Factor analysis and Psychometrika: Major developments

Papers on factor analysis appearing inPsychometrika reflect the initial efforts of the Thurstonians to reformulate psychology as a quantitative science. The Thurstonians' emphasis on the development of factor analysis as an exploratory methodology was not new with them but was taken from British statisticians and psychologists who preceded them, whose literature the Thurstonians otherwise tended to ignore. The Thurstonians' rejection of general factors and focus on rotation to simple structure reflected an attempt to avoid statistical artifact and to identify factors with psychological substance. Much of the literature on factor analysis inPsychometrika concerned solving technical problems in the exploratory factor analysis method. Factor analysis took a major shift in direction in the 1970's with the development of confirmatory methodologies, many of which now receive greater attention than the method of exploratory factor analysis, most of the problems of which are now resolved.     

Engaging the anomalous: reflections from the anthropology of the paranormal

Abstract

This review article looks at some of the parallels between the contents of this special issue on the paranormal and insights from the anthropology of religion, the anthropology of consciousness, transpersonal anthropology and the anthropology of the paranormal. The paper introduces the history of anthropology’s engagement with the paranormal, from the early evolutionist perspectives of anthropology’s pioneers to the most recent experiential approaches of the anthropology of consciousness. The paper concludes by highlighting the potential benefits of a cross-pollination of psychotherapeutic and anthropological research on the paranormal.     

Consciousness-Raising Groups in the 1970's

Based on a 1974 nationwide survey, this paper describes the characteristics of 1, 669 women in consciousness-raising (CR) groups. Most women in the survey are white, middle- and upper-middle class women who joined their first CR group during the 1970's. They learned about CR groups primarily from women friends and joined a group with friends or through a women's organization. Sixty-five percent of the women considered themselves to be members of the women's movement prior to their joining a CR group. Most women identified themselves as liberal (58%) or radical (21%). Women's primary reason for joining a CR group was to learn from, share with, and gain support from other women; they joined to examine personal issues within the context of their common social roles. Sharing experiences and feelings as women was the most salient group process. Women in this survey were highly satisfied with their CR group experience and encouraged other women to join a CR group.     

Quartic rotation criteria and algorithms

Most of the currently used analytic rotation criteria for simple structure in factor analysis are summarized and identified as members of a general symmetric family of quartic criteria. A unified development of algorithms for orthogonal and direct oblique rotation using arbitrary criteria from this family is given. These algorithms represent fairly straightforward extensions of present methodology, and appear to be the best methods currently available.The research done by R. I. Jennrich was supported by NSF Grant MCS-8301587.     

Estimating the standard errors of rotated factor loadings by jackknifing

The jackknife by groups and modifications of the jackknife by groups are used to estimate standard errors of rotated factor loadings for selected populations in common factor model maximum likelihood factor analysis. Simulations are performed in whicht-statistics based upon these jackknife estimates of the standard errors are computed. The validity of thet-statistics and their associated confidence intervals is assessed. Methods are given through which the computational efficiency of the jackknife may be greatly enhanced in the factor analysis model.Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by NIH Special Research Resources Grant RR-3.The author wishes to thank his doctoral committee co-chairmen, Drs James W. Frane and Robert I. Jennrich, UCLA, for their contributions to this research.     

P-technique factor analyses of the Multiple Affect Adjective Check List (MAACL)

The Multiple Affect Adjective Check List (MAACL) has been found to have five first-order factors representing Anxiety, Depression, Hostility, Positive Affect, and Sensation Seeking and two second-order factors representing Positive Affect and Sensation Seeking (PASS) and Dysphoria. The present study examines whether these first- and second-order conceptions of affect (based on R-technique factor analysis) can also account for patterns of intraindividual variability in affect (based on P-technique factor analysis) in eight elderly women. Although the hypothesized five-factor model of affect was not testable in all of the present P-technique datasets, the results were consistent with this interindividual model of affect. Moreover, evidence of second-order (PASS and Dysphoria) and third-order (generalized distress) factors was found in one data set. Sufficient convergence in findings between the present P-technique research and prior R-technique research suggests that the MAACL is robust in describing both inter- and intraindividual components of affect in elderly women.This paper is based on the doctoral research of the first author and was partially supported by the National Institute of Aging Grant T32 AC 00048-12 to The Pennsylvania State University and a Grant-in-Aid of Research from Sigma Xi, The Scientific Research Society. The authors wish to thank John R. Nesselroade for his helpful comments on an early draft of this paper.     

The relationship between external variables and common factors

A theorem is presented which gives the range of possible correlations between a common factor and an external variable (i.e., a variable not included in the test battery factor analyzed). Analogous expressions for component (and regression component) theory are also derived. Some situations involving external correlations are then discussed which dramatize the theoretical differences between components and common factors.Support by the National Research Council of Canada (NRC Grant No. A4640) and the University of British Columbia (UBC Humanities and Social Sciences Grant 26-9718) is gratefully acknowledged.This paper is based in part on the author's Ph.D. dissertation. I am particularly grateful to my dissertation advisor, Dr. Peter H. Schönemann. Thanks also to the editor and the anonymous reviewers, who contributed many helpful comments and suggestions.     

Development and validation of the Indonesian Well‐being Scale

The present study describes the development and validation of a new instrument to measure the well‐being of Indonesian people. Items were generated by taking into account the recent cross‐cultural developments in the literature. Participants (N = 1,028) from a number of provinces in Indonesia completed an online or a paper questionnaire containing a battery of measures, including the new well‐being instrument. The total sample was randomly split into two equal groups. An exploratory factor analysis (n = 516) was conducted on one half to explore the factor structure of the new scale, which resulted in a 24‐item scale with a four‐factor solution. The four factors were (a) Basic Needs, (b) Social Relation, (c) Acceptance, and (d) Spirituality. A confirmatory factor analysis was conducted on the second half (n = 516), which confirmed the four‐factor structure with 20 items emerging as the best and most parsimonious fit of the data. The psychometric properties of the final scale were tested on the whole sample. The new scale displayed sound internal consistency, test‐retest reliability, and divergent, convergent, and discriminant validity. The scale has the potential to be used in future research which examines well‐being in the Indonesia context. Future directions and limitations of the study are discussed.     

Language, bilingualism, and executive functioning in early development

Okanda, et al. (2010) reported new evidence concerning associations between language ability, bilingualism, and executive functioning early in development. The paper adds to a growing body of literature suggesting that bilingualism is associated with advantages in executive functioning generally, and the Dimensional Change Card Sort task in particular. However, as with all findings that hinge on between-group comparisons, there is a need to exercise caution before drawing firm conclusions about the effects of bilingualism on the development of executive control. Several lines of recent evidence are outlined that challenge key assumptions underlying the standard account of the bilingual advantage. Okanda, et al.'s findings are discussed in light of this evidence.     

Psychopathology and response styles in the SCL-90 responses of acutely distressed persons

Using the responses of 197 suicidal and nonsuicidal patients of a crisis and short-term intervention unit, the item factor structure of the SCL-90 was examined. Results suggested a reduced dimensionality for the checklist rather than supporting the nine scales associated with the instrument's scoring key. The influence of various response styles on the SCL-90's dimensionality was also explored. Although a social desirability response style was strongly related to all SCL-90 subscales and factors, it did not offer a complete explanation for the checklist's apparent unidimensionality. Other explanations relating to methods of test construction and to patients' inability to differentiate symptoms were also preferred. Finally, although subscale scores may facilitate clinical interpretation, it was suggested that the SCL-90 might best be scored as a single index of general symptomatology.We wish to thank G. C. Fekken and R. N. MacLennan for their assistance with this project.This work was supported in part by Social Sciences and Humanities Research Council of Canada Grant 410-85-1043 and by an Ontario Ministry of Health Research Personnel Award.     

Reexamining the factor structure of the 20-item Toronto alexithymia scale: commentary on Gignac, Palmer, and Stough

Gignac, Palmer, and Stough (2007/this issue) test a number of different latent factor models for the TAS-20 using a community sample of 355 participants and conclude that this scale is best represented by a "nested factors model," with five substantive factors and a method factor. Gignac et al. also report that the correlated three-factor model and a comparable higher order model supported by most studies produced poor levels of incremental close fit. In this article, we challenge Gignac et al.'s unheralded and largely unsupported use of nested model fitting and the uncritical acceptance of exceptionally high cutoff levels to assess goodness of fit (GOF). Using more traditional and empirically supported model testing procedures and a more flexible approach to the interpretation of multiple tests of GOF, we interpret Gignac et al.'s results as actually supportive of the traditional three-factor model and one that has been recovered in 17 of the 24 factor analytic studies of the TAS-20.     

Exploratory factor analysis for small samples

Traditionally, two distinct approaches have been employed for exploratory factor analysis: maximum likelihood factor analysis and principal component analysis. A third alternative, called regularized exploratory factor analysis, was introduced recently in the psychometric literature. Small sample size is an important issue that has received considerable discussion in the factor analysis literature. However, little is known about the differential performance of these three approaches to exploratory factor analysis in a small sample size scenario. A simulation study and an empirical example demonstrate that regularized exploratory factor analysis may be recommended over the two traditional approaches, particularly when sample sizes are small (below 50) and the sample covariance matrix is near singular.     

Oddities in Kirkpatrick, et al.'s study of children of lesbian mothers

Kirkpatrick, et al.'s 1976 study of what happened to 20 lesbians' children has received considerable attention, apparently later being matched with 20 heterosexuals' children. In 2004, Kirkpatrick generally acknowledged Schumm's caution that her findings are less impressive than are needed, yet, Kirkpatrick stated her "early findings have been reinforced" and that "no evidence of differences in the children grouped by the mother's sexual orientation" have been documented by subsequent research. Close examination of the data of these studies indicates that children from 13 lesbian mothers were compared with children from 13 divorced heterosexuals. Further, there are contradictions between the published reports regarding the nature of samples and various findings. Analysis of Kirkpatrick, et al.'s study suggests that children do less well when raised by homosexual parents.     

Early education as community intervention: Assisting an ethnic minority to be ready for school

An early education program designed for an ethnic minority of Native Hawaiians implemented at the community rather than the individual child level of intervention is described. The program development effort is theory driven and provides an opportunity to investigate the application of neo-Vygotskian theory to an applied community educational problem. Though not specifically derived from the work of O'Donnell, Tharp, and Wilson (1993), the project reported here shares a common intellectual heritage. This paper demonstrates the parallels between the early education program developed for Hawaiian children and the applicability of the theory presented in the work of O'Donnell et al. Portions of this research were supported by Grant #40212121 and Grant #MCJ495051 from the Bureau of Maternal and Child Health and Resource Management, U.S. Department of Health and Human Services awarded to the Center of Development of Early Education, Kamehameha School, Honolulu, Hawaii 96817, and to the Early Intervention Research Institute, Center for Persons with Disabilities, Utah State University, respectively.     

Factor analysis for non-normal variables

Factor analysis for nonnormally distributed variables is discussed in this paper. The main difference between our approach and more traditional approaches is that not only second order cross-products (like covariances) are utilized, but also higher order cross-products. It turns out that under some conditions the parameters (factor loadings) can be uniquely determined. Two estimation procedures will be discussed. One method gives Best Generalized Least Squares (BGLS) estimates, but is computationally very heavy, in particular for large data sets. The other method is a least squares method which is computationally less heavy. In one example the two methods will be compared by using the bootstrap method. In another example real life data are analyzed.This paper has partly been written while the author was a visiting scholar at the Department of Psychology, University of California, Los Angeles. He wants to thank Peter Bentler who made this stay at UCLA possible and for his valuable contributions to this paper. This research was supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O) under number R56-150 and by USPHS Grant DA01070.     

Comparison of several shortened versions of the EMBU: exploratory and confirmatory factor analyses

The aim of the present study was to analyze the psychometric properties of different versions of the EMBU (Egna Minnen av Barndoms Uppfostran – My memories of upbringing) in a non-clinical sample of adolescents. The factor structure of the questionnaire was studied by means of more adequate exploratory and confirmatory factor procedures in order to ascertain which version achieves a better fit to data. The 64-item version of the EMBU was administered to a non-clinical sample of 832 adolescents. Exploratory and Confirmatory factor analyses were carried out for successive versions of 64, 37, 24 and 23 items. The theoretical four-factor structure of the 64-item version is not replicated in a factor analysis through principal axis extraction with direct oblimin rotation. The "Favoring Subject" factor was not found. 37 items present loadings equal to or larger than 0.30 for the "Rejection", "Emotional Warmth" and "Overprotection" factors. A re-analysis of these items shows a clear three-factor structure. When Arrindell et al .'s (1999 ) 23-item version was analysed, the three expected factors were also found. Confirmatory factor analyses allow us to reduce the 36-item version to a shorter one of 24 items. This last version achieves the best fit to data, including the 23-item version. The new 24-item version improves the construct validity of the EMBU and presents similar reliability coefficients.     

A feasible method for standard errors of estimate in maximum likelihood factor analysis

A jackknife-like procedure is developed for producing standard errors of estimate in maximum likelihood factor analysis. Unlike earlier methods based on information theory, the procedure developed is computationally feasible on larger problems. Unlike earlier methods based on the jackknife, the present procedure is not plagued by the factor alignment problem, the Heywood case problem, or the necessity to jackknife by groups. Standard errors may be produced for rotated and unrotated loading estimates using either orthogonal or oblique rotation as well as for estimates of unique factor variances and common factor correlations. The total cost for larger problems is a small multiple of the square of the number of variables times the number of observations used in the analysis. Examples are given to demonstrate the feasibility of the method.The research done by R. I. Jennrich was supported in part by NSF Grant MCS 77-02121. The research done by D. B. Clarkson was supported in part by NSERC Grant A3109.     

Traumatic Brain Injury as a Risk Factor for Alzheimer's Disease: A Review

Accumulating epidemiological evidence implicates traumatic brain injury as a pathogenic agent in the development of Alzheimer's disease (AD). Considering the increase in the prevalence of both traumatic brain injury and AD in recent times, the possibility that brain trauma may provoke the early development of AD has important implications for health service planning, preventative efforts, and medico-legal compensation settlements. This paper evaluates the plausibility of the proposed link between traumatic brain injury and AD, largely by way of exploring a theoretical perspective advanced by Satz (1993) and considering recent contributions from the epidemiological, neuropathological, and biochemical literature that are pertinent to this issue. The literature reviewed provides sufficient support and empirical vindication to give credence to the proposed association between these two neuropsychological entities at the statistical, theoretical, and biological level.     

On the factor score controversy

A summary and interpretation of the recent literature on the indeterminacy of factor scores is given in simple terms. A good index of factor score determinacy is the squared multiple correlation of the factor with the observed variables.     

Development of the Inventory of College Students' Resilience and evaluating the measurement invariance

In order to help students adapt well to stressful situations or adversity, many researchers have explored the issue of students' resilience. The main purpose of this study was to develop the Inventory of College Students' Resilience (ICSR), for assessing resilience of college students. The present study recruited 993 participants to conduct item analysis, exploratory factor analysis and reliability analysis. We then administered the questionnaire to another 1490 participants in order to conduct confirmatory factor analysis and assess criterion-related validity. The results showed the proposed model fit the data well and the ICSR had both internal consistency and criterion-related validity. The ICSR was also found to have measurement invariance across gender. We conclude that the ICSR can help students to identify strengths and weaknesses in order to reinforce their resilience and improve their response to life stress and trauma.