Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric

In an addendum to his seminal 1969 article Jöreskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix (Jöreskog in Advances in factor analysis and structural equation models, pp. 40–43, 1979). These condition sets, formulated under factor correlation and factor covariance metrics, respectively, were claimed to be equivalent and to lead to global rotational uniqueness of the factor solution. It is shown here that the conditions for the oblique factor correlation structure need to be amended for global rotational uniqueness, and, hence, that the condition sets are not equivalent in terms of unicity of the solution.     

Canonical versus factor analytic perspectives on the structure of associations between the MMPI and the Buss-Durkee Hostility Inventory

A canonical correlational analysis of MMPI profiles versus Buss-Durkee hostility and aggression scales was conducted, resulting in the identification of a general hostility-aggression-maladjustment dimension and three relatively specific aggression-personality relationships. These findings were contrasted with those obtained from a factor analysis of the combination of both sets of scores. Though often used in previous studies of associations between the Buss-Durkee Hostility Inventory and other measures, factor analysis was seen to be less than optimally suited to such a purpose. It was concluded that canonical correlation is preferable to factor analysis when seeking to clarify the multivariate structure of relationships between two sets of variables.     

CFA Models with a General Factor and Multiple Sets of Secondary Factors

We propose a class of confirmatory factor analysis models that include multiple sets of secondary or specific factors and a general factor. The general factor accounts for the common variance among manifest variables, whereas multiple sets of secondary factors account for the remaining source-specific dependency among subsets of manifest variables. A special case of the model is further proposed which constrains the specific factor loadings to be proportional to the general factor loadings. This proportional model substantially reduces the number of model parameters while preserving the essential structure of the general model. Furthermore, the proportional model allows for the interpretation of latent variables as the expected values of the observed manifest variables, decomposition of the variances, and the inclusion of interactions, similar to generalizability theory. We provide two applications to illustrate the utility of the proposed class of models.     

How shared are age-related influences on cognitive and noncognitive variables?

Several theories have suggested that age-related declines in cognitive processing are due to a pervasive unitary mechanism, such as a decline in processing speed. Structural equation model tests have shown some support for such common factor explanations. These results, however, may not be as conclusive as previously claimed. A further analysis of 4 cross-sectional data sets described in Salthouse, Hambrick, and McGuthry (1998) and Salthouse and Czaja (2000) found that although the best fitting model included a common factor in 3 of the data sets, additional direct age paths were significant, indicating the presence of specific age effects. For the remaining data set, a factor-specific model fit at least as well as the best fitting common factor model. Three simulated data sets with known structure were then tested with a sequence of structural equation models. Common factor models could not always be falsified--even when they were false. In contrast, factor-specific models were more easily falsified when the true model included a unitary common factor. These results suggest that it is premature to conclude that all age-related cognitive declines are due to a single mechanism. Common factor models may be particularly difficult to falsify with current analytic procedures.     

Evaluating the structure of human values with confirmatory factor analysis

This is the first statistical test of a theory of the structure of human values (Schwartz, 1992). The theory postulates that 10 basic values are discriminated in all societies and that these values form a quasi-circumplex structure based on the inherent conflict or compatibility between their motivational goals. Past support for the theory came from subjective judgments of visual plots of the relations among value items in samples from over 60 countries. We formally test the postulated structure and several potential refinements. We employ a specially designed confirmatory factor analysis (CFA) approach with new data from two sets of 23 samples from 27 countries (N=10,857). In both data sets, CFAs confirm the 10 basic values, a modified quasi-circumplex rather than a simple circumplex structure, and the claim that values form a motivational continuum.     

Investigating the influence of social desirability on personality factor structure

This study provides a comprehensive investigation into whether social desirability alters the factor structure of personality measures. The study brought together 4 large data sets wherein different organizational samples responded to different personality measures. This facilitated conducting 4 separate yet parallel investigations. Within each data set, individuals identified through a social desirability scale as responding in an honest manner were grouped together, and individuals identified as responding in a highly socially desirable manner were grouped together. Using various analyses, the fit of higher order factor structure models was compared across the 2 groups. Results were the same for each data set. Social desirability had little influence on the higher order factor structures that characterized the relationships among the scales of the personality measures.     

Cross-cultural investigation of the Questionnaire of Smoking Urges in American and Spanish smokers

This study evaluated the factor structure of the Questionnaire of Smoking Urges (QSU) across American and Spanish smokers. Using confirmatory factor analyses, the fits of one-, two-, and four-factor models of smoking craving in American and Spanish data sets were compared. The two-factor model provided the best fit in both samples. However, negatively worded items confounded the interpretation of the two-factor structure in both the American and Spanish data. The first factor had positively and negatively worded items, whereas the second had only positively worded items. The two-factor structure was reexamined, removing either the positively or the negatively worded items. Using only positively worded items resulted in a loss of fit, whereas using only negatively worded items improved model fit substantially. Thus, the results supported the generalization of smoking craving across Spanish and American smokers and suggested that negatively worded items play a larger role in the two-factor structure of the QSU than originally thought.     

The relationship of engagement and job satisfaction in working samples

The present study explored the factor structure of engagement and its relationship with job satisfaction. The authors hypothesize that work engagement comprises 3 constructs: vigor, dedication, and absorption. Using structural equation modeling, the authors analyze data from 3 archival data sets to determine the factor structure of engagement. In addition, they examine the hypothesis that engagement and job satisfaction are separate but related constructs, using structural equation modeling and hierarchical regression. The authors test models in which engagement and job satisfaction items loaded onto a single latent variable and 1 in which they loaded onto 2 separate variables. Results from the confirmatory factor analysis indicate engagement has 3 factors. In addition, confirmatory factor analysis and hierarchical regressions indicate engagement and job satisfaction are separate constructs. Last, hierarchical regressions demonstrated the constructs have different relationships with the areas of work-life scale. Implications for theory and research are discussed.     

What needs to be explained to account for age-related effects on multiple cognitive variables?

Structural equation methodology was used to investigate age-related influences across a number of cognitive variables in 204 adults ranging from 18 to 91 years of age with a hierarchical structure that contained 4 1st-order factors and 1 2nd-order common factor. Direct age relations were found to the common factor as well as to 1st-order speed and memory factors. Replicability of the findings was explored by investigating the same structure of age relations, using 2 different data sets, and a similar patten was found in each. These results suggest that at least 3 statistically distinct types of age-related influences are operating on a wide variety of cognitive variables and presumably require separate explanatory mechanisms.     

The Experiences in Close Relationship Scale (ECR)-short form: reliability, validity, and factor structure

We developed a 12-item, short form of the Experiences in Close Relationship Scale (ECR; Brennan, Clark, & Shaver, 1998) across 6 studies. In Study 1, we examined the reliability and factor structure of the measure. In Studies 2 and 3, we cross-validated the reliability, factor structure, and validity of the short form measure; whereas in Study 4, we examined test-retest reliability over a 1-month period. In Studies 5 and 6, we further assessed the reliability, factor structure, and validity of the short version of the ECR when administered as a stand-alone instrument. Confirmatory factor analyses indicated that 2 factors, labeled Anxiety and Avoidance, provided a good fit to the data after removing the influence of response sets. We found validity to be equivalent for the short and the original versions of the ECR across studies. Finally, the results were comparable when we embedded the short form within the original version of the ECR and when we administered it as a stand-alone measure.     

The structure of infant intelligence: An historical overview

An historical overview of investigations that were concerned with delineating the structure and composition of infant intellectual activity is presented. The events which both preceded and culminated in the conceptualization of infant intelligence as a unitary trait, or factor, are traced. Thereafter, recent studies are reviewed which have guided contemporary investigators to contend that infant intellectual activity is comprised of varied sets of relatively independent abilities and factors. Several conclusions are made concerning the points of view which various investigators have held regarding the structure of infant intelligence.     

The factor structure of the MMPI-2 Restructured Clinical (RC) scales

We investigated the MMPI-2 Restructured Clinical (RC) scales (Tellegen et al., 2003) to determine if they had a more differentiated factor structure than the MMPI-2 Clinical scales. When factored alone, the RC scales had a 5-dimensional structure; the Clinical scales had 3 dimensions. When factored in combination with the Content scales, both sets of scales produced 5 dimensions. However, the RC and Content factors generally provided more efficient and logical markers of psychopathology than the Clinical and Content factors. We discuss interpretive considerations.     

The Multidimensionality of Motivation for Jewish Religious Behavior: Content, Structure, and Relationship to Religious Identity

The present study examined the content and structure of self–reported motivation for Jewish religious behavior. Initial items were generated from comprehensive and detailed responses to a semi–structured interview and an open–ended questionnaire. Principal component factor analysis with orthogonal rotation was carried out on the responses of a sample of 323 research participants to two parallel sets of the 111 items produced by the above process. The factor structures for each of these sets of items were highly similar to each other and consisted of the following five reliable factors: belief in a divine order, ethnic identity, social activity, family activity, and upbringing. These factors appear to reflect the way religious behavior can contribute to the satisfaction of a number of general human motives. Persons with different religious identities were found to attribute their performance of religious ritual to different motives, providing a partial explanation for the apparent anomaly of the performance of religious ritual by persons who identify themselves as secular.     

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.     

Factor validation of the Consideration of Future Consequences Scale: evidence for a short version

The author examined the factor structure of the 12-item Consideration of Future Consequences (CFC) Scale (A. Strathman, F. Gleicher, D. S. Boninger, & S. Edwards, 1994) among 664 undergraduate university students enrolled in human development courses. A principal-components factor analysis with varimax rotation yielded 2 factors. The author used confirmatory factor analysis procedures to examine the fit of 4 models, according to the principal-components factor analysis findings, with the observed covariance. The author used a number of fit indices to compare the 4 models. Both sets of analysis provided the greatest support for an 8-item short version of the CFC Scale. The author discussed findings in regard to the CFC Scale as an instrument to measure future time perspective.     

Multilevel Mixture Factor Models

Factor analysis is a statistical method for describing the associations among sets of observed variables in terms of a small number of underlying continuous latent variables. Various authors have proposed multilevel extensions of the factor model for the analysis of data sets with a hierarchical structure. These Multilevel Factor Models (MFMs) have in common that—as in multilevel regression analysis—variation at the higher level is modeled using continuous random effects. In this article, we present an alternative multilevel extension of factor analysis which we call the Multilevel Mixture Factor Model (MMFM). It is based on the assumption that higher level units belong to latent classes that differ in terms of the parameters of the factor model specified for the lower level units. We demonstrate the added value of MMFM compared with MFM, both from a theoretical and applied perspective, and we illustrate the complementarity of the two approaches with an empirical application on students' satisfaction with the University of Florence. The multilevel aspect of this application is that students are nested within study programs, which makes it possible to cluster these programs based on their differences in students' satisfaction.     

Factor copula models for mixed data

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models.     

Studying Dimensions of God Representation: Choosing Closed or Open-Ended Research Questions

God representation was studied by means of a questionnaire and by means of an open-ended question in a representative sample of students at the Katholieke Universiteit Leuven, Belgium. Data were analyzed for the two approaches by means of factor analysis and cluster analysis. Comparison of the two methods indicates that the answer structure of the two data sets is similar, but that the item list gave a somewhat better prediction of the answer to the open-ended question than vice versa.