Higher-order factors in the differential emotions scale (DES-III)

The 30-item version of Izard's Differential Emotions Scale (DES-III) was submitted to an iterative principal factoring plus oblique (direct Oblimin) rotation to simple structure, on a sample of 204 University of Delaware undergraduates. The intercorrelation matrix for the eight primary emotional-state factors derived, was subsequently subjected to a higher-order factoring. Four second-order factors accounted readily for the variance measured in the DES-III scales and this suggests that the multivariate mood-state instrument might be more profitably scored for secondary factors, in certain instances. This conclusion in no way detracts from the importance of the DES-III primaries, but adds to the usefulness of the instrument in applied studies.     

FIRO-B: factors and facets

10 FIRO-B intercorrelation matrices were factor analysed; one matrix was derived from new FIRO-B data, all the other matrices were found in the literature. The correlation matrices were also subjected to meta-analysis. The findings suggested that the four FIRO-B scales associated with Inclusion and Affection are facets of the ubiquitous interpersonal superfactor, Nurturance, but the two FIRO-B Control scales each express an orthogonal construct both of which relate to the super-factor, Dominance.     

The fit between Strong-Campbell Interest Inventory General Occupational Themes and Holland's hexagonal model

Using a multidimensional scaling procedure, the present study examined the fit of Holland's RIASEC hexagon model to the internal relationships among the Strong-Campbell Interest Inventory (SCII) General Occupational Theme scales. SCII intercorrelation matrices for both sexes as reported in the SCII Manual were submitted, separately for each sex, to TORSCA 9 nonmetric scaling analysis. The Wakefield and Doughtie procedure was used to compare obtained TORSCA coordinates with expectations from Holland's hexagonal model. As a comparison, identical analyses were performed on Vocational Preference Inventory (VPI) scale intercorrelation matrices, these data having originally served as the basis for advancing the utility of the hexagon model. For females, the SCII-hexagon fit was not good, with a near reversal of the Social and Enterprising scales. For males, the SCII-hexagon fit was good. For either SCII or VPI scales, the female data met expectations from Holland's model less often than the male data. A replication study on SCII data for 305 female clients of a vocational assessment clinic confirmed the previously observed sex differences. Sex differences in the structure of vocational preferences are discussed.     

Note on detection of cue intercorrelation in multiple-cue probability learning

Abstract.— After completion of learning tasks with two different levels of cue intercorrelation (r _u=0.00 and 0.80) the detection of cue intercorrelation was tested with either a reproduction or a recognition method in a 2×2 factorial design. The reproduction method yielded an almost perfect matching between the reproduced intercorrelations and the intercorrelations of the tasks, while the recognition method resulted in systematically lower subjective intercorrelations. For the recognition method the subjective intercorrelation was found to vary with the criterion of recognition, so that the stricter the criterion, the higher the subjective intercorrelation.     

Separation of data as a principle in factor analysis

Two systems of factor analysis—factoring correlations with units in the diagonal cells and factoring correlations with communalities in the diagonal cells—are considered in relation to the commonly used statistical procedure of separating a set of data (scores) into two or more parts. It is shown that both systems of factor analysis imply the separation of the observed data into two orthogonal parts. The matrices used to achieve the separation differ for the two systems of factor analysis.     

Differential construct validity of a preschool battery for blacks,whites, males,and females

Seven major preschool tests were administered to a group of 322 kindergarten children. Scaled scores from the instruments were submitted to principal factoring, with iterations for the total sample and separately by race/sex groupings. The average intercorrelation of the pretests was similar across race and sex. A two-factor solution of the battery was derived for the total group and for each of the four subgroups (WF, WM, BF, BM). The two-factor solution was highly similar across race and sex, as indicated by the large coefficients of congruence obtained between factors derived within each group, thus supporting the equivalence of internal psychometric properties of the battery across race and sex. No evidence was determined to support sexual or racial dimorphism in the early structure of cognitive abilities.     

A modified procedure for parallel analysis of ordered categorical data

Parallel analysis has been well documented to be an effective and accurate method for determining the number of factors to retain in exploratory factor analysis. The O'Connor (2000) procedure for parallel analysis has many benefits and is widely applied, yet it has a few shortcomings in dealing with missing data and ordinal variables. To address these technical issues, we adapted and modified the O'Connor procedure to provide an alternative method that better approximates the ordinal data by factoring in the frequency distributions of the variables (e.g., the number of response categories and the frequency of each response category per variable). The theoretical and practical differences between the modified procedure and the O'Connor procedure are discussed. The SAS syntax for implementing this modified procedure is also provided.     

Psychometric properties of the Minnesota Multiphasic Personality Inventory-Adolescent (MMPI-A) Clinical, Content, and Supplementary scales in a forensic sample

In this study, we evaluated the internal psychometric properties and external correlates of scores on the Clinical, Content, and Supplementary scales in a forensic sample of 496 adolescents (315 boys and 181 girls) who were court-ordered to receive psychological evaluations. We examined Cronbach's alpha coefficients, scale intercorrelation matrices, and frequencies of scale elevations. Further, we found varying degrees of support for the convergent and discriminant validity of scores on the MMPI-A (Butcher et al., 1992 ) Clinical, Content, and Supplementary scales. This study adds to the body of literature establishing the utility of the MMPI-A in forensic evaluations.     

Consistency of adherence across regimen demands

The extent to which adherence to one demand of the diabetic treatment regimen is related to adherence to other regimen demands was explored in a sample of 227 diabetic patients. Adherence to weight control, urine/blood testing, medication taking, symptom reporting, and safety demands was assessed using a variety of methods: (a) patients' report in relation to physician's criteria, (b) patients' report in relation to their own understanding of those criteria, (c) significant others' reports, (d) nurses' ratings, and (e) physicians' ratings. Based on attribution theory, it was proposed that informed others would view patients as more consistent than patients themselves did. Separate intercorrelation matrices were created for each method. The correlations, however, were uniformly low (most rs less than .25) and mean correlations did not differ significantly between matrices. The relative independence of adherence to different demands of the diabetic regimen has important implications for the conceptualization and measurement of treatment adherence.     

Determining a simple structure when loadings for certain tests are known

A rigorous and an approximate solution are found for the problem: Given a primary trait matrix forn tests andr ₁ traits, and a matrix for the samen tests andr ₂ reference axes, to discover the transformation which will transform the second matrix into the first, or primary trait matrix. Formulas for determining the limits of the effect of using the approximate solution are presented. The method is applied to a set of twenty hypothetical tests, defined by their loadings on four orthogonal primary traits. After factoring the inter-correlations of these variables by Thurstone's centroid method, approximating the diagonals, the original hypothetical matrix is reproduced with a root mean square discrepancy of .014 by assuming as known the primary trait loadings of only the first eight tests. The method is applied to the results of factoring two batteries of 14 tests, having 8 tests in common, to give the factor loadings of the two batteries on the same reference axes. The method provides a means of comparing directly and quantitatively the results of two different factor studies, provided they have tests in common, and of testing the stability of simple structure under changes in the battery. The relations of the method here developed to certain problems in multiple correlation are shown.     

Components of reliability

As an alternative to the analysis of variance approach to reliability a multiple-factor analysis approach is illustrated. The one-factor and the multiple-factor models for reliability are compared. Tests on the latent roots associated with the principal components of intercorrelation matrices are used to determine the number of components to be retained. Conditions under which one or more of the principal components should be utilized are discussed.This investigation was completed at the Oregon Research Institute and supported by NIMH grant MH-0892-01 and NSF grant GB-257. Computations were performed at the Western Data Processing Center and the Health Sciences Computing Facility, University of California at Los Angeles.     

On the Misconception of Multicollinearity in Detection of Moderating Effects: Multicollinearity Is Not Always Detrimental

Due to its extensive applicability and computational ease, moderated multiple regression (MMR) has been widely employed to analyze interaction effects between 2 continuous predictor variables. Accordingly, considerable attention has been drawn toward the supposed multicollinearity problem between predictor variables and their cross-product term. This article attempts to clarify the misconception of multicollinearity in MMR studies. The counterintuitive yet beneficial effects of multicollinearity on the ability to detect moderator relationships are explored. Comprehensive treatments and numerical investigations are presented for the simplest interaction model and more complex three-predictor setting. The results provide critical insight that both helps avoid misleading interpretations and yields better understanding for the impact of intercorrelation among predictor variables in MMR analyses.     

Generating multivariate data from nonnormal distributions: Mihal and Barrett revisited

An algorithm described by Graybill (1969) factors a population correlation matrix, R, into an upper and lower triangular matrix, T and T′, such that R=T′T. The matrix T is used to generate multivariate data sets from a multinormal distribution. When this algorithm is used to generate data for nonnormal distributions, however, the sample correlations are systematically biased downward. We describe an iterative technique that removes this bias by adjusting the initial correlation matrix. R, factored by the Graybill algorithm. The method is illustrated by simulating a multivariate study by Mihal and Barrett (1976). Large-N simulations indicate that the iterative technique works: multivariate data sets generated with this approach successfully model both the univariate distributions of the individual variables and their multivariate structure (as assessed by intercorrelation and regression analyses).     

Estimating, testing, and comparing specific effects in structural equation models: the phantom model approach

The phantom model approach for estimating, testing, and comparing specific effects within structural equation models (SEMs) is presented. The rationale underlying this novel method consists in representing the specific effect to be assessed as a total effect within a separate latent variable model, the phantom model that is added to the main model. The following favorable features characterize the method: (a) It enables the estimation, testing, and comparison of arbitrary specific effects for recursive and nonrecursive models with latent and manifest variables; (b) it enables the bootstrapping of confidence intervals; and (c) it can be applied with all standard SEM programs permitting latent variables, the specification of equality constraints, and the bootstrapping of total effects. These features along with the fact that no manipulation of matrices and formulas is required make the approach particularly suitable for applied researchers. The method is illustrated by means of 3 examples with real data sets.     

A multiple group method of factoring the correlation matrix

There are a number of methods of factoring the correlation matrix which require the calculation of a table of residual correlations after each factor has been extracted. This is perhaps the most laborious part of factoring. The method to be described here avoids the computation of residuals after each factor has been computed. Since the method turns on the selection of a set of constellations or clusters of test vectors, it will be calleda multiple group method of factoring. The method can be used for extracting one factor at a time if that is desired but it will be considered here for the more interesting case in which a number of constellations are selected from the correlation matrix at the start. The result of this method of factoring is a factor matrixF which satisfies the fundamental relationFF'=R.This study is one of a series of investigations in the development of multiple factor analysis and application to the study of primary mental abilities. We wish to acknowledge the financial assistance from the Social Science Research Committee of The University of Chicago which has made possible the work of the Psychometric Laboratory.     

Confirmatory factor analysis of the WPPSI for language-impaired children

The present study used a maximum-likelihood confirmatory factor analysis (CFA) to test the hypothesis that a four-factor model is the most parsimonious explanation of the structure of the WPPSI for language-impaired children. Four separate maximum-likelihood confirmatory factor analyses were performed on a sample of 198 Norwegian language-impaired children tested with the WPPSI, and on the Norwegian (n = 563) and American (n = 1200) standardization samples. A one-factor (general), a two-factor (verbal and performance), three-factor (parallel to the WISC-R) and a four-factor solution composed of "processing dependent" ("knowing how" and "seeing how") and "knowledge dependent" ("knowing that" and "seeing that") were imposed on the average intercorrelation matrices of the 11 WPPSI subtests. Confirmatory factor analysis indicated that the four-factor latent construct model was the most parsimonious explanation of the structure of the WPPSI for language-impaired children, as well as for normally developing children.     

Response format and factor structure in mood adjective check lists

Abstract.— Different response formats designed for mood measurement were analyzed and compared. The interest was focused upon the effects of ( a ) symmetry versus asymmetry and ( b ) inclusion versus exclusion of a "cannot decide"-category on intercorrelation between variables and thus, factor structure. It was found that the proportions of positive and negative responses were equivalent in the symmetric format but also in the asymmetric if the "cannot decide"-category was included. Generally it was found that the asymmetric format with the "cannot decide"-category resulted in a drop of both positive and negative correlations. Data emanating from the different formats were factor analyzed and it was found that the symmetric format caused marked bipolar factors which absorbed more of common variance than those of the other formats. It was established that the symmetric format best reflected an external criterion concerning rated degree of dissimilarity between variables.     

An analysis of Guttman's simplex

Applying a Spearman formula for factor loadings to a variant of the diagonal method, the Guttman simplex model is factored algebraically inton/2 additive factors. The finding that communalities can be discovered such that the rank of a simplex becomesn/2 is contradictory to Guttman's contention that the minimal rank isn — 2. Certain matrices of 4 and 5 variables presented by Guttman as simplexes, can, in general, be considered 2-factor matrices, easily analyzed to simple structure without rotation. One example of 6 variables is factored by the method described to a 3-factor structure.Prepared under Contract 816(02) between the Office of Naval Research and Washington University and presented in part at a meeting of the Southern Society for Philosophy and Psychology, St. Louis, Missouri, March 27, 1959. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.     

Dimensions of perception of posture in dance

This study reports a preliminary investigation designed to assess the possibility of using a semantic differential in the appraisal of expressive characteristics of posture in dance.Twenty still photographs of postures displayed by one female dancer were judged on 25 bipolar scales by 50 Ss. Ratings of eight of these Ss were used for estimating reliabilities of the scales — resulting in elimination of five scales. Intercorrelation matrices of the 20 remaining scales were obtained for each of the 42 remaining Ss. Consideration of homogeneity of the distribution of these matrices led to the exclusion of four of them, leaving 38 matrices for further analysis.After random division of these matrices into two equally sized subgroups, principal component analyses with VARIMAX rotation were carried out on the average intercorrelation matrix for each subgroup. This resulted in two very similar three-factor solutions. The three factors, identified as similar to Osgood's well-known factors of activity, evaluation and potency, accounted for about 55% of the total variance. The results, discussed in terms of Berlyne's conception, suggest that the semantic differential may be a reliable instrument for measuring connotations of posture in dance.