当代大学生自比型价值观数据的潜在结构

本研究对采自3796名在校大学生的Rokeach Value Survey自比型数据进行了因素分析和多维尺度分析。因素分析从两组价值观选项中分别获得6个双极因素,虽然内容各不相同,但均体现出个人指向-亲社会指向的特点。多维尺度分析所获得的两组选项的2维空间距离分布结果也体现类似特点,结果显示终极性价值观可分为四类,工具性价值观可分为五类。当前大学生价值观中存在着舒适的物质生活、兴奋的生活、幸福、快乐和自尊以及雄心壮志的、勇敢的和诚实的等个人取向内容占优势的可能性。在两种分析方法中,多维尺度分析更适合对自比型价值观数据潜在结构的探究。     

Joint-space analysis of “pick-any” data: Analysis of choices from an unconstrained set of alternatives

Social and naturally occurring choice phenomena are often of the pick-any type in which the number of choices made by a subject as well as the set of alternatives from which they are chosen is unconstrained. These data present a special analytical problem because the meaning of non-choice among pick-any choice data is always ambiguous: A non-chosen alternative may be either unacceptable, or acceptable but not considered, or acceptable and considered but not chosen. A model and scaling method for these data are introduced, allowing for this ambiguity of non-choice. Subjects are represented as points whose coordinates are proportional to the centroids of the points representing their choices. Alternatives are represented at points whose coordinates are proportional to the centroids of the points representing subjects who have chosen them. This centroid scaling technique estimates multidimensional joint spaces from the pick-any data.I am indebted to John Baird, Clyde Coombs, David Eames, John Hunter, Michael J. Levine, Elliot Noma, Robert Z. Norman, William S. Roy, Joseph Schwartz, Daniel Velleman, the editor, and anonymous reviewers for ideas and suggestions that have been incorporated into this work. Conferences organized by Hans J. Hummel for the Deutsche Forschungsgemeinschaft (1977) and by Samuel Leinhardt for the National Science Foundation (1975) were instrumental in the development of this work.     

Effects on indscal of non-orthogonal perceptions of object space dimensions

A general question is raised concerning the possible consequences of employing the very popular INDSCAL multidimensional scaling model in cases where the assumptions of that model may be violated. Simulated data are generated which violate the INDSCAL assumption that all individuals perceive the dimensions of the common object space to be orthogonal. INDSCAL solutions for these various sets of data are found to exhibit extremely high goodness of fit, but systematically distorted object spaces and negative subject weights. The author advises use of Tucker's three-mode model for multidimensional scaling, which can account for non-orthogonal perceptions of the object space dimensions. It is shown that the INDSCAL model is a special case of the three-mode model.     

Upper bounds for Kruskal's stress

In this paper the relationships between the two formulas for stress proposed by Kruskal in 1964 are studied. It is shown that stress formula one has a system of nontrivial upper bounds. It seems likely that minimization of this loss function will be liable to produce solutions for which this upper bound is small. These are regularly shaped configurations. Even though stress formula two yields less equivocal results, it seems to be expected that minimization of this loss function will tend to produce configurations in which the points are clumped. These results give no clue as to which of the two loss functions is to be preferred.This study has been supported by the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (Netherlands Organization for the Advancement of Pure Research), under grant 56-146.Comments by Willem Heiser and Frank Critichley have been very helpful.The second author presently is employed by the Netherlands Central Bureau of Statistics, Voorburg.     

The joint analysis of direct ratings,pairwise preferences,and dissimilarities

In studies involving judgments of similarity or dissimilarity, a variety of other variables may also be measured. Examples might be direct ratings of the stimuli, pairwise preference judgments, and physical measurements of the stimuli with respect to various properties. In such cases, there are important advantages to joint analyses of the dissimilarity and collateral variables. A variety of models are described for relating these and algorithms described for fitting these to data. A number of hypothesis tests are developed and an example offered.The research reported here was supported by grant number APA 320 to the author by the National Research Council of Canada.     

Restricted multidimensional scaling models for asymmetric proximities

Restricted multidimensional scaling models [Bentler & Weeks, 1978] allowing constraints on parameters, are extended to the case of asymmetric data. Separate functions are used to model the symmetric and antisymmetric parts of the data. The approach is also extended to the case in which data are presumed to be linearly related to squared distances. Examples of several models are provided, using journal citation data. Possible extensions of the models are considered. This research was supported in part by USPHS Grant 0A01070, P. M. Bentler, principal investigator, and NIMH Grant MH-24819, E. J. Anthony and J. Worland, principal investigators. The authors wish to thank E. W. Holman and several anonymous reviewers for their valuable suggestions concerning this research.     

Differentiability of Kruskal's stress at a local minimum

It is shown that Kruskal's multidimensional scaling loss function is differentiable at a local minimum. Or, to put it differently, that in multidimensional scaling solutions using Kruskal's stress distinct points cannot coincide.     

Random effects diagonal metric multidimensional scaling models

By assuming a distribution for the subject weights in a diagonal metric (INDSCAL) multidimensional scaling model, the subject weights become random effects. Including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the INDSCAL, ALSCAL, and other multidimensional scaling programs. Unlike traditional models, the number of parameters does not increase with the number of subjects, and, because the distribution of the subject weights is modeled, the construction of linear models of the subject weights and the testing of those models is immediate. Here we define a random effects diagonal metric multidimensional scaling model, give computational algorithms, describe our experiences with these algorithms, and provide an example illustrating the use of the model and algorithms.We would like to thank J. Douglas Carroll for early consultation of this research, and Robert I. Jennrich for commenting on an earlier draft of this paper and for help on the computational algorithms. James O. Ramsay and Forrest W. Young were instrumental in providing the example data. This work was supported in part by National Institute of Mental Health grant 1 R43 MH57559-01. We would also like to thank the anonymous referees for comments that helped to clarify our work.     

Nonmetric multidimensional scaling with clustering of subjects

A new nonmetric multidimensional scaling method is devised to analyze three-way data concerning inter-stimulus similarities obtained from many subjects. It is assumed that subjects are classified into a small number of clusters and that the stimulus configuration is specific to each cluster. Under this assumption, the classification of subjects and the scaling used to derive the configurations for clusters are simultaneously performed using an alternating least-squares algorithm. The monotone regression of ordinal similarity data, the scaling of stimuli and the K -means clustering of subjects are iterated in the algorithm. The method is assessed using a simulation and its practical use is illustrated with the analysis of real data. Finally, some extensions are considered.     

Improved bounds for optimal intervals in weakly constrained regression problems

The solution of weakly constrained regression problems typically requires the iterative search, in a given interval, of a point where a certain function has a zero derivative. This note deals with improved bounds for the interval to be searched.     

Additive similarity trees

Similarity data can be represented by additive trees. In this model, objects are represented by the external nodes of a tree, and the dissimilarity between objects is the length of the path joining them. The additive tree is less restrictive than the ultrametric tree, commonly known as the hierarchical clustering scheme. The two representations are characterized and compared. A computer program, ADDTREE, for the construction of additive trees is described and applied to several sets of data. A comparison of these results to the results of multidimensional scaling illustrates some empirical and theoretical advantages of tree representations over spatial representations of proximity data.We thank Nancy Henley and Vered Kraus for providing us with data, and Jan deLeeuw for calling our attention to relevant literature. The work of the first author was supported in part by the Psychology Unit of the Israel Defense Forces.     

An upper bound for sstress

In this note we derive an upper bound for the minimum for the multidimensional scaling loss function sstress. We conjecture that minimum sstress solution will be biased towards regular positioning of clumps of points over the surface of a sphere.This study has been supported by the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Netherlands Organization for the Advancement of Pure Research) under grant 56–97.     

Robust multidimensional scaling

A method for multidimensional scaling that is highly resistant to the effects of outliers is described. To illustrate the efficacy of the procedure, some Monte Carlo simulation results are presented. The method is shown to perform well when outliers are present, even in relatively large numbers, and also to perform comparably to other approaches when no outliers are present.This research was supported by Grant A8351 from the Natural Sciences and Engineering Research Council of Canada to Ian Spence.     

Three-way metric unfolding via alternating weighted least squares

Three-way unfolding was developed by DeSarbo (1978) and reported in DeSarbo and Carroll (1980, 1981) as a new model to accommodate the analysis of two-mode three-way data (e.g., nonsymmetric proximities for stimulus objects collected over time) and three-mode, three-way data (e.g., subjects rendering preference judgments for various stimuli in different usage occasions or situations). This paper presents a revised objective function and new algorithm which attempt to prevent the common type of degenerate solutions encountered in typical unfolding analysis. We begin with an introduction of the problem and a review of three-way unfolding. The three-way unfolding model, weighted objective function, and new algorithm are presented. Monte Carlo work via a fractional factorial experimental design is described investigating the effect of several data and model factors on overall algorithm performance. Finally, three applications of the methodology are reported illustrating the flexibility and robustness of the procedure.We wish to thank the editor and reviewers for their insightful comments.     

都市人智慧隐含理论的初步调查

本研究对上海市高校教师及其他成年市民的智慧隐含理论进行调查,经筛选获得40项智慧特征并对其进行非度量多维标度分析,鉴别出三个双极维度,分别解释为六个因子：超脱谦和的处世风格、杰出的认知能力、出色的人际互动能力、丰富的知识与经验、非凡的自知和自控能力、良好的性格特质。本文就中国人与西方人的智慧隐含理论进行跨文化比较分析。