Orthogonal rotations to maximal agreement for two or more matrices of different column orders

Methods for orthogonal Procrustes rotation and orthogonal rotation to a maximal sum of inner products are examined for the case when the matrices involved have different numbers of columns. An inner product solution offered by Cliff is generalized to the case of more than two matrices. A nonrandom start for a Procrustes solution suggested by Green and Gower is shown to give better results than a random start. The Green-Gower Procrustes solution (with nonrandom start) is generalized to the case of more than two matrices. Simulation studies indicate that both the generalized inner product solution and the generalized Procrustes solution tend to attain their global optima within acceptable computation times. A simple procedure is offered for approximating simple structure for the rotated matrices without affecting either the Procrustes or the inner product criterion.The authors are obliged to Charles Lewis for helpful comments on a previous draft of this paper and to Frank Brokken for preparing a computer program that was used in this study.     

Rotational equivalence of factor loading matrices with specified values

Under mild assumptions, when appropriate elements of a factor loading matrix are specified to be zero, all orthogonally equivalent matrices differ at most by column sign changes. Here a variety of results are given for the more complex case when the specified values are not necessarily zero. A method is given for constructing reflections to preserve specified rows and columns. When the appropriatek(k – 1)/2 elements have been specified, sufficient conditions are stated for the existence of 2 ^k orthogonally equivalent matrices.This research was supported in part by the National Institute of Health Grant RR-3.     

Admissible values of γ in direct oblimin rotation

It is shown that for nonpositive values of the parameter in the oblimin criterion, the criterion achieves a minimum on the manifold of all possible oblique rotations of any given full rank initial loading matrixA. For every positive value of , on the other hand, it is shown that there exists a full rank initial loading matrixA for which the oblimin criterion does not achieve a minimum over the manifold of all oblique rotations ofA. These results help explain the sometimes divergent behavior that results from using direct oblimin algorithms with set to a positive value.This research was supported in part by National Institutes of Health Grant RR-3.     

Mental rotation and handedness: differences in object-based and egocentric transformations

This study investigates mental rotation performance of right- and left-handers in object-based and egocentric mental rotation tasks using human body stimuli with an outstretched arm in front and back view. Previous literature suggests that right-handers show a slightly better mental rotation performance than left-handers. 42 participants, 14 left-handers and 28 right-handers, completed a mental rotation task with object-based and egocentric transformation of a human figure which was displayed either in front or back view. The main result was a three-way interaction between the factors “kind of transformation”, “handedness” and “view” in a way, that right-handers show significantly faster reaction times then left-handers in front view object-based transformations because of the additional in-depth rotation for front view stimuli. This difference disappeared in egocentric tasks due to the modification of onés own perspective to solve the task. The results of this study show that right-handers not generally outperform left-handers in mental rotation tasks but only if more cognitive resources are needed.     

Dissociating the effects of angular disparity and image similarity in mental rotation and object recognition

Performance is often impaired linearly with increasing angular disparity between two objects in tasks that measure mental rotation or object recognition. But increased angular disparity is often accompanied by changes in the similarity between views of an object, confounding the impact of the two factors in these tasks. We examined separately the effects of angular disparity and image similarity on handedness (to test mental rotation) and identity (to test object recognition) judgments with 3-D novel objects. When similarity was approximately equated, an effect of angular disparity was only found for handedness but not identity judgments. With a fixed angular disparity, performance was better for similar than dissimilar image pairs in both tasks, with a larger effect for identity than handedness judgments. Our results suggest that mental rotation involves mental transformation procedures that depend on angular disparity, but that object recognition is predominately dependent on the similarity of image features.     

Asymmetric learning transfer between imagined viewer- and object-rotations: Evidence of a hierarchical organization of spatial reference frames

Neural resources subserving spatial processing in either egocentric or allocentric reference frames are, at least partly, dissociated. However, it is unclear whether these two types of representations are independent or whether they interact. We investigated this question using a learning transfer paradigm. The experiment and material were designed so that they could be used in a clinical setting. Here, we tested healthy subjects in an imagined viewer-rotation task and an imagined object-rotation task. The order of the tasks was counterbalanced across subjects. The results showed that subjects who did the viewer-rotation task first had fewer errors and shorter latencies of response in the object-rotation task, whereas subjects who did the object-rotation task first had little if any advantage in the viewer-rotation task. In other words, the results revealed an asymmetric learning transfer between tasks, which suggests that spatial representations are hierarchically organized. Specifically, the results indicate that the viewer-rotation task engaged allocentric representations and egocentric representations, whereas the object-rotation task engaged only egocentric representations.     

复合字母刺激心理旋转加工中的整体优先效应

采用复合字母材料结合正镜像判断任务,首次揭示了心理旋转加工中的整体优先效应。实验一延长复合字母材料的呈现时间,检验心理旋转实验常用的正/镜像判断任务中的视知觉整体优先效应;实验二将实验一的复合字母材料旋转一定角度,考察心理旋转加工中的整体优先效应。结果发现：（1）延长复合字母呈现时间后的字母正镜像判断任务中,被试判断大字母和判断小字母的时间没有显著差异,并且大小字母是否一致对大字母判断和小字母判断的影响无显著差异;（2）在排除了视知觉的整体优先效应存在的情况下,发现心理旋转加工中存在明显的整体优先效应,大字母（整体）旋转条件下的反应时显著短于小字母（局部）旋转条件下的反应时;（3）旋转角度一致性对大字母旋转和小字母旋转条件下的反应时均无显著影响,表明心理旋转的整体优先效应模式可能有别于视知觉加工的整体优先效应模式     

探索性因素分析、目标旋转与因素结构的一致性

在因素结构水平上评估跨群体的一致性是在心理学研究中常常遇见的一个问题,对此问题的解答,可以选择探索性因素分析→目标旋转→一致性评估这一途径。本文首先介绍正交目标旋转的简单原理,然后介绍其在心理研究中的应用以及相关软件和程序。目标旋转之后,结构一致性的量化可以采用一致性系数等指标,这些指标可采用一定的实证分布、近似处理或经验标准进行统计检验。之后采用一项实证数据,演示探索性因素分析、目标旋转以及结构一致性的评估方法。     

自我旋转面孔识别的ERPs研究

本研究采用事件相关电位技术考察平面旋转角度对自我面孔识别影响的时间进程。实验采用面孔异同匹配范式(same-different judgment), 首先呈现一张正立的自我或他人内特征的探测面孔, 然后再呈现一张旋转至某个角度(0°、90°、180°)的自我或他人的目标面孔, 要求被试判断两张面孔是否属于同一个人, 并记录其判断的反应时和ERP成分。实验发现, 在N170 (180~240 ms)和N2 (240~300 ms)成分上, 旋转至90°、180°的面孔刺激比正立条件下的面孔刺激分别在枕颞叶和额区诱发了更大的平均波幅。在LPP (400~500 ms)成分上, 对于自我面孔, 正立条件、旋转至90°、旋转至180°所诱发的波幅差异显著。而对于他人面孔, 3个角度所诱发的波幅无显著差异。结果表明, 面孔识别早期阶段是自动化的结构编码, 旋转角度增加了面孔结构编码的难度; 在面孔识别晚期阶段, 大脑对面孔的特异性信息进行精细加工, 自我面孔会占用个体有限认知资源进行下一步精细的心理旋转加工, 因此平面旋转角度会调节晚期个体对自我面孔的加工过程, 并且其影响时间约为100 ms。     

First demonstration of effective spatial training for near transfer to spatial performance and far transfer to a range of mathematics skills at 8 years

There is evidence that spatial thinking is malleable, and that spatial and mathematical skills are associated (Mix et al. [2016] Journal of Experimental Psychology: General, 145, 1206; Mix et al. [2017] Journal of Cognition and Development, 18, 465; Uttal et al. [2013] Psychological Bulletin, 139, 352). However, few studies have investigated transfer of spatial training gains to mathematics outcomes in children, and no known studies have compared different modes of spatial instruction (explicit vs. implicit instruction). Based on a sample of 250 participants, this study compared the effectiveness of explicit and implicit spatial instruction in eliciting near transfer (to the specific spatial skills trained), intermediate transfer (to untrained spatial skills) and far transfer (to mathematics domains) at age 8. Spatial scaling and mental rotation skills were chosen as training targets as previous studies have found, and proposed explanations for, associations between these skills and mathematics in children of this age (Journal of Experimental Psychology: General, 145, 2016 and 1206). In this study, spatial training led to near, intermediate and far transfer of gains. Mental visualization and proportional reasoning were proposed to explain far transfer from mental rotation and spatial scaling skills respectively. For most outcomes, except for geometry, there was no difference in the effectiveness of implicit (practice with feedback) compared to explicit instruction (instructional videos). From a theoretical perspective, the study identified a specific causal effect of spatial skills on mathematics skills in children. Practically, the results also highlight the potential of instructional videos as a method of introducing spatial thinking into the classroom.