics and visual perception

What makes two images look similar? Here we test the hypothesis that perceived similarity of artwork is related to basic image statistics to which the early visual system is attuned. In two experiments, we employ multidimensional scaling (MDS) analysis of paired-image similarity ratings from observers for paintings. Two sets of images, classified as “landscapes” and “portraits/still-life”, are tested separately. For the landscapes, we find that one of the first two MDS scales of similarity is strongly correlated with a basic greyscale image statistic, whereas the other dimension can be accounted for by a semantic variable (representation of people). For portrait/still-life, the first two MDS scales of similarity are most highly correlated with semantic variables. Linear combinations of statistical and nonstatistical features achieve improved predictive values for the first two MDS scales for both sets. The statistics that play the largest role in shaping similarity judgements in our tests are the activity fraction measure of sparseness and the log-log slope of the spatial frequency amplitude spectrum. We discuss these results in the context of scene perception and in terms of efficient coding of statistical regularities in scenes.     

Multidimensional modeling with unidimensional approximations

This paper advances nonparametric multidimensional item response theory by reporting experimental results on the use of nonmetric multidimensional scaling (MDS) to synthesize a multidimensional model from several approximating one-dimensional models. A two-dimensional simulation data set contains items in which the two-component traits combine linearly (dominance model items) and items in which the two-component traits combine quadratically (ideal point items). Several unidimensional approximations of the two-dimensional model were obtained by running unidimensional estimation software on the simulated data set. The graphs reconstructed from MDS of the unidimensional approximations at selected points clearly separate dominance items from ideal point items, and also various types of dominance or ideal point models. MDS also succeeded in determining the dimensionality of the simulation model items from the observable item responses.     

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.     

COUNSELING IN INDUSTRY: A SELECTED REVIEW OF THE LITERATURE

This paper reviews the literature on counseling in business and industry. It summarizes what is known about (a) the extent to which personal and career counseling services exist within industry and (b) the effectiveness of various counseling programs in dealing with specific employee problems or concerns. The review is divided into three major sections. The first describes various programs and research involving counseling for personal problems. This is followed by a summary of efforts by industry to provide various forms of career counseling and guidance. Finally, the last section offers several conclusions about the current state of counseling in industry and discusses some implications for future research and evaluation such as the need for more clarity in what is typically referred to as counseling, increased specification of objectives and outcome criteria, comparison of different types of counseling approaches, a broader examination of the extensiveness of counseling in industry, and a higher standard for practitioner-oriented magazines which publish articles about counseling in industry.     

ConPar: a method for identifying groups of concordant subject proximity matrices for subsequent multidimensional scaling analyses

A common representation of data within the context of multidimensional scaling (MDS) is a collection of symmetric proximity (similarity or dissimilarity) matrices for each of M subjects. There are a number of possible alternatives for analyzing these data, which include: (a) conducting an MDS analysis on a single matrix obtained by pooling (averaging) the M subject matrices, (b) fitting a separate MDS structure for each of the M matrices, or (c) employing an individual differences MDS model. We discuss each of these approaches, and subsequently propose a straightforward new method (CONcordance PARtitioning—ConPar), which can be used to identify groups of individual-subject matrices with concordant proximity structures. This method collapses the three-way data into a subject×subject dissimilarity matrix, which is subsequently clustered using a branch-and-bound algorithm that minimizes partition diameter. Extensive Monte Carlo testing revealed that, when compared to K-means clustering of the proximity data, ConPar generally provided better recovery of the true subject cluster memberships. A demonstration using empirical three-way data is also provided to illustrate the efficacy of the proposed method.     

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.     

Adolescent males' view on the use of mental health counseling services

This study investigated adolescent males' view on mental health counseling. Additionally, participants were asked if they had ever used mental health counseling services, if they expected to use such services in the future, and what types of services/activities would constitute a successful counseling experience. The participants' responses indicated that they associated mental health counseling with mental illness and pathology. Eighty-eight percent of the participants reported having never used mental health counseling services. Surprisingly, 69% reported a willingness to use mental health counseling services for life's concerns. Finally, the participants identified a preference for action-oriented counseling strategies. Implications for mental health counseling practice are discussed.     

Career and personal counseling: Comparing process and outcome

Increasingly, there is a call to support the integration of career and personal counseling. However, few empirical studies have examined the overlap between these 2 domains. This study examined how career and personal counseling compared on both process and outcome measures. The participants included real clients who sought career and personal counseling at 3 college counseling centers in the U.S. The findings indicated that except in the area of expectations about counseling, there were no significant differences between career counseling and personal counseling. The implications for counseling practice and training are discussed.