On rotating to smooth functions

Tucker has outlined an application of principal components analysis to a set of learning curves, for the purpose of identifying meaningful dimensions of individual differences in learning tasks. Since the principal components are defined in terms of a statistical criterion (maximum variance accounted for) rather than a substantive one, it is typically desirable to rotate the components to a more interpretable orientation. Simple structure is not a particularly appealing consideration for such a rotation; it is more reasonable to believe that any meaningful factor should form a (locally) smooth curve when the component loadings are plotted against trial number. Accordingly, this paper develops a procedure for transforming an arbitrary set of component reference curves to a new set which are mutually orthogonal and, subject to orthogonality, are as smooth as possible in a well defined (least squares) sense. Potential applications to learning data, electrophysiological responses, and growth data are indicated.Portions of this research were supported by the National Research Council of Canada, Grant A8615 to the second author. We thank Jagdeth Sheth for supplying his raw data.     

Two-step weighted least squares factor analysis of dichotomized variables

A two-step weighted least squares estimator for multiple factor analysis of dichotomized variables is discussed. The estimator is based on the first and second order joint probabilities. Asymptotic standard errors and a model test are obtained by applying the Jackknife procedure.     

EMPLOYING TASK ARRANGEMENTS AND VERBAL CONTINGENCIES TO PROMOTE VERBALIZATIONS BETWEEN RETARDED CHILDREN1

This study investigated the effects of arranging task events for interdependence, to increase the probability of social responding. During task interdependence, the subjects, participating in dyads and a four-person group, obtained task materials (a puzzle piece) from their partner before completing their task (appropriately placing the puzzle piece). The verbal contingency required a verbal request to precede a subject's receiving a task material from his partner. The verbal contingency yoked with task interdependence made task completion contingent on the appropriate verbalization. The findings from two experiments suggested that task interdependence was sufficient to increase partner-directed verbalizations for three of the four subjects. When the verbal contingency was added, all subjects increased their requests and other verbalizations to partner. Applied to a four-person group, the verbal contingency yoked with varying levels of task interdependence correspondingly affected the pattern and level of group communications. The greater the task interdependence, i.e., the more members each subject depended on to complete his task, the more complex the social network of verbal contacts, and the higher the level of both requests and other verbalizations for the group.     

Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study

In order to make the parallel analysis criterion for determining the number of factors easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. The correlation matrices were derived from distributions of normally distributed random numbers. The independent variables are log (N–1) and log {[n(n–1)/2]–[(i–1)n]}, whereN is the number of observations;n, the number of variables; andi, the ordinal position of the eigenvalue. The results were excellent, with multiple correlation coefficients ranging from .9948 to .9992.This research was supported by the Office of Naval Research under Contract N00014-67-A-0305-0012, Lloyd G. Humphreys, principal investigator, and by the Department of Computer Science of which Richard G. Montanelli, Jr., is a member.     

Comments on “the measurement of factorial indeterminacy”

Guttman's index of indeterminacy (2² – 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation ² for predicting the factor from the observed variables is the average correlation _AB between independently selected alternative solutionsA andB, while var ( _AB )=(1 – ²)²/s, wheres is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, ² is the lower bound for E( _AB ); however, E( _AB ) need not be a modal value in the distribution of _AB . Guttman's index and E( _AB ) measure different aspects of the same indeterminacy problem.     

A look,by simulation,at the validity of some asymptotic distribution results for rotated loadings

In the last few years, a number of asymptotic results for the distribution of unrotated and rotated factor loadings have been given. This paper investigates the validity of some of these results based on simulation techniques. In particular, it looks at principal component extraction and quartimax rotation on a problem with 13 variables. The indication is that the asymptotic results are quite good.     

不同SOA条件下的情感启动效应研究

在150ms和250ms两种SOA条件下,以彩色图片为启动刺激,以汉语双字词为目标刺激,通过评价分类任务考察情感启动效应。结果表明在两种SOA条件下均存在显著的情感启动效应;积极启动和消极启动对目标词产生了不同的影响。类似Stroop效应的反应冲突机制可解释本研究所获得的结果。     

A preliminary sketch of a Jungian socioanalysis – an emerging theory combining analytical psychology,complexity theories,sociological theories,socio- and psycho-analysis,group analysis and affect theories1

This paper presents a preliminary sketch of what we have termed a Jungian socioanalysis – an emerging theory combining analytical psychology, complexity theories, sociological theories, socio- and psycho-analysis, group analysis and affect theories. Our assumption is that Jungian theory and practice need to attend to and focus more on social contexts, sociality and the influence of societal developments. But also, on the other hand, that analytical psychology, primarily Jung’s theory of individuation and the transcendent function as well as the broad complexity perspective of his theory of psyche, can be extended to a ‘socio’ and not just a ‘psycho’ perspective. The paper presents five foundational assumptions for a Jungian socioanalysis, with the following headings: 1) A Jungian socioanalysis calls for a complex psychology; 2) (Un)consciousness is social and sociality has a dimension of (un)consciousness; 3) A Jungian socioanalysis explores social fields ‘from within’ by smaller groups; 4) A Jungian socioanalysis enables and is enabled by emerging metaphors and affect-imagery; 5) Socio-cultural fields have an impulse toward individuation. This is the first of two papers in the present edition of the journal – the second paper gives socio-clinical illustrations of our thesis in this paper.     

Interactive effects of social network centrality and social identification on stress

The present study aimed to integrate the social identity approach to health and well-being with social network analysis. Previous research on the effects of social network centrality on stress has yielded mixed results. Building on the social identity approach, we argued that these mixed results can be explained, in part, by taking into account the degree to which individuals identify with the social network. We hence hypothesized that the effects of social network centrality on stress are moderated by social identification. Using a full roster method, we assessed the social network of first-year psychology students right after the start of their study programme and three months later. The effects of network centrality (betweenness, closeness, eigenvector centrality) and social identification on stress were examined using structural equation models. As predicted, our results revealed a significant interaction between network centrality and social identification on stress: For weakly or moderately identified students, network centrality was positively related to stress. By contrast, for strongly identified students, network centrality was unrelated to stress. In conclusion, our results point to the perils of being well-connected yet not feeling like one belongs to a group.