Exploratory factor analysis of African Self-Consciousness Scale scores

This study replicates and extends prior studies of the dimensionality, convergent, and external validity of African Self-Consciousness Scale scores with appropriate exploratory factor analysis methods and a large gender balanced sample (N = 348). Viable one- and two-factor solutions were cross-validated. Both first factors overlapped significantly and were labeled "Embracing African Heritage." The second subscale of the two-factor solution was labeled "Refusal to Deny African Heritage." Only the structural validity of the first factor of the two-factor solution was fully consistent with prior findings. Partial evidence of convergent validity was found for all factors, and only the second factor of the two-factor solution received external validity support. Implications for usage of the African Self-Consciousness Scale and recommendations for further investigation are discussed.     

Regression among factor scores

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.     

Quadratic prediction of factor scores

Factor scores are naturally predicted by means of their conditional expectation given the indicatorsy. Under normality this expectation is linear iny but in general it is an unknown function ofy. It is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic function ofy.The authors would like to thank Edith Nijenhuis, the anonymous referees, and the associate editor for their helpful comments and suggestions.     

Approaches to univocal factor scores

Two current methods of deriving common-factor scores from tests are briefly examined and rejected. One of these estimates a score from a multiple-regression equation with as many terms as there are tests in the battery. The other limits the equation to a few tests heavily saturated with the desired factor, with or without tests used to suppress the undesired factors. In the proposed methods, the single best test for each common factor is the starting point. Such a test ordinarily has a very few undesired factors to be suppressed, frequently only one. The suppression test should be univocal, or nearly so. Fortunately, there are relatively univocal tests for factors that commonly require suppression. Equations are offered by which the desired-factor test and a single suppression test can be weighted in order to achieve one or more objectives. Among the objectives are (1) maximizing the desired factor variance, (2) minimizing the undesired factor variance, (3) a compromise, in which the undesired variance is materially reduced without loss in desired variance, and (4) a change to any selected ratio of desired to undesired variance. A more generalized solution is also suggested. The methods can be extended in part to the suppression of more than one factor. Equations are derived for the suppression of two factors.     

Agoraphobia in women: factor analysis of symptoms and personality correlates of factor scores in a clinical population

One hundred and sixty female patients with a DSM-III diagnosis of agoraphobia completed a measure of fears and general symptoms (FSS) and personality (HDHQ). Many patients had significant psychological symptoms in addition to their agoraphobia. FSS scores were factor analysed. First-order analysis revealed agoraphobia as a heterogeneous clinical entity occurring independently of a large General Symptoms factor which included panic attacks. Second-order analysis revealed a General Symptoms/Social Phobia factor and a well-defined but heterogeneous Agoraphobia factor comprising the lower-order factors Claustrophobia, Travel Fears and Agoraphobia (fear of crowded public places). Correlations of first- and second-order factors with HDHQ scores showed that the Travel Fears factor was not associated with abnormal personality traits, whereas the Claustrophobia and Agoraphobia factors were. This suggested that travel fears should respond well to behaviour therapy per se, whereas additional treatment aimed at modifying abnormal personality traits may sometimes be indicated for claustrophobia and fear of crowded places. The heterogeneous nature of agoraphobia and the large size of the independent General Symptoms factor underlined the desirability of a multi-modal approach to treatment and research.     

A comparison of factor scores under conditions of factor obliquity

Six different methods of computing factor scores were investigated in a simulation study. Population scores created from oblique factor patterns selected from the psychological literature served as the bases for the simulations, and the stability of the different methods was assessed through cross-validation in a subject-sampling model. Results from 5 evaluative criteria indicated that a simplified, unit-weighting procedure based on the factor score coefficients was generally superior to several unit-weighting procedures based on the pattern or structure coefficients. This simplified method of computing factor scores also compared favorably with an exact-weighting scheme based on the full factor score coefficient matrix. Results are discussed with regard to their potential impact on current practice, and several recommendations are offered.     

Concurrent validity of the WISC-R factor scores

This study investigated the efficacy of predicting academic achievement as measured by the Wide Range Achievement Test using the factor scores of the Wechsler Intelligence Scale for Children-Revised as potential predictors. Both instruments were administered to 200 school children referred for psychological evaluations. Factor scores for the WISC-R were computed according to equations provided by Gutkin (1978). These factor scores then were regressed in a stepwise manner on the Reading, Spelling, and Arithmetic standard scores from the Wide Range Achievement Test. Stepwise regressions also were performed using the traditional Verbal and Performance IQs as the potential predictors. A comparison was made between the results obtained by use of the factors or the more common scores. The results indicated that the Freedom From Distractibility factor score significantly aided in the prediction of Reading and Spelling achievement and was of primary importance in predicting Arithmetic achievement. When the stepwise results using the different scores were contrasted, the factor scores accounted for appreaciably more variance in Arithmetic than did the traditional Verbal and Performance IQs. Derived regression equations are reported along with a discussion of the interpretability of the Freedom From Distractibility factor.     

Two-subtest estimations of WAIS-III factor index scores

The reliability and validity of various short forms of the Wechsler Adult Intelligence Scale-Third Edition (WAIS-III; D. Wechsler, 1997) were evaluated in a sample of 100 patients with traumatic brain injury and in a demographically matched subgroup from the standardization sample. All short forms were based on 2-subtest estimations of the respective factor indexes. Although acceptable estimates could be obtained from all short forms for Verbal Comprehension, none of the possible short forms for Perceptual Organization consistently met the minimum criterion regarding the percentage of cases that fell within the 90% confidence interval of the full-length index. It is concluded that short-form estimates of the WAIS-III are not appropriate for clinical use when the goal is to obtain factor indexes.     

Construct validity of Wechsler factor scores.

The construct validity of the Verbal Comprehension. Perceptual Organization, and Freedom from Distractibility factor scores was examined in a sample of school-aged referred children. Examination of correlations between factor scores and neuropsychological and achievement tests generally supported the construct validity of the factors. The Verbal Comprehension factor was associated with verbal, quantitative, and concept-formation abilities. The Perceptual Organization factor was related to nonverbal concept formation, tactual performance, and visual attention. The Freedom from Distractibility factor demonstrated a complex pattern of correlations and appeared to reflect a range of abilities including quantitative, language, attentional, and concept formation.     

Differences in factor content of rights and wrongs scores

The right-response scores and wrong-response scores of speeded aptitude tests were factor analyzed to determine whether they differ in factorial content. The information thus obtained was used to derive scoring formulas that yield purer measures of a factor than do scoring formulas derived in other ways.This paper is a revision of a dissertation submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree at the University of Southern California, 1948, and a paper read to the American Psychological Association in September, 1949. The writer is greatly indebted to Dr. J. P. Guilford for providing the intercorrelation and distribution data from the files of the School of Aviation Medicine and for general guidance throughout the study. He also wishes to express his appreciation to T/Sgt. Frank C. Ivens and Sgt. James R. MacDonald for computational assistance in the extraction and rotation of the centroid factors, which were performed while the writer was a civilian employee of the Air Training Command, Human Resources Research Center. The opinions expressed are those of the writer and do not necessarily reflect the official views of the USAF.     

An exploratory factor analysis of children's depression inventory scores in young children of substance abusers

A factor analytic study of scores obtained on the Children's Depression Inventory from a sample of 202 young children (M = 7.5 yr., SD = 2.2) of alcoholics and substance abusers was completed. A principal components factor analysis with an oblique rotation yielded five separate factors related to Negative Self-concept, Acting-out. Somatic/Disturbed Symptoms, Mood, and Hopelessness. In previous factor analytic studies of the Children's Depression Inventory with normal and clinical populations the primary factor obtained was formed by mood-related items. In contrast, the primary factor of the present analysis was formed by items concerning perceptions of self-concept, not mood. These results corroborated previously reported data from the Child Behavior Checklist suggesting that the depressive symptoms displayed by children of substance abusers are related to self-concept and externalization.     

A microcomputer program for evaluating WISC-R factor scores

A data analysis routine was developed for the Apple II series microcomputer that allows school psychologists to quickly calculate WISC-R factor scores and evaluate the significance of differences between the factors and individual subtest deviations within the Verbal Comprehension and Perceptual Organization factors. The source code written in Applesoft BASIC is provided. With minor modifications the program can be adapted to run on other computer systems.     

A comparison of four methods of constructing factor scores

Four least-squares methods for constructing factor scores have been described in the literature. The formal properties of these scores are developed, and they are compared in terms of four generally desirable properties of constructed factor scores. In particular, it is shown that two of the methods yield scores that are conditionally unbiassed, and univocal in the sense of Guilford and Michael, though not orthogonal, while one of the other methods yields orthogonal scores.It is shown that constructed factor scores cannot be simultaneously univocal and orthogonal, unless we choose the special basis in factor space given by Canonical Factor Analysis.The general problem of choosing between the methods is discussed, on the basis of the theoretical relations obtained.EDITOR'S NOTE: The reader will quickly discover that this article develops several of the generalizations given in the second part of the preceding article, On Factors and Factor Scores. Independent development of the same generalizations is, of course, not a new phenomenon. Because the Presidential Address automatically is accepted for publication and given space in the December issue, it was decided that the only fair thing to do was to print this article in the same issue.     

The origin of factor scores: Spearman,Thomson and Bartlett

The indeterminacy of factor scores has been a perennial source of debate since the time of Spearman. The main purpose of this paper is to show that, in spite of his inadequate tools and concepts, Sir Godfrey Thomson's approach of 70 years ago was on the right lines. His thinking was constrained by the primitive state of his statistical understanding but it is illuminated by his substantial exchange of the correspondence with M. S. Bartlett in the 1930s, most of which has survived in the Godfrey Thomson archive at the University of Edinburgh. In order to justify our claim and clarify the issues, we have found it necessary to fill in some of the gaps in the original derivations of Spearman, Thomson and Bartlett and to express their work in terms which are intelligible today. The opportunity is taken to relate this earlier work to contemporary debates.     

A Bayesian predictive analysis of test scores

In the classical test theory, a high-reliability test always leads to a precise measurement. However, when it comes to the prediction of test scores, it is not necessarily so. Based on a Bayesian statistical approach, we predicted the distributions of test scores for a new subject, a new test, and a new subject taking a new test. Under some reasonable conditions, the predicted means, variances, and covariances of predicted scores were obtained and investigated. We found that high test reliability did not necessarily lead to small variances or covariances. For a new subject, higher test reliability led to larger predicted variances and covariances, because high test reliability enabled a more accurate prediction of test score variances. Regarding a new subject taking a new test, in this study, higher test reliability led to a large variance when the sample size was smaller than half the number of tests. The classical test theory is reanalyzed from the viewpoint of predictions and some suggestions are made.     

Age and cohort effects on personality factor scores across sexes and racial/ethnic groups

Substantial differences exist across ethnic groups and sexes in generational changes in status among groups residing in Hawaii. Despite these generational differences across groups, age differences in personality are remarkably consistent across sexes and racial/ethnic groups, and the few Sex x Age, Ethnicity x Age or Sex x Ethnicity x Age interactions account for little variance in scores. It is concluded that age/generational differences in personality factor scores in these populations result from age and not, to any major degree, from cohort effects.