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.     

Factor structure of the Beck Depression Inventory in a university sample

Factor analysis was performed on the Beck Depression Inventory with a university sample to examine its potential multidimensionality. A principal components analysis with an oblimin and varimax rotation produced a two-factor solution. These factors were labeled Cognitive-Affective and Physiological and accounted for approximately 39% of the common variance. This finding is consistent with multidimensionality of the inventory and with a similar study of college students. The commonalities of the two studies suggest the reliability (internal consistency) of the Cognitive-Affective and Physiological constructs among "minimally" depressed university samples.     

Comparison Of Oblique And Orthogonal Simple Structure Solutions For Personality And Interest Factors

The study was directed to the need to structure in a few variables the domain measured by personality and interest measures commonly employed in educational counseling: Strong, Kuder, EPPS and the Study of Values. Despite initial uncertainty regarding number of factors to be employed, effects of ipsative scores and of mixing test formats, both an oblique and orthogonal rotation yielded nearly identical results. Of the twenty factors identified by both the biquartimin and varimax solutions, Seven linked vocational interest clusters with personality. Two of the remaining factors had only interest loadings, while of the eleven personality factors, only four were scale specific. Definition of the 16 common factors required that extraction proceed beyond the unit latent root criterion. The results offer evidence that over- extracting factors does not confuse the results of rotation. Further, psycho- metric differences between tests had essentially no effect on the factors found. Of three oblimin rotations attempted, only the biquartimin was successful, yielding results essentially like those of the varimax solution. Because of the vast difference in computation time for these two solutions (computer time 20 times greater for biquartimin), however, the orthogonal varimax remains the method of choice.     

Verbal aggressiveness of physical education teachers and students' self-reports of behavior

The purpose of this study was to develop a test for describing verbally aggressive behaviors of physical education teachers as perceived by secondary school students. The sample of 130 students (70 boys and 60 girls) were students in the second year of secondary school in Greece. 12 items designed for students were structured to describe possible verbal aggressive behaviors of physical education teachers as perceived by students and students' intention to respond. Exploratory factor analysis using the principal components method and varimax rotation yielded three factors, namely, (i) personal insults, threats, irony and their effect, (ii) intention to respond, and (iii) insults and threats toward others. Eigenvalues were greater than 1.00 for each of three factors which accounted for 69% of the total variance. Values of Cronbach alpha were .86, .88, and .78 for the three factors, respectively.     

Structure of the Mini-Mental State Examination: a comparison between normal and clinical subjects

The Mini-Mental State Examination was administered to a sample of 133 Italians ranging from 60 to 80 years of age. From a Principal Components Analysis three factors were retained, being results of both varimax and oblimin rotations. These were labeled (1) Memory, (2) Verbal Comprehension, and (3) Attention. These factors are similar to those obtained with normal elderly Americans, but they are different from the factors based on clinical samples. No age differences in the factor scores were found among the normal elderly subjects when education was considered. In contrast, significant differences were found between a group of 25 demented patients and a matched group randomly extracted from the normal sample.     

Adolescent loneliness assessment

The aim of the present work was to develop a loneliness scale for adolescents in order to assess their perceptions of the quality of their relationships with parents and peers. The scale was administered to 1,233 Argentine secondary school students, aged 13-16 years. Factor analyses (principal axes, oblimin solution) were conducted. Four factors were obtained, which accounted for 43.13% of the variance: Peer Rejection, Family Deficits and Parent Rejection, Personal Inadequacy, and Significant Separation. The internal consistency assessed through Cronbach's alpha was satisfactory. We believe that this proposal, which aims at evaluating the different processes that cause and are caused by a feeling of loneliness, allows for an integral approach to the issue.     

The Spanish version of the Vividness of Visual Imagery Questionnaire: factor structure and internal consistency reliability

We examined the factor structure and internal consistency reliability of the Spanish version of the Vividness of Visual Imagery Questionnaire which was applied to a sample of 850 secondary school students. Factor structure investigated by principal components analysis, followed by varimax orthogonal rotation, indicated that a single factor explained 37% of the variance. The internal consistency of the questionnaire was good (Cronbach alpha=.88). We conclude that the Spanish version of the questionnaire, like the English version, has a single factor and high internal consistency reliability.     

A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

Temporal stability of the intrinsic motivation inventory

To examine the temporal stability of the Intrinsic Motivation Inventory a Greek version was administered to 144 undergraduate students after an endurance field test. The same procedure was repeated one week later. Factor analysis followed by varimax rotation showed that three factors (Perceived Competence, Interest/enjoyment, and Effort/importance) explained 65.26% of the total variance. Computed intraclass correlation coefficients (ICC) were .61 for the Perceived Competence subscale, .86 for the Interest/enjoyment, .60 for the Effort/importance, and .70 for the overall scale. The results, however, were modified when the sample was divided in two groups. The first represented small changes in perceived competence between the first and the second measurement, while the second one represented large changes between the two measurements. Recalculated intraclass correlation coefficients for individuals whose Perceived Competence score remained relatively stable yield a high value (.92), whereas individuals whose Perceived Competence changed yield an extremely low value (.60). It was concluded that the Intrinsic Motivation Inventory provides a temporally stable measure, given that perceived competence has not been markedly changed.     

认知评价、心理控制感、社会支持与高考压力关系的研究

采用问卷法,随机选取河北省三类中学(重点、普通、私立)324名高三考生为被试,考察了学生对高考的认知评价、心理控制感、社会支持与高考压力的关系.结果表明:(1)重点中学、普通中学学生心理控制感显著高于私立中学学生,女生在社会支持的寻求上显著高于男生;(2)积极认知评价、心理控制感和社会支持与高考压力有显著负相关,而消极认知评价与高考压力有显著的正相关;(3)消极认知评价、心理控制感和社会支持对高考压力有直接影响;而积极认知评价通过心理控制感和社会支持间接影响高考压力.     

Death anxiety and death obsession in Spanish students

This study examined the dimensional structure of Templer's Death Anxiety Scale and Abdel-Khalek's Death Obsession Scale. The responses of 289 Spanish students to the Spanish forms of both scales were evaluated by means of a principal components analysis with varimax rotation. Three significant factors were identified: Death Obsession, Cognitive-Affective, and Death Anxiety. The distribution of the factor loadings for the items of both scales on Factors 1 and 3 supported the discriminant validity of the constructs specific to each of the scales, while Factor 2 showed a common component in both scales characterized by cognitive and affective aspects in relation to the idea of death.     

Admissible values of γ in direct oblimin rotation

It is shown that for nonpositive values of the parameter in the oblimin criterion, the criterion achieves a minimum on the manifold of all possible oblique rotations of any given full rank initial loading matrixA. For every positive value of , on the other hand, it is shown that there exists a full rank initial loading matrixA for which the oblimin criterion does not achieve a minimum over the manifold of all oblique rotations ofA. These results help explain the sometimes divergent behavior that results from using direct oblimin algorithms with set to a positive value.This research was supported in part by National Institutes of Health Grant RR-3.     

神经质人格对中小学生抑郁的影响：班级环境的跨层调节作用

基于素质-应激理论考察神经质人格及班级环境对中小学生抑郁的作用机制,对30个班级共933名中小学生进行问卷调查。多层分析结果显示：（1）中小学生抑郁存在显著的班级聚集效应;（2）神经质人格正向预测中小学生抑郁,班级人际环境、班级学习环境均负向预测中小学生抑郁;（3）班级学习环境跨层调节神经质人格与中小学生抑郁之间的关系,即积极的班级学习环境削弱了神经质人格对中小学生抑郁的影响。结果表明,我国教学制度下的班级学习环境在中小学生抑郁预防过程中可发挥重要作用。     

Factor structure of the Depression Self-Rating Scale in an Iranian adolescent sample

Previous research showed concurrent validity for the Depression Self-rating Scale for Iranian adolescents, so the present purpose was to evaluate construct validity. The scale was distributed to 2012 school students in Grades 5 to 10. Factor analysis using varimax rotation yielded four factors interpretable as depressed mood, hopelessness, lack of pleasurable activities, and physiological symptoms. These factors accounted for 44% of the variance and provide some support for construct validity of the scale in Iranian adolescents.     

Reliability, validity, and factor structure of the Arabic version of the 12-item General Health Questionnaire.

The aim was to examine the psychometric properties of the Arabic 12-item General Health Questionnaire in a sample of university students. A sample of 157 university students was screened using this questionnaire and the Hopkins Symptom Checklist-90. A standardized clinical interview using SCID was conducted on a subset of screened students. Reliability, validity, and factor analysis of the questionnaire were evaluated. Using factor score discrimination between cases and noncases was also evaluated. The Arabic version of the GHQ-12 proved to be reliable as indicated by Cronbach alpha of .86. The best balance between sensitivity and specificity was found at the General Health Questionnaire cut-off point of 15/16: at this threshold, sensitivity was .88 and was paired with a specificity of .84. Principal component analysis with varimax rotation identified three factors, namely, Factor A (general dysphoria), Factor B (lack of enjoyment), and Factor C (social dysfunction). Factors A and C discriminated between clinically distressed and clinically nondistressed subjects. The General Health Questionnaire-12 as a whole is a reliable and valid screening tool in university settings.     

Reduced approach motivation following nonreward: Extension of the BIS/BAS scales

The current study describes the development and validation of a new subscale to be used with the BIS/BAS scales (Carver & White, 1994). This subscale measures lowered approach motivation following nonreward. Factor analysis of the new subscale was carried out within a sample of 308 University students, test–retest reliability was established within a sample of 62 individuals, and construct validity was explored in a sample of 86 individuals by comparing scores on the new subscale with those on an existing self-report measure of apathy and on a behavioural measure of persistence. Reliability and validity of the new frustrative nonreward responsiveness subscale was found to be adequate within the populations studied. The findings are discussed in relation to theoretical accounts of BAS and BIS sensitivity.     

积极同伴压力、自尊对青少年不同冒险行为的影响

该研究基于问题行为理论,采用问卷法对普通高中、中职院校689名青少年学生进行调查,探讨了积极同伴压力、自尊对青少年不同冒险行为的影响及其交互作用和学校差异。结果表明:(1)中职院校生的积极同伴压力和冒险行为都显著高于普通高中生;(2)积极同伴压力不能预测青少年的适应不良冒险行为,但可显著预测普通高中生的社会可接受冒险行为;(3)自尊可显著负向预测青少年的适应不良冒险行为,显著正向预测普通高中生的社会可接受冒险行为;(4)自尊仅可以调节普通高中生的积极同伴压力与社会可接受冒险行为的关系:高自尊增强了高积极同伴压力对青少年社会可接受冒险行为的影响;但它不能调节无论哪所学校青少年的积极同伴压力与适应不良冒险行为的关系。     

Measuring emotional intelligence

The purposes of this study were (a) to develop a measure of emotional intelligence, the Emotional Intelligence Inventory and (b) to find the underlying dimensions of the inventory by testing 111 high school students at a bilingual college preparatory school. The inventory has 45 items. After excluding the four weakest items, the reliability coefficient alpha was .83. Subsequently, 319 junior and senior high school students at the same school were administered the 41 items. The reliability coefficient was .81. A maximum likelihood factor analysis with a varimax rotation yielded four factors of empathy, utilization of feelings, handling relationships, and self-control. Psychometric properties were sound, and the revised Emotional Intelligence Inventory can be recommended for use in the investigation of emotional intelligence.     

Psychometric characteristics of the Science Teaching Efficacy Belief Inventory in South Africa

The psychometric properties of the Science Teaching Efficacy Belief Inventory are reported, based on responses of 200 (88 men and 112 women) elementary science teachers in the Eastern Cape, South Africa. Previous factor analytic studies of this inventory have identified a two-factor solution but this has not been investigated in a South African context. The reliability estimated as internal consistency (Cronbach alpha) was .87. Principal components analysis with varimax rotation indicated a two-factor solution accounting for 38.1% of variance, with Cronbach alphas of .92 and .73 for the Personal Science Teaching Efficacy Belief subscale (Factor 1) and the Science Teaching Outcome Expectancy subscale (Factor 2), respectively. Principal components analysis of the Science Teaching Efficacy Belief Inventory yielded two conceptually meaningful components, similar to those reported in literature. Although one item did not meet the conditions for acceptance, this inventory may be useful in understanding science teachers' efficacy beliefs in South Africa. These particular findings are preliminary but hopeful. Studies using confirmatory analysis to address the cross-national invariance of this inventory are needed.     

Factor analysis of MCMI-II and PACL basic personality scales in a college sample

This study examined factor dimensions common to the eight basic personality scales of the Millon Clinical Multiaxial Inventory-II (MCMI-II; Millon, 1987) and Personality Adjective Check List (PACL; Strack, 1987, 1990). Subjects were 140 college students (65 men and 75 women). MCMI-II weighted raw scores (WRS) and WRS corrected for number of items endorsed true by regression were employed for analysis along with PACL T-scores. Principal components analyses with varimax and direct oblimin rotations were carried out separately on the two sets of MCMI-II and PACL scores. MCMI-II and PACL scales measuring the same personalities were usually correlated most highly with each other, although some divergences were noted. WRS yielded three bipolar dimensions and a fourth unipolar method factor that loaded only the five MCMI-II scales that were strongly correlated with number of items endorsed true. Residual scores yielded a more meaningful set of three bipolar dimensions labeled Social Introversion-Extraversion, Emotionality-Restraint, and Social Dominance-Submissiveness, without the method factor, that were very similar to personality dimensions found separately in the two tests. More research is needed to clarify the response bias issue in the MCMI-II and to further explicate similarities and differences between the MCMI-II and the PACL.