Orthomax rotation and perfect simple structure

A loading matrix has perfect simple structure if each row has at most one nonzero element. It is shown that if there is an orthogonal rotation of an initial loading matrix that has perfect simple structure, then orthomax rotation with 0 1 of the initial loading matrix will produce the perfect simple structure. In particular, varimax and quartimax will produce rotations with perfect simple structure whenever they exist.     

A semi-analytical method of factorial rotation to simple structure

A factorial rotational method is presented which represents a compromise between the use of subjective judgment characteristic of graphical methods and the routine application of analytical methods. At present the analytical methods seem to be inadequate for the discovery of a simple structure, while graphical methods require more subjective judgment. The method herein presented locates the axes for subgroups of tests by an analytical method. The judgments used in the selection of subgroups are based on graphic data concerning interrelation of the factors.     

Simplimax: Oblique rotation to an optimal target with simple structure

Factor analysis and principal component analysis are usually followed by simple structure rotations of the loadings. These rotations optimize a certain criterion (e.g., varimax, oblimin), designed to measure the degree of simple structure of the pattern matrix. Simple structure can be considered optimal if a (usually large) number of pattern elements is exactly zero. In the present paper, a class of oblique rotation procedures is proposed to rotate a pattern matrix such that it optimally resembles a matrix which has an exact simple pattern. It is demonstrated that this method can recover relatively complex simple structures where other well-known simple structure rotation techniques fail.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences. The author is obliged to Jos ten Berge for helpful comments on an earlier version.     

Factorial similarity of letter and number series comprising identical rules

Letter series and number series tests, comprising items based on identical rules, were administered in a counterbalanced design to 320 undergraduates in order to determine the similarity of factorial structure by means of Tucker’s coefficients of congruence. Results indicated that the letter and number series tests, in which each item in one had a same-rule counter-part in the other, possessed limited factorial similarity because only 4 of the 8 identically constituted factors yielded coefficients of congruence between .80 and .91 (median = .85). Examination of item-wise patterns of responses of the persons, whose total scores on the letter series tests were five or more points lower than their total scores on the corresponding number series tests, revealed certain tactics of this group (n = 92) that might account for the lack of adequate factorial similarity.     

Factorial similarity of letter and number series comprising identical rules

Letter series and number series tests, comprising items based on identical rules, were administered in a counterbalanced design to 320 undergraduates in order to determine the similarity of factorial structure by means of Tucker’s coefficients of congruence. Results indicated that the letter and number series tests, in which each item in one had a same-rule counter-part in the other, possessed limited factorial similarity because only 4 of the 8 identically constituted factors yielded coefficients of congruence between .80 and .91 (median = .85). Examination of item-wise patterns of responses of the persons, whose total scores on the letter series tests were five or more points lower than their total scores on the corresponding number series tests, revealed certain tactics of this group (n = 92) that might account for the lack of adequate factorial similarity.     

Factorial similarity of the WISC-R for Anglos and Chicanos referred for psychological services

Two- and three-factor principal factor solutions to the WISC-R (Wechsler, 1974) were compared across race for referred Anglo and Chicano children. Additional comparisons of these factor solutions were made with those for normal Anglo, Chicano, Black, and Papago students (Reschly, 1978, Note 1) and the WISC-R standardization sample (Wechsler, 1974). Substantial congruence occurred across race for both the two- and three-factor solutions, though the two-factor solution was clearly most appropriate for the present sample.     

Factorial structure and reliability of Zimbardo Time Perspective Inventory

Time orientation is a fundamental psychological variable, what it flows all aspects of human behaviour. Past, present, and future orientation decomposed of allocated into different temporal frames the continual flow of behaviour, providing meaning and coherence. It has been proposed the Zimbardo Time Perspective Inventory (ZTPI) so multidimensional measure of time orientation, which include positive and negative evaluation of past and present, as well as future evaluation. The factorial structure and reliability of ZTPI was analysed on Spanish adult population. The participants were 756 adults with age range 19-67 years old ( M = 40.1, SD = 15.45). The principal components analyses showed five factors, very similar to obtain on nort-american undergraduate samples, even thought a little difference in composition of the present-fatalist factor. The reliability of each factor was suitable. Age and gender differences analysis showed that older groups were more future oriented and less present hedonist, female were high orientation to past negative, past positive and present fatalist, while young females were more future oriented than older females.     

Phonological similarity effects in simple and complex span tasks

Three experiments were conducted to examine the effect of phonological similarity in simple and complex memory span tasks. In Experiment 1, participants performed either a simple or a complex span task, and the memoranda within lists were either phonologically similar or distinct. Phonologically similar lists consisted of words that rhymed.The simple span task was word span. There were two complex span tasks; one was the original reading span task, and the other was a variant of reading span in which all the sentences within a list were contextually related. The classic phonological similarity decrement was observed in word span. In contrast, phonological similarity facilitation was observed in both versions of reading span. This facilitation effect was further investigated in Experiment 2 using two new versions of reading span. In Experiment 2, the sentences in reading span were either short or long, and the memoranda were presented separately from, and were unrelated to, the sentences. Again, words within phonologically similar lists rhymed, and again, facilitation was observed. In Experiment 3, phonological similarity was operationalized in terms of feature overlap, rather than rhyme. The classic phonological similarity decrement was still observed in word span, but facilitation was not observed in complex span. The results suggest that phonological similarity, when operationalized using words that rhyme, serves as a list retrieval cue and that complex span tasks are more dependent on cue-driven memory retrieval mechanisms than are simple span tasks.     

Factorial structure of the suicide intervention response inventory

Previous research has reported the development and validation of the Suicide Intervention Response Inventory (SIRI), a self-report instrument assessing a counselor's ability to select an appropriate response to the life-threatening client. The present study examined whether the response skill measured by the instrument might be multidimensional, rather than unitary as previously assumed. Inventories completed by 457 paraprofessional counselors from five suicide and crisis intervention services throughout the United States were factor-analyzed to yield their simple structure. Results suggested that the instrument is indeed multifactorial, with four component factors identified as Elaboration of the Complaint, Exploration of Suicidality, Involvement, and Reflection of Negative Feelings. The implications of these findings for training in crisis counseling and for the further psychometric development of the instrument are noted.     

A simple general method for oblique rotation

A simple and very general algorithm for oblique rotation is identified. While motivated by the rotation problem in factor analysis, it may be used to minimize almost any function of a not necessarily square matrix whose columns are restricted to have unit length. The algorithm has two steps. The first is to compute the gradient of the rotation criterion and the second is to project this onto a manifold of matrices with unit length columns. For this reason it is called a gradient projection algorithm. Because the projection step is very simple, implementation of the algorithm involves little more than computing the gradient of the rotation criterion which for many applications is very simple. It is proven that the algorithm is strictly monotone, that is as long as it is not already at a stationary point, each step will decrease the value of the criterion. Examples from a variety of areas are used to demonstrate the algorithm, including oblimin rotation, target rotation, simplimax rotation, and rotation to similarity and simplicity simultaneously. While it may be, the algorithm is not intended for use as a standard algorithm for well established problems, but rather as a tool for investigating new methods where its generality and simplicity may save an investigator substantial effort.The author would like to thank the review team for their insights and recommendations.     

The German TEIQue-SF: Factorial structure and relations to agentic and communal traits and mental health

Recent research illuminated the links between Agency, Communion, trait emotional intelligence (TEI), and internalizing mental health difficulties (IMHDs). However, for a more complete picture, unmitigated Agency and Communion have also to be considered. Drawing on a sample of N = 405 female occupational therapists, the present study examined (a) the factorial validity of the German TEI Questionnaire Short Form, (b) the relations of TEI to Agency, Communion, and their unmitigated variants, and (c) a multiple predictor-TEI-IMHDs mediation model. The factor structure suggested by TEI theory fitted approximately to the data. Agency and Communion related positively and both unmitigated traits related negatively to TEI. Indirect effects via TEI on IMHDs emerged for all four traits. The results help to integrate TEI within the Agency–Communion framework and suggest that TEI is an important intervening variable that helps to clarify the links of agentic and communal traits to mental health.     

Factorial structure of pathological personality as evaluated by peers

This study explored how individuals apply features of personality disorders (PDs) to peers. Members of groups nominated peers who exhibited symptoms for each of the 10 PDs in the DSM-IV. Data were gathered in 2 samples: 1st-year college students (n = 1,440) and Air Force recruits (n = 2,075). The peer method reliably identified group members exhibiting specific PD features. Factor analyses identified a clearly interpretable structure relevant to the pathological personality constructs being assessed. The structure replicated well across samples and showed expected relationships to broader models of normal personality. However, cross-method correlations of factor scores were only moderate, suggesting that peer reports are reliably different from self-reports regarding the presence of pathological personality traits.     

Factorial structure of the kidcope in Hong Kong adolescents

The Kidcope (A. Spirito, L. J. Stark, & C. Williams, 1988), a brief screening measure of coping strategies for children and adolescents, was subjected to exploratory and confirmatory factor analyses in a sample of adolescents in Hong Kong. A 2-factor model was found to fit the data when only the 2 emotional regulation items were treated separately and were allowed to load on the 2 different factors. Further analyses showed that factor loadings, factor variances, and factor covariance were invariant across age and gender. On the basis of the factor analyses, the authors created 2 composite scores, representing control-oriented and escape-oriented coping strategies. Implications for the use of the Kidcope in research and preventive intervention are discussed.     

Factorial structure and invariance across gender of the Swedish self-consciousness scale

In this study, I tested different factor models and the factorial invariance across gender for the Self-Consciousness Scale (Fenigstein, Scheier, & Buss (1975) using confirmatory factor analyses. University students (251 women and 259 men) completed the Swedish version of the scale. A respecified (Item 15 loading on the factor Internal State Awareness [ISA] instead of on the factor Self-Reflection [SR]) 17-item, 4-factor model of Burnkrant and Page (1984) including the factors SR, ISA, Public Self-Consciousness, and Social Anxiety demonstrated the best fit for both men and women. Factor intercorrelations were overall stronger for women. The respecified model demonstrated factorial invariance across gender. I discuss the strengthening of scale reliability through the expansion of subscale items and invariance testing across groups.