Multidimensional scaling: I. Theory and method

Multidimensional scaling can be considered as involving three basic steps. In the first step, a scale of comparative distances between all pairs of stimuli is obtained. This scale is analogous to the scale of stimuli obtained in the traditional paired comparisons methods. In this scale, however, instead of locating each stimulus-object on a given continuum, the distances between each pair of stimuli are located on a distance continuum. As in paired comparisons, the procedures for obtaining a scale of comparative distances leave the true zero point undetermined. Hence, a comparative distance is not a distance in the usual sense of the term, but is a distance minus an unknown constant. The second step involves estimating this unknown constant. When the unknown constant is obtained, the comparative distances can be converted into absolute distances. In the third step, the dimensionality of the psychological space necessary to account for these absolute distances is determined, and the projections of stimuli on axes of this space are obtained. A set of analytical procedures was developed for each of the three steps given above, including a least-squares solution for obtaining comparative distances by the complete method of triads, two practical methods for estimating the additive constant, and an extension of Young and Householder's Euclidean model to include procedures for obtaining the projections of stimuli on axes from fallible absolute distances.This study was carried out while the author was an Educational Testing Service Psychometric Fellow at Princeton University. The author expresses his appreciation to his thesis adviser, Dr. H. Gulliksen, for his guidance throughout the study and to Dr. B. F. Green, Jr., for valuable assistance on several of the derivations.     

Scale values derived from the method of choices

In many a psychometric problem, particularly in practical problems, the only data conveniently obtainable are the first choices given to certain stimuli among a list of stimuli that are available for selection. By assuming that such choices represent real comparative judgments, we may apply Thurstone's law of comparative judgments, extract experimental proportions from the numbers of first choices, and compute psychological scale values for the stimuli. Two procedures are proposed for estimating such proportions and examples of their applications are given. A procedure for allocating a meaningful zero point on the scale by the use of absolute judgments is explained and demonstrated. Suggestions are added for overcoming certain weaknesses and limitations of the method of choices.     

AN EMPIRICAL APPLICATION OF A NEW CASE OF THE LAW OF COMPARATIVE JUDGMENT

A case of the law of comparative judgment which does not assume equal variances and covariances has been applied in the scaling of conservatism from seven attitude scale items. The scale values are in good agreement with those computed from previously known cases. There is also some covariation between comparatal dispersions from Case IV and the new case.     

Discrimination of loudness similarity

Interval and ratio scale values were derived from measures of variability in the discrimination of loudness similarity. The interval values are linearly related to interval values based on equisection judgments (Garner, 1954), cumulating jnds (Riesz, 1933), and the dispersion of absolute judgments (Gamer, 1952). Scale values based on three diverse discriminability procedures and on the method of equisection are thus in good agreement. The ratio lvalues, however, are at variance with ratio values determined by direct ratio estimations (Stevens, 1955).     

The law of comparative judgment in the successive intervals and graphic rating scale methods

The law of comparative judgment is applied to the successive intervals and graphic rating scale methods. A procedure for estimating the modal discriminal process and discriminal dispersion of the stimuli, as well as the value of the boundaries of the intervals on the continuum, is given. From the estimated values it is possible to determine the theoretical proportions and to compare them with the actual experimental proportions. The agreement between these values is an indication of the adequacy of the assumptions made.     

结构化面试中评分量表对评分准确性的影响

采用2(组内变量:量尺大小(25分和9分))×2(组间变量:评分方法(相对和绝对))的混合实验设计探讨评分量表对115名大学生新手评委评分准确性的影响。对于评分准确性,采用Cronbach1955年提出的四个指标,Elevation(EL)、Differential elevation(DE)、Stereotype accuracy(SA)、Differential Accuracy(DA)。结果发现,评分方法只在SA上主效应显著,量尺大小在只在DA上主效应边缘显著,评分方法和量尺大小在DE、SA和DA三个指标上均有交互作用。总体上看,在结构化面试评分中,对于评分准确性,相对评分量表优于绝对评分量表,小量尺量表优于大量尺量表。     

The Multiplicative AHP,SMART and ELECTRE in a Common Context

This paper presents a comparative study of three popular methods for multicriteria decision analysis based on a particular model of human preferential judgement. Since decisions are invariably made within a given context, we model relative preferences as ratios of increments or decrements in an interval on an axis of desirability. Next we sort the ratio magnitudes into a small number of categories, represented by numerical values on a geometric scale. We explain why the analytic hierarchy process (AHP) and the French collection of ELECTRE methods, typically based on pairwise comparison methods, are concerned with categories of ratio magnitudes, whereas the simple multiattribute rating technique (SMART) essentially uses orders of magnitude of these ratios. This phenomenon provides a common basis for the analysis of the methods in question and for a cross-validation of their results. We illustrate the approach via a well-known case study, the choice of a location for a nuclear power plant. We conclude by discussing the scope of the comparative study. © 1997 John Wiley & Sons, Ltd.     

脂多糖受体mCD14定量研究的方法探讨

本文通过横断面研究,时100例正常人群（一次性）采集外周全血2ml,选用流式细胞技术测定单核细胞群、mCD14平均荧光强度值,行盲法测定。观察正常人群外周血mCD14的表达水平,探讨正常人群mCD14定量研究的方法。结果显示单核细胞与淋巴细胞的比值比单个读取mCD14的平均荧光强度值更具可重复性,集中趋势较好,有利于临床应用和比较研究。此方法可作为流式细胞仪定量检测数据校正的方法参考。     

Optimal scaling for ordered categories

This paper deals with the determination of optimal weights for points on scoring scales for subjective comparative experiments. A scoring scale with a specific number of points is considered, and it is assumed that verbal or other indications imply an order to the scale points. The optimal spacing for the scale points is obtained in the sense that treatment or item differences are maximized relative to error or within-treatment variation. The method is presented in sufficiently generalized form to be used directly with any experimental design leading to the analysis of variance. An iterative procedure, suitable for computer use, yields the optimal differences among the ordered scale points. Properties of this procedure are discussed.Research sponsored in part by the Statistics Branch, Office of Naval Research, and in part by the Research Center, the General Foods Corporation. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

BRIGHTNESS SCALES FOR MONOCHROMATIC LIGHT

By means of amethod of ratio estimation, scale values were obtained for the subjective brightness of various physical intensities of monochromatic light of various wave lengths. In a second experiment the scale was constructed by a method of magnitude estimation. The brightness functions were studied by plotting the scale values against stimulus intensity for each wave length. The two experiments gave essentially the same results. It was shown: (1) Brightness of monochromatic light is a power function of stimulus intensity. The exponent of the function is approximately one-third for all wave lengths. (2) Properties of the brightness functions can explain certain empirical relations between brightness, hue and saturation.     

Testing the identity of trends under the restriction of monotonicity in repeated measures designs

Procedures are described for the analysis of profiles of means in repeated measures designs under order restriction for patterns of mean change. The exact likelihood ratio is derived for the case of two groups of subjects, and a computationally simple alternative to the exact likelihood ratio test is provided for designs involving more than two groups. Tables of critical values are provided for the case of simple-order alternatives.The author wishes to thank Joseph C. Saunders for his editorial assistance.     

A METHOD FOR SCALING VERBAL DISQUALIFICATION

A disqualification is a message that says something “without really saying it”—one that is evasive, indirect, or effectively ambiguous in some other way. This article describes the rationale for, and development of, an objective method for measuring the degree of disqualification in brief written messages: nonexpert judges independently assess four basic elements of the message (sender, content, receiver, context) for ambiguity, by use of a physical scale of length. The raw scale values are standardized for each judge, and the reliability of these values is quite high. Research uses of the method, as well as its limitations and possible modifications, are discussed.     

A social-value analysis of postmaterialism

The author investigated the relationship between social values and R. Inglehart's (1971, 1981, 1990) Postmaterialism concept. In his theory, Materialism and Postmaterialism are basic value dimensions motivated by a person's need for security and short-term survival (on the one hand) and the desire to address needs that transcend material concerns (on the other). The aim of the present study was to attempt to locate Postmaterialism relative to politically nonspecific social values. Participants were 161 New Zealand university undergraduate men and women who completed P. R. Abramson and R. Inglehart's (1995) Postmaterialism scale and a 56-item Social Values Inventory (S. H. Schwartz, 1992). Analyses of Postmaterialism scale scores and aggregated scores reflecting the motivations underlying different groups of social values supported the hypothesis that Postmaterialism, as measured by this scale, is positively related to values associated with Self-Direction and Universalism motivations and negatively related to Security motivations. The results indicate that previous research had been limited to the application of values representing only a small part of the overall values space.     

On the evaluation and application of different scales for quantifying pairwise comparisons in fuzzy sets

One of the most critical issues in many applications of fuzzy sets is the successful evaluation of membership values. A method based on pairwise comparisons provides an interesting way of evaluating membership values. That method was proposed by Saaty, almost 20 years ago, and since then has captured the interest of many researchers around the world. However, recent investigations reveal that the original scale may cause severe inconsistencies in many decision-making problems. Furthermore, exponential scales seem to be more natural for humans to use in many decision-making problems. In this paper two evaluative criteria are used to examine a total of 78 scales which can be derived from two widely used scales. The findings in this paper reveal that there is no single scale that can outperform all the other scales. Furthermore, the same findings indicate that a few scales are very efficient under certain conditions. Therefore, for a successful application of a pairwise-comparison-based method the appropriate scale needs to be selected and applied.     

A comparative modeling approach to a large decision support system

A comparative modeling approach is proposed for a decision support framework enabling users to have access to different modeling techniques within a single system (depending on the problem and the resources available). Three modeling techniques were selected to illustrate a marketing strategic decision support system: analytic, heuristic, and data-driven. The preimplementation choice and the trade-offs of each technique are explained qualitatively. Subsequently, the unification of the three techniques is discussed, and the benefits and problems associated with the comparative modeling approach are evaluated. Hean Lee Poh received his Diplom-Ingenieur in electrical engineering from the University of Paderborn, Germany, in 1982, his M.S. in computer science from California Institute of Technology in 1987, and his M.S. and Ph.D. in engineering-economic systems from Stanford University in 1991. His main research interests are neural network algorithms and their application in marketing strategies, financial modeling, and decision support systems. He is also interested in quantitative business modeling. He teaches courses in fourth-generation languages and information systems research methodology. He has been with the National University of Singapore since 1984 and is currently a lecturer.     

社会比较对大学生抑郁的影响:有调节的中介效应

探讨社会比较对大学生抑郁的影响机制,采用社会比较倾向量表、物质主义价值观量表、正念注意觉知量表和抑郁问卷,对980名大学生进行了调查研究。结果表明:1.社会比较和物质主义价值观都显著正向预测了大学生抑郁; 2.物质主义价值观在社会比较对大学生抑郁的影响中起部分中介作用; 3.正念在社会比较通过物质主义价值观对大学生抑郁产生影响的中介过程中起调节作用,正念调节了中介过程的后半路径。因此,在社会比较对大学生抑郁的影响过程中,物质主义价值观起到了部分中介作用,正念起到了调节作用。     

SUCCESSIVE INTERVALS SCALING WITH UNEQUAL VARIANCES AND COVARIANCES

The paper describes a solution for scale values in successive intervals scaling which does not assume equal covariances and variances. A more restrictive distribution assumption is made, however. Advantages and disadvantages of the method are discussed in relation to the two available conventional scaling techniques for scaling with unequal variances.     

A theory of relative judgment

This paper is concerned with the scaling method of “ratio estimation.” The simple theory that equates reported ratio judgments to ratios of psychological magnitudes is first considered, then two close relatives of this theory are formulated, each of which places weaker constraints on the structure of the data. Structural conditions are stated that express the relations that must hold among observed ratio judgments for each of the models. The models proposed are “cumulative” in the sense that the second is a weakened version of the first, and the third a weakened version of the second. A special feature of the models is that they may be tested entirely in terms of observables, avoiding the necessity of scale construction prior to testing. Tests were carried out on data from 9 published studies. The strongest model, typically used in scale construction using ratio estimation data, was generally inadequate, showing large systematic errors. However, the weakest version generally passed the tests of internal consistency, and the model equation provided a basis for constructing ratio scales utilizing bias parameters.