A note on the interpretation of the factor pattern of the California Psychological Inventory

The intercorrelation matrix between the scales of the California Psychological Inventory, given in the manual, was factor analyzed. Three factors were extracted and rotated by varimax. The matrix was rescaled, first normalizing the rows, then standardizing the columns to a mean sum of squares of one. Unity was used as a cut-off point for determination of salient loadings. The first two factors were similar to the results reported in a previous Study by Nichols and Schnell. The third factor was interpreted as an independence-dependence dimension.     

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.     

Factor structure of the Preschool Personality Questionnaire in Iran

This study is of Triandis's pseudoetic variety, not a cross-cultural study per se. The Preschool Personality Questionnaire which was standardized in the SA and partially standardized in Colombia was administered to 600 preschool children in Iran. Data from the entire sample were analyzed by both principal components, maximum likelihood, and alpha factor analyses. 14 factors were derived. Odd and even records were likewise factored. Six of the first seven factors were found and matched from odd to even cases. At least five of the total sample factors were judged by inspection to match similar dimensions in the USA. Factor scores for children in the standardizing sample were created by postmultiplying the raw score matrix by the 14-factor "reduced" factor structure matrix. These raw factor scores were then converted to STEN scores. Utilizing the entire sample factor structure matrix, factor scores and sten scores were derived for each of the 4-, 5-, and 6-yr.-old groups. By use of the norms based on this sample of Iranian children, further experiments can be carried out to investigate development of preschool children and other variables in Iran similar to those studied in the West.     

Orthogonal rotation to congruence

Two problems are considered. The first is that of rotating two factor solutions orthogonally to a position where corresponding factors are as similar as possible. A least-squares solution for transformations of the two factor matrices is developed. The second problem is that of rotating a factor matrix orthogonally to a specified target matrix. The solution to the second problem is related to the first. Applications are discussed.This research was supported in part by contract Nonr 228 (22) between the office of Naval Research and the University of Southern California. Portions of this paper were presented at the American Psychological Association Convention, Los Angeles, September, 1964.     

Piaget's data and spearman's theory—An empirical reconciliation and its implications for academic achievement

A hierarchical simple structure factor solution was obtained for item scores from a psychometrized battery of Piagetian-type tasks individually administered to 660 kindergarten children. At the first level of factors were the Piagetian theoretical entities of seriation, classification, conservation of number, and temporal and spatial reasoning, with numeration loading on seriation and classification as indicated by the theory. At the second level were two factors identified as Piaget's logicomathematical and infralogical operations. A third-level factor was identified as a g factor. The association of the Piagetian-type tasks with kindergarden and first grade academic achievement was through the third-level g factor. The second-level factors appeared to be similar to Vernon's k:m and v:ed but, like the first level factors, made no important contribution to predicted achievement above that contributed by the g factor. A socioeconomic factor made no unique contribution to predicted first grade achievement. It was concluded that the Piagetian concrete operations variables have no unique role in the prediction of kindergarten or first grade academic achievement.     

Some rao-guttman relationships

An examination of the determinantal equation associated with Rao's canonical factors suggests that Guttman's best lower bound for the number of common factors corresponds to the number of positive canonical correlations when squared multiple correlations are used as the initial estimates of communality. When these initial communality estimates are used, solving Rao's determinantal equation (at the first stage) permits expressing several matrices as functions of factors that differ only in the scale of their columns; these matrices include the correlation matrix with units in the diagonal, the correlation matrix with squared multiple correlations as communality estimates, Guttman's image covariance matrix, and Guttman's anti-image covariance matrix. Further, the factor scores associated with these factors can be shown to be either identical or simply related by a scale change. Implications for practice are discussed, and a computing scheme which would lead to an exhaustive analysis of the data with several optional outputs is outlined.     

Higher‐order factors of creativity within Guilford's structure‐of‐intellect model: A re‐analysis of a fifty‐three variable data base

Both exploratory factor analyses (varimax and promax solutions) and confirmatory maximum likelihood factor analyses were used to re‐examine a correlation matrix of 53 tests from a battery administered to a sample of more than 400 Air Force officers. The data base originated in a report from the University of Southern California Aptitudes Research Project (Guilford, Wilson, & Christensen, 1952), which was intended to identify factors of creative thinking. The major objective of this study was to ascertain whether the covariation among the test variables that were conceptualized as first‐order factors within the structure‐of‐intellect model could be explained parsimoniously in terms of a number of higher‐order creative abilities. Application of a relatively objective oblique exploratory factor analytic technique (promax) afforded a replication of four of Guilford's creativity factors—two divergent production constructs of ideational fluency and word fluency, one construct representing sensitivity to problems, and another identified as redefinition or flexibility of closure typically involving transformations. Although substantial support was found for higher‐order factor models which distinguished among five types of psychological operations and three kinds of test content, statistical indicators of closeness‐of‐fit suggested that a mixed model of both first‐order and higher‐order factors was required to describe creativity thinking, perhaps within some form of hierarchical ordering. In addition to recognition of divergent production as a key component of creative endeavor, it appeared that a higher‐order convergent production factor involving primarily semantic and symbolic transformations constituted a dimension of potential importance to the creative thinking of mathematicians, scientists, engineers, and inventors. It was hypothesized that in creative thinking a variety of psychological operations within a dynamic interactive system is employed almost simultaneously in a forward and backward manner.     

Piagetian tasks measure intelligence and intelligence tests assess cognitive development: A reanalysis

A reanalysis of the intercorrelations of Wechsler subtests, achievements tests, and Piagetian tasks originally published by Stephens et al. (1972) has corrected errors in the original design and has used models which allow both differences and similarities to appear. Unit weighted composites of the two sets of tests were formed after first partialling chronological age out of the complete table of intercorrelations. The correlation between the composites is .876 which corrects, using split-half estimates of reliabilities, to .918. Next the matrix of partial correlations was factored and the factors rotated to a hierarchical structure. Piagetian tasks contribute almost equally to the definition of the general factor in intelligence along with the Wechsler subtests and the achievement tests. The general factor, furthermore, makes the single largest contribution to the variance of most of the measures of both sets. The smaller group factors consist of an Academic Achievement factor and three Piagetian factors. Of the latter the largest and most clearly identified is the factor called Operational Thought in the earlier analysis, but is here described simply as Conservation. It is concluded that the evidence for communality in function far outweighs the differences between intelligence tests and Piagetian tasks.     

A note on the discovery of ag factor by means of Thurstone's centroid method of analysis

A fictitious factor matrix including 16 tests and 3 factors, one of which was ag factor, was prescribed. From it two typical factor problems, including errors of sampling, were derived. Students in training, without awareness of the factor patterns, arrived at essentially correct solutions by the use of Thurstone's centroid method with rotation of axes. Errors in the calculated factor matrix were very close in size to the sampling errors in the correlation coefficients. It is concluded that ag factor need not escape detection by Thurstone's procedures if the criteria of complete simple structure are not demanded.     

Student-teacher concordance on dimensions of student social competence: A multitrait-multimethod analysis

Teacher and self-ratings of social competence were obtained for 669 (341 males, 328 females) grades 3–6 students using the Social Behavior Assessment—Revised (SBA-R) and a self-report scale consisting of the identical items reworded in first person. Factor analysis and multitrait-multimethod matrix analysis were used to validate construct interpretations. The previous four-factor structure of the SBA-R was not replicated. However, the three-factor structure that did emerge was better defined. Although student-teacher concordance was moderate for the Self-Control/Social Convention and Academic Responsibility factors, it was minimal for the Social Participation factor. Evidence of discriminant validity was weak. As with other studies using rating scales, method bias was in evidence. Sex differences were found in terms of variance explained by each factor and convergent validity. Discussion focuses on problems associated with construct validation in general and validation of school-related social competence in particular.     

CATTELL AND EYSENCK FACTOR SCORES RELATED TO COMREY PERSONALITY FACTORS

The Eysenck Personality Inventory, the Cattell 16 PF Inventory, and the Comrey Personality Inventory were administered to 272 volunteers. Eysenck and Cattell factor scores were correlated with scores over homogeneous item groups (FHIDs) which define the Comrey test factors. This matrix was factor analyzed to relate the Eysenck and Cattell factor scores to the factor structure underlying the Comrey test. The Eysenck Neuroticism, Comrey Neuroticism, and Cattell second-order Anxiety factors appeared to match. The Eysenck Introversion and the Comrey Shyness factors also matched. The 16 Cattell primary factors overlapped but did not match with the Comrey factors.     

MIRT模型中多维能力及其相关矩阵估计的影响因素

多维项目反应理论因其模型本身的天然优势及其兼具因素分析与项目反应理论于一身的优点,而被广大研究者及应用者所重视.本研究在前人研究基础上,重点讨论MIRT多维能力及能力间相关矩阵的参数估计问题.研究采用Monte Carlo模拟方法进行,在三因素完全随机设计（4 ×3×3）下,使用MCMC算法,探讨测验维度数、维度间的相关大小和测验项目数三个因素对MIRT能力及其相关矩阵估计的影响.     

FACTORIAL INVARIANCE OF BIOGRAPHICAL FACTORS

A biographical information blank (BIB) was administered to students in grades 7, 9, and 11, and was subsequently analyzed to determine the stability of both its factor pattern and structure. This was done by deriving a single average factor pattern matrix which was rotated to simple structure and then to similarity to each of three factor matrices at each grade level. Of 11 factors extracted, all but three showed reasonably good stability. Those factors that showed the greatest change, in terms of their presence over the three grade levels, were General Appreciation of School Courses, Social Activities, and High Level Literary Activities. Implications of stability in factor pattern and structure for further BIB development and for utilization in the framework of a longitudinal study are discussed.     

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.     

A factor analysis of mental abilities and personality traits

The relationship between measures of verbal fluency and certain personality traits is examined by factor techniques. From a matrix of eight factor scores derived from mental tests plus five personality scores, six factors were obtained. An oblique solution lends limited support to the hypothesized relationship between the two domains.This study was supported by a grant from the Research Foundation of the University of Utah.Currently on leave of absence with the National Research Council.     

What is anger provoking? A psychophysical study of perceived causes of anger

From a pool of nearly 900 situations, anonymously described by young people from prepuberty to adolescence as anger provoking, 60 situations were randomly drawn. Twelve advanced students of psychology independently rated the similarity between each possible pair of situations with respect to the perceived cause of anger. The resultant averaged similarity matrix was subjected to factor analysis, and ten factors were deemed an optimal solution, both psychologically and statistically. The factor structure is described and discussed, and other findings of situational dimensions, not made explicit by the factor analysis, are also discussed.     

Factor invariance of the Millon Clinical Multiaxial Inventory

Several factor analyses of the Millon Clinical Multiaxial Inventory (MCMI) have resulted in very similar solutions. Interpretation of this consistency is hampered by the fact that the 20 scales of the inventory share items. Overlapping items cause the scales to be linearly dependent and may create structure in the interscale correlation matrix which is separate from the subject response patterns. A factor analysis was performed on the matrix of item-overlap coefficients which describes the underlying artifactual structure of the instrument. Data from two new subject samples were factor analyzed and compared to previously published studies. Similarity coefficients among factors across studies were calculated.     

A NEW MATRIX FOR THE ASSESSMENT OF FACTOR CONTRIBUTIONS

The matrix product of the initial factor loading matrix times the least- squares orthonormal approximation to the general oblique transformation matrix is suggested to be the most adequate matrix for the evaluation of the contributions of factors to variables. This factor contribution matrix can also re- place the primary factor pattern matrix in evaluating oblique simple structure.     

The MacQuarrie test for mechanical ability

Data originally analyzed by Charles H. Goodman on the MacQuarrie Test for Mechanical Ability are subjected to the principal axes factoring method. The maximum variance was extracted with three factors. Rotation to an oblique simple structure yielded a factor pattern which satisfies the simple structure concept more adequately than the orthogonal factor matrix, thus leading to greater clarity of interpretation of the factors.