The integration of multidimensional scaling and multivariate analysis with optimal transformations

The recent history of multidimensional data analysis suggests two distinct traditions that have developed along quite different lines. In multidimensional scaling (MDS), the available data typically describe the relationships among a set of objects in terms of similarity/dissimilarity (or (pseudo-)distances). In multivariate analysis (MVA), data usually result from observation on a collection of variables over a common set of objects. This paper starts from a very general multidimensional scaling task, defined on distances between objects derived from one or more sets of multivariate data. Particular special cases of the general problem, following familiar notions from MVA, will be discussed that encompass a variety of analysis techniques, including the possible use of optimal variable transformation. Throughout, it will be noted how certain data analysis approaches are equivalent to familiar MVA solutions when particular problem specifications are combined with particular distance approximations.This research was supported by the Royal Netherlands Academy of Arts and Sciences (KNAW). An earlier version of this paper was written during a stay at McGill University in Montréal; this visit was supported by a travel grant from the Netherlands Organization for Scientific Research (NWO). I am grateful to Jim Ramsay and Willem Heiser for their encouragement and helpful suggestions, and to the Editor and referees for their constructive comments.     

On the robustness of maximum likelihood scaling for violations of the error model

A Monte Carlo study was conducted to investigate the robustness of the assumed error distribution in maximum likelihood estimation models for multidimensional scaling. Data sets generated according to the lognormal, the normal, and the rectangular distribution were analysed with the log-normal error model in Ramsay's MULTISCALE program package. The results show that violations of the assumed error distribution have virtually no effect on the estimated distance parameters. In a comparison among several dimensionality tests, the corrected version of thex ² test, as proposed by Ramsay, yielded the best results, and turned out to be quite robust against violations of the error model.     

Probabilistic multidimensional scaling: Complete and incomplete data

Simple procedures are described for obtaining maximum likelihood estimates of the location and uncertainty parameters of the Hefner model. This model is a probabilistic, multidimensional scaling model, which assigns a multivariate normal distribution to each stimulus point. It is shown that for such a model, standard nonmetric and metric algorithms are not appropriate. A procedure is also described for constructing incomplete data sets, by taking into consideration the degree of familiarity the subject has for each stimulus. Maximum likelihood estimates are developed both for complete and incomplete data sets. This research was supported by National Science Grant No. SOC76-20517. The first author would especially like to express his gratitude to the Netherlands Institute for Advanced Study for its very substantial help with this research.     

A multidimensional scaling model for the size-weight illusion

The kinds of individual differences in perceptions permitted by the weighted euclidean model for multidimensional scaling (e.g., INDSCAL) are much more restricted than those allowed by Tucker's Three-mode Multidimensional Scaling (TMMDS) model or Carroll's Idiosyncratic Scaling (IDIOSCAL) model. Although, in some situations the more general models would seem desirable, investigators have been reluctant to use them because they are subject to transformational indeterminacies which complicate interpretation. In this article, we show how these indeterminacies can be removed by constructing specific models of the phenomenon under investigation. As an example of this approach, a model of the size-weight illusion is developed and applied to data from two experiments, with highly meaningful results. The same data are also analyzed using INDSCAL. Of the two solutions, only the one obtained by using the size-weight model allows examination of individual differences in the strength of the illusion; INDSCAL can not represent such differences. In this sample, however, individual differences in illusion strength turn out to be minor. Hence the INDSCAL solution, while less informative than the size-weight solution, is nonetheless easily interpretable.This paper is based on the first author's doctoral dissertation at the Department of Psychology, University of Illinois at Urbana-Champaign. The aid of Professor Ledyard R Tucker is gratefully acknowledged.     

Redundancy gain for categorical targets depends on display configuration and duration

Redundancy gain is an improvement in speeded target detection when the number of targets associated with a single response is increased within a single display. The effect has been clearly demonstrated with specific targets, but it is not clear if it occurs in categorization tasks with non-identical targets. The current study tested the effect of target redundancy on speed and accuracy in a go/no-go categorization task. Targets were digits tilted 45° to the left, and were displayed in unilateral, bilateral, or central displays for either 1500?ms or 100?ms. Redundancy gain only occurred for brief targets displayed bilaterally in the upper visual field. The results indicate that redundancy gain is possible for categorization tasks with some bilateral configurations, supporting a role for interhemispheric processing in redundancy gain. Additionally, the results may indicate that processing strategies mask redundancy gain when participants can view targets for a long period of time.     

Capturing the noonday demon: development and validation of the State Boredom Inventory

For centuries, scholars have positioned state boredom as an impediment to organizational productivity and performance given its unpleasant and distracting qualities. However, research on state boredom has been impeded by a lack of definitional consensus and measurement issues. In this article, we sought to advance organizational research on state boredom by developing the State Boredom Inventory (SBI), an 11-item measure grounded in a theoretically derived definition of state boredom. Across five studies using 10 independent samples, we develop the SBI and provide validity evidence for our measure, including content validity and convergent and discriminant validity. Our data support the conceptualization of state boredom as a higher-order multidimensional construct with three underlying dimensions: disengagement, unpleasant low arousal, and inattention.     

Peering into the opaque mind

Abstract

Carolyn Saarni’s pioneering research showed that young children learn how to hide their feelings—to conceal disappointment with a smile or to conceal amusement with a neutral expression. By 6 years of age, children understand the implications of such concealment. They can distinguish between: (i) an individual’s true but hidden emotion; (ii) the emotion that the individual overtly expresses; and (iii) the emotion that other people might mistakenly attribute to the individual. Effectively, young children grasp that the mind is opaque. Its contents can remain hidden from others. We examine two issues raised by this important conceptual insight. First, we ask how it emerges in young children—what experiences lead them to acknowledge the mind’s opacity? Second, in light of Saarni’s emphasis on the impact of cultural beliefs and practices, we discuss anthropological evidence that in certain cultures the mind’s opacity is regarded as a social desideratum so that enquiries into, or speculations about, a person’s private mental states are regarded as inappropriate. We consider the understanding of hidden emotion that children will acquire if they grow up in such a culture. We propose—paradoxically—that they will readily differentiate between what is actually felt and what is overtly expressed. We conclude by reviewing recent cross-cultural evidence lending initial support to that prediction.     

大学生亲社会倾向、亲社会推理以及它们的相关模式

采用《亲社会倾向测量》和《亲社会推理客观测量》研究了17至20岁大学生的六类亲社会倾向和亲社会推理的状况。发现大学生将利他的亲社会倾向列为六类倾向中的首位,接下来依次是紧急的、情绪性的、依从的、匿名的和公开的亲社会倾向;在亲社会推理五种类型中大学生选择比率最高的是内化价值定向的推理,接下来依次是刻板定向、需要定向和享乐主义定向的推理,所占比率最低的是赞扬定向的推理;六类亲社会倾向与亲社会推理之间具有特定的棚关模式．利他的和匿名的亲社会倾向与内化价值定向和刻板定向的推理正相关、与享乐主义定向及赞扬定向的推理负相关,公开的亲社会倾向与赞扬定向的推理正相关、与需要定向的推理负相关。跨文化比较证实,中美大学生的上述三个方面表现出一定的差异。     

Constrained multidimensional unfolding of confusion matrices: Goal point and slide vector models

Two constrained multidimensional unfolding models, the goal point and slide vector models, are proposed for analyzing confusion matrices. In both models, the row and column stimuli are expressed as two sets of points in a low-dimensional space, where the difference vector connecting a column point to the corresponding row point indicates the change in the stimulus representation through a cognitive process. The difference vector is constrained by the hypothesis that the trend in the representational change is invariant across stimuli: the goal point model constrains all difference vectors to point toward a single point, and the slide vector model constrains all difference vectors to be parallel to each other. In both models the coordinates of points are estimated by the maximum-likelihood method. Examples illustrate that the two models allow us to examine hypotheses about invariant trends in representational changes and to grasp such trends from the resulting configurations.