平衡秤任务复杂性的事前与事后分析

任务复杂性的分析和评估是心理测量学和认知心理学都非常关注的重要主题。以264名小学四、五、六年级儿童为被试,平衡秤任务为研究材料,考察任务在未旋转时第一个因素上的载荷(事后分析)能否作为评价任务复杂性的一个指标,以及关系-表征复杂性模型对平衡秤任务复杂性分析(事前分析)的有效性两个问题。结果表明:平衡秤任务施测后所得所有项目的因素载荷与其难度之间没有显著正相关,即因素载荷的高低没有反映平衡秤任务复杂性的大小;而基于关系-表征复杂性模型对任务的事前分析所确定的任务等级复杂性和知识经验对任务难度的解释率为95.0%,可见,关系-表征复杂性模型提供的分析任务复杂性的思路和方法是较为合理的。     

Factors of style and personality

In an attempt to find relationships between psychological and linguistic variables, style samples of short stories, 300 words each, were analyzed according to formal criteria and the results were correlated with scores on personality tests. The number of significant correlations supported the hypothesis that style is related to personality. A factor analysis, using the principal component solution and Varimax rotation (Harman, 1967), of the correlation matrix resulted in six identifiable factors of style, three factors of psychological tests, and a large number of small factors, each represented only by two to five experimental variables with significant loadings. A significant loading for interpretation purposes was defined in agreement with Guilford (1956) as 0.30 or greater, positive or negative. A close examination of style factors led to the tentative differentiation of a basic language factor as resulting from grammatical constraint, and several factors of subjective style of individuals. Some of these later factors had enough loadings on personality variables to permit cautious psychological interpretation.     

An appraisal of the validity of the factor loadings employed in the construction of the primary social attitude scales

In this article the authors examine the effect of including alternate test forms in a factor matrix upon the validity of the resultant factor loadings, finding that in this particular instance the effect is negligible. Comparisons of the factor loadings derived from matrices in which only one of the alternate test forms is included with those in which both forms are included reveal practically no difference in the magnitude of either the original or rotated factor loadings, or in that of the computed communalities.     

Exploratory second-order analyses for components and factors

Abstract: Exploratory methods using second‐order components and second‐order common factors were proposed. The second‐order components were obtained from the resolution of the correlation matrix of obliquely rotated first‐order principal components. The standard errors of the estimates of the second‐order component loadings were derived from an augmented information matrix with restrictions for the loadings and associated parameters. The second‐order factor analysis proposed was similar to the classical method in that the factor correlations among the first‐order factors were further resolved by the exploratory method of factor analysis. However, in this paper the second‐order factor loadings were estimated by the generalized least squares using the asymptotic variance‐covariance matrix for the first‐order factor correlations. The asymptotic standard errors for the estimates of the second‐order factor loadings were also derived. A numerical example was presented with simulated results.     

Measures of invariance and comparability in factor analysis for fixed variables

New procedures are presented for measuring invariance and matching factors for fixed variables and for fixed or different subjects. Two of these, the coefficient of invariance for factor loadings and the coefficient of factor similarity, utilize factor scores computed from the different sets of factor loadings and one of the original standard score matrices. Another, the coefficient of subject invariance, is obtained by using one of the sets of factor loadings in conjunction with the different standard score matrices. These coefficients are correlations between factor scores of the appropriate matrices. When the best match of factors is desired, rather than degree of resemblance, the method of assignment is proposed.     

The influence of communality andN on the sampling distributions of factor loadings

The effects ofN and communality on the variability of zero and nonzero factor loadings were assessed using a Monte Carlo approach. It was found that increasingN or communality resulted in decreased sampling error of individual factor loadings, but for zero loadingsN was found to have the greatest influence. It was also found that distributions of factor loadings become relatively elongated as communality increases.     

Assessing the Climate for Creativity (KEYS): Confirmatory factor analysis and psychometric examination of a Taiwan version

Understanding the feasibility of using KEYS to assess the organizational climate for creativity in non‐Western societies is essential for researchers studying cultural influences on workers' perceptions of workplace climates. This study reports on the effectiveness of translating KEYS, using data from 401 employees of 13 different companies in Taiwan. A confirmatory factor analysis was performed and its results indicated a satisfactory fit for a 10‐factor model. However, six items tackling environmental obstacles had low factor loadings (<0.3) and should either be eliminated or amended. The results raise questions regarding the role of cultural influences in international studies that assess creativity climates. Further research into the conceptualization of organizational creativity in Chinese societies is warranted.     

Influence curves for factor loadings

Influence curves for the initial and rotated loadings are derived for the maximum likelihood factor analysis (MLFA) model. Cook's distances based on the empirical influence curves of factor loadings are proposed for the identification of influential observations. The distances are shown to be invariant under scale transformation and factor rotation. We find that an observation with a very large Cook's distance based on the sample influence curve may not necessarily exert an excessive influence on the factor loadings pattern but may change the ordering of the factors. The issue of the switching of factors is also studied by means of the empirical influence curve and factor scores.     

A method of factor analysis by means of which all coordinates of the factor matrix are given simultaneously

In general, the methods of factor analysis developed during the past five years are based on the reduction of the correlational matrix by successive steps. The first factor loadings are determined and eliminated from the correlational matrix, giving a residual matrix. This process is continued for successive factor loadings until the elements of the last obtained residual matrix may be regarded as due to chance. The method outlined in this paper assumes the maximum number of factorsm in the correlational matrix. Them factor vectors are solved for simultaneously. Once them factor vectors are found, any vectors having only negligible factor loadings may be discarded.     

THE RELATIONSHIP BETWEEN DIFFICULTY AND FACTOR LOADINGS OF SOME VISUAL-PERCEPTUAL TESTS

WERDELIN, I. & STJERNBERG, G. The relationship between difficulty and factor loadings of some visual-perceptual tests. Scand. J. Psychol. , 1971, 12, 21–28. – The study aimed at investigating whether it is possible to change factor loadings by varying the difficulty and complexity of the same visual-perceptual tests. 171 sixth grade pupils were given 27 tests. Some of these defined reference factors, others were differently difficult versions of four tests from separate parts of the visual-perceptual field. Data were treated by factor analysis, yielding the four factors R, S, N and P. It was found that the more difficult the test the higher its loadings on the S and R factors, and the easier the test the higher its loadings on the N and particularly the P factor.     

On the relations among regular, equal unique variances, and image factor analysis models

We investigate under what conditions the matrix of factor loadings from the factor analysis model with equal unique variances will give a good approximation to the matrix of factor loadings from the regular factor analysis model. We show that the two models will give similar matrices of factor loadings if Schneeweiss' condition, that the difference between the largest and the smallest value of unique variances is small relative to the sizes of the column sums of squared factor loadings, holds. Furthermore, we generalize our results and discus the conditions under which the matrix of factor loadings from the regular factor analysis model will be well approximated by the matrix of factor loadings from Jöreskog's image factor analysis model. Especially, we discuss Guttman's condition (i.e., the number of variables increases without limit) for the two models to agree, in relation with the condition we have shown, and conclude that Schneeweiss' condition is a generalization of Guttman's condition. Some implications for practice are discussed.Kentaro Hayashi is a visiting Assistant Professor, Department of Mathematics, Bucknell University, Lewisburg PA 17837, and Peter M. Bentler is Professor, Departments of Psychology and Statistics, University of California, Los Angeles CA 90095-1563. (Emails: Khayashi@bucknell.edu, bentler@ucla.edu) Parts of this paper were discussed in a session on Factor Analysis (J. ten Berge, Chair) at the IFCS-98 International Conference, Rome, July, 1998. This work was supported by National Institute on Drug Abuse grant DA 01070. The authors thank Professors Hans Schneeweiss and Ke-Hai Yuan, and four anonymous referees, for their invaluable comments which led to an improved version of this paper.     

The relation between factor loadings and biserial correlations in item analysis

The first centroid factor loadings obtained from various interitem relations are compared with item discrimination indices commonly used in item analysis. Depending upon what type of matrix is factored, the factor loadings are shown to be related to point biserial and biserial correlations.     

Factor Analysis via Components Analysis

When the factor analysis model holds, component loadings are linear combinations of factor loadings, and vice versa. This interrelation permits us to define new optimization criteria and estimation methods for exploratory factor analysis. Although this article is primarily conceptual in nature, an illustrative example and a small simulation show the methodology to be promising.     

Selection of variables in exploratory factor analysis: An empirical comparison of a stepwise and traditional approach

The purpose of this study was to investigate and compare the performance of a stepwise variable selection algorithm to traditional exploratory factor analysis. The Monte Carlo study included six factors in the design; the number of common factors; the number of variables explained by the common factors; the magnitude of factor loadings; the number of variables not explained by the common factors; the type of anomaly evidenced by the poorly explained variables; and sample size. The performance of the methods was evaluated in terms of selection and pattern accuracy, and bias and root mean squared error of the structure coefficients. Results indicate that the stepwise algorithm was generally ineffective at excluding anomalous variables from the factor model. The poor selection accuracy of the stepwise approach suggests that it should be avoided.     

A non-graphical method for transforming an arbitrary factor matrix into a simple structure factor matrix

The most commonly used method of factoring a matrix of intercorrelations is the centroid method developed by L. L. Thurstone. It is, however, necessary to transform the centroid matrix of factor loadings into a simple structure matrix in order to facilitate the interpretation of the factor loadings. Current methods for effecting this transformation are chiefly graphical and require considerable experience and personal judgment. This paper presents a new method for transforming an arbitrary factor matrix into a simple structure matrix by methods almost completely objective. The theory underlying the method is developed and approximation procedures are derived. The method is applied to a matrix of factor loadings previously analyzed by Thurstone.     

对齐法在单因子和三因子多组比较中允许的不等参数率

在传统的多组验证性因子分析中,进行因子均值比较的前提条件是模型满足强测量不变性假设,但该假设在实证研究中很难满足。这时,Asparouhov和Muthén(2014)提出的对齐法是一种可供备选的多组分析法。通过蒙特卡洛模拟研究,探究了在对齐法精确估计模型参数前提下所允许的不等参数率范围。研究发现：在平均组样本量充足,识别算法为固定识别算法等理想状态下,对齐法在单因子模型多组比较中所允许的不等参数率可以是100%;在三因子模型中所允许的不等参数率上限是20%至30%;在此范围内,对齐法允许更多高程度不等参数;在组数目从30、15或9降至3时,对齐法能允许更多的不等参数在模型中。     

The Psychometric Properties of Dispositional Flow Scale-2 in Internet Gaming

This study examined the psychometric properties of the Dispositional Flow Scale-2 (DFS-2; Jackson and Eklund in Journal of Sports and Exercise Psychology, 24:133-150, 2002). One thousand five hundred and seventy-eight secondary school students (One thousand and seventy four males, four hundred and eleven females, ninety-three missing) from six schools in Singapore completed the questionnaires. Confirmatory factor analysis (CFA) was used to evaluate the factorial structure of the DFS-2. A nine-first-order factor model was compared to a higher order model with a global flow factor. Support was found for the higher order factor. Multigroup analysis demonstrated invariance of the factor forms, factor loadings, factor variances, and factor covariances across age and sex. The DFS-2 subscales were found to have acceptable reliability estimates, and convergent validity. We conclude that DFS-2 is a valid instrument for assessing global flow experience in Internet gaming.     

Obtaining maximum-likelihood estimates of factor loadings and communalities using an easily implemented iterative computer procedure

This paper considers the problem of computing estimates of factor loadings, specific variances, and communalities for a factor analytic model. The equations for maximum-likelihood estimators are discussed. Iterative formulas are developed to solve the maximum-likelihood equations and a simple and efficient method of implementation on a digital computer is described. Use of the iterative formulas and computing techniques for other estimators of factor loadings and communalities is also considered to provide a very general approach for this aspect of factor analysis.     

Changes in common-factor loadings as tests are altered homogeneously in length

Formulas are derived by which, given the factor loadings and the internal reliability of a test of unit length, the following estimates can be made: (1) the common-factor loadings for a similar (homogeneous) test of lengthn; (2) the number of times (n) that a test needs to be lengthened homogeneously to achieve a factor loading of a desired magnitude; and (3) the correlation between two tests, either or both of which have been altered in length, as a function of (a) the new factor loadings in the altered tests or (b) the original loadings in the unit-length tests. The appropriate use of the derived formulas depends upon the fulfillment of four assumptions enumerated.This article is based on a paper read by the authors at the annual meeting of the Western Psychological Association in Eugene, Oregon, June 25, 1949.     

Independent component analysis as a rotation method: A very different solution to Thurstone's box problem

In this paper we consider the well‐known Thurstone box problem in exploratory factor analysis. Initial loadings and components are extracted using principal component analysis. Rotating the components towards independence rather than rotating the loadings towards simplicity allows one to accurately recover the dimensions of each box and also produce simple loadings. It is shown how this may be done using an appropriate rotation criterion and a general rotation algorithm. Methods from independent component analysis are used, and this paper may be viewed as an introduction to independent component analysis from the perspective of factor analysis.