A simple multivariate probabilistic model for preferential and triadic choices

Multidimensional probabilistic models of behavior following similarity and choice judgements have proven to be useful in representing multidimensional percepts in Euclidean and non-Euclidean spaces. With few exceptions, these models are generally computationally intense because they often require numerical work with multiple integrals. This paper focuses attention on a particularly general triad and preferential choice model previously requiring the numerical evaluation of a 2n-fold integral, wheren is the number of elements in the vectors representing the psychological magnitudes. Transforming this model to an indefinite quadratic form leads to a single integral. The significance of this form to multidimensional scaling and computational efficiency is discussed.The authors would like to thank Jean-Claude Falmagne and Norman Johnson for suggestions and advice concerning quadratic forms.     

A direct solution for pairwise rotations in Kaiser's varimax method

The present note contains a completing-the-squares type approach to the varimax rotation problem. This approach yields a direct proof of global optimality of a solution for optimal rotation in a plane. Because varimax rotation can be interpreted as diagonalization of a set of symmetric matrices, the present solution also applies to the diagonalization problem.The author is obliged to Jos M. F. ten Berge for helpful comments.     

Generalizations of the partial,part and bipartial canonical correlation analysis

Theg ₁- andg ₂-bipartial canonical correlation analyses are developed as generalizations of the partial, part, and bipartial canonical correlation analysis. Illustrative examples are provided.     

Analysis of contingency tables by ideal point discriminant analysis

Cross-classified data are frequently encountered in behavioral and social science research. The loglinear model and dual scaling (correspondence analysis) are two representative methods of analyzing such data. An alternative method, based on ideal point discriminant analysis (DA), is proposed for analysis of contingency tables, which in a certain sense encompasses the two existing methods. A variety of interesting structures can be imposed on rows and columns of the tables through manipulations of predictor variables and/or as direct constraints on model parameters. This, along with maximum likelihood estimation of the model parameters, allows interesting model comparisons. This is illustrated by the analysis of several data sets.Presented as the Presidential Address to the Psychometric Society's Annual and European Meetings, June, 1987. Preparation of this paper was supported by grant A6394 from the Natural Sciences and Engineering Research Council of Canada. Thanks are due to Chikio Hayashi of University of the Air in Japan for providing the ISM data, and to Jim Ramsay and Ivo Molenaar for their helpful comments on an earlier draft of this paper.     

Applications of mental rotation figures of the Shepard and Metzler type and description of a mental rotation stimulus library

The 3D cube figures used by Shepard and Metzler [Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701-703] have been applied in a broad range of studies on mental rotation. This note provides a brief background on these figures, their general use in cognitive psychology and their role in studying spatial behavior. In particular, it is pointed out that large sex differences with the 3D mental rotation figures tend to be observed only in particular tasks, such as the Vandenberg and Kuse test [Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47, 599-604] that involve multiple figures within a single problem. In contrast, pairwise presentation of the same 3D figures yields either small or no significant sex differences. In the context of the very broad range of ongoing research done with 3D figures, and the desirability of uniformity in the stimulus material used, we introduce a library of 16 cube mental rotation figures, each presented in orientations ranging from 0 to 360 degr in 5 degr steps, and with its mirror image, for a total of 2336 figures. This library, freely available to researchers, will help in the creation of mental rotation tasks both for presentation on the computer screen and for pencil and paper applications.     

Frames of reference in spatial span

In four experiments, a computerized Corsi-like paradigm was used to assess which of the many reference frames are used in visuospatial short-term memory. By varying the relative orientation (slanted +/–45° or in an upright position) of the head and the displays, we modulate the utility of the allocentric, egocentric (eye- and head-centred), and template-centred reference frames. The results of all experiments showed the crucial importance of the gravitational allocentric reference frames while using visuospatial short-term memory to retain a spatial sequence of elements. The results also provide some support for a mental rotation process involved in recognition following angular displacement of a multi-item display.     

Mental Rotation in False Belief Understanding

This study examines the spontaneous use of embodied egocentric transformation (EET) in understanding false beliefs in the minds of others. EET involves the participants mentally transforming or rotating themselves into the orientation of an agent when trying to adopt his or her visuospatial perspective. We argue that psychological perspective taking such as false belief reasoning may also involve EET because of what has been widely reported in the embodied cognition literature, showing that our processing of abstract, propositional information is often grounded in concrete bodily sensations which are not apparently linked to higher cognition. In Experiment 1, an agent placed a ball into one of two boxes and left. The ball then rolled out and moved either into the other box (new box) or back into the original one (old box). The participants were to decide from which box they themselves or the agent would try to recover the ball. Results showed that false belief performance was affected by increased orientation disparity between the participants and the agent, suggesting involvement of embodied transformation. In Experiment 2, false belief was similarly induced and the participants were to decide if the agent would try to recover the ball in one specific box. Orientation disparity was again found to affect false belief performance. The present results extend previous findings on EET in visuospatial perspective taking and suggest that false belief reasoning, which is a kind of psychological perspective taking, can also involve embodied rotation, consistent with the embodied cognition view.     

An investigation of mental rotation in infancy using change detection

Two experiments were conducted to examine mental rotation in 6- to 12-month-old infants (N = 166) using a change detection task. These experiments were replications of Lauer and Lourenco (Lauer et al., 2015; Lauer & Lourenco, 2016), using identical stimuli and variations of their procedure, including an exact replication conducted in a laboratory setting (Experiment 1), and an online assessment using Lookit (Scott et al.,2017; Scott & Schulz, 2017) (Experiment 2). Both experiments failed to replicate the results of the original study; in neither experiment did infants’ behavior provide evidence that they mentally rotated the object. Results are discussed in terms of the robustness of mental rotation in infancy and about limits in our experimental procedures for uncovering perceptual and cognitive abilities in infants.     

Mental rotation and temporal contingencies.

A task that requires subjects to determine whether two forms of the same shape, but in different orientations, are mirror images or identical except for orientation is called a handedness recognition task. Subjects' reaction times (RT) on this task are consistently related to the angular disparity (termed alpha) between the two presented forms. This pattern of data has been interpreted to indicate that subjects solve the task by imagining that one of the forms rotates into the orientation of the other (termed mental rotation). The speed with which one imagines one of the forms rotating has been widely considered a fixed capability of the individual, and thus immune to the effect of contingencies. We present an experiment that assesses the effects of temporal contingencies in a handedness recognition task on the slope of the function RT = f(alpha). The data indicate that the slope of this function can come under the control of temporal contingencies.     

对三维心理旋转操作任务特性的效应的初步研究

在认知心理学领域,对心理旋转的研究主要是以反应时范式为基础。本研究试图突破反应时范式,把心理测量学和实验的方法相结合,以现代测量理论——项目反应理论的项目参数（如项目难度、区分度、猜测参数）为指标,对心理旋转测验中,操作任务的若干特性对测验项目特性的影响进行研究,结果发现：对于以Ｓｈｅｐａｒｄ三维旋转材料编制的心理旋转测验、测验材料的复杂程度,标准图形和匹配图形的角度差,以及匹配图形的编排位置等对测验项目的诸特性均无显著影响。