Factorial analysis of Thurstone's seven primary abilities

Intercorrelation coefficients among Thurstone's seven primary mental abilities scores were obtained from scores of 170 freshmen engineering students on the experimental edition of thePrimary Mental Abilities Tests. These correlation coefficients were factored to four factors, interpreted as a general factor, a reasoning factor, a verbal factor, and, tentatively, a specific memory factor. The finding of a general factor for a college population corroborates the Thurstones' finding of a general factor for eighth-grade children.     

Investigating Group Differences on Cognitive Tests Using Spearman's Hypothesis: An Evaluation of Jensen's Method

Jensen has posited a research method to investigate group differences in cognitive tests. This method consists of first extracting a general intelligence factor by means of exploratory factor analysis. Secondly, similarity of factor loadings across groups is evaluated in an attempt to ensure that the same constructs are measured. Finally, the correlation is computed between the loadings of the tests on the general intelligence factor and the mean differences between groups on the tests. This part is referred to as a test of "Spearman's Hypothesis", which essentially states that differences in g account for the main part of differences in observed scores. Based on the correlation, inferences are made with respect to group differences in general intelligence.

The validity of these inferences is investigated and compared to the validity of inferences based on multi-group confirmatory factor analysis. For this comparison, population covariance matrices are constructed which incorporate violations of the central assumption underlying Jensen's method concerning the existence of g and/or violations of Spearman's Hypothesis. It is demonstrated that Jensen's method is quite insensitive to the violations. This lack of specificity is observed consistently for all types of violations introduced in the present study. Multi-group confirmatory factor analysis emerges as clearly superior to Jensen's method.     

A Moderated Nonlinear Factor Model for the Development of Commensurate Measures in Integrative Data Analysis

Integrative data analysis (IDA) is a methodological framework that allows for the fitting of models to data that have been pooled across 2 or more independent sources. IDA offers many potential advantages including increased statistical power, greater subject heterogeneity, higher observed frequencies of low base-rate behaviors, and longer developmental periods of study. However, a core challenge is the estimation of valid and reliable psychometric scores that are based on potentially different items with different response options drawn from different studies. In Bauer and Hussong (2009) we proposed a method for obtaining scores within an IDA called moderated nonlinear factor analysis (MNLFA). Here we move significantly beyond this work in the development of a general framework for estimating MNLFA models and obtaining scale scores across a variety of settings. We propose a 5-step procedure and demonstrate this approach using data drawn from n = 1,972 individuals ranging in age from 11 to 34 years pooled across 3 independent studies to examine the factor structure of 17 binary items assessing depressive symptomatology. We offer substantive conclusions about the factor structure of depression, use this structure to compute individual-specific scale scores, and make recommendations for the use of these methods in practice.     

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.     

Method effects due to social desirability as a parsimonious explanation of the deviation from unidimensionality in LOT-R scores

Dispositional optimism measured by the Life Orientation Test (Revised; LOT-R, Scheier et al., 1994) was originally proposed as a unidimensional construct pertaining to individual differences in positive outcome expectancies. However, factor analytic research has suggested two separate “optimism” and “pessimism” factors associated with positively and negatively worded items respectively. Using confirmatory factor analysis with data from N = 658 students it is shown that a general optimism model with method effects of the positively worded items fits even better than the “optimism–pessimism” model in terms of the AIC statistic, which accounts for both model parsimony and model fit. Furthermore, an attempt is made to explain the method effects by social desirability: impression management, one of two components of socially desirable responding, correlates significantly with the method factor whereas the other component, self-deceptive enhancement, is related to the general optimism factor. Thus it is shown that the deviation from unidimensionality of observed scores does not imply deviation from unidimensionality of optimism when method effects are incorporated in the model.     

The Prospective and Retrospective Memory Questionnaire (PRMQ): Normative data and latent structure in a large non-clinical sample

The Prospective and Retrospective Memory Questionnaire (PRMQ; Smith, Della Sala, Logie, & Maylor, 2000) was developed to provide a self-report measure of prospective and retrospective memory slips in everyday life. It consists of sixteen items, eight asking about prospective memory failures, and eight concerning retrospective failures. The PRMQ was administered to a sample of the general adult population (N = 551) ranging in age between 17 and 94. Ten competing models of the latent structure of the PRMQ were derived from theoretical and empirical sources and were tested using confirmatory factor analysis. The model with the best fit had a tripartite structure and consisted of a general memory factor (all items loaded on this factor) plus orthogonal specific factors of prospective and retrospective memory. The reliabilities (internal consistency) of the Total scale and the Prospective and Retrospective scales were acceptable: Cronbach's alpha was 0.89, 0.84, and 0.80, respectively. Age and gender did not influence PRMQ scores, thereby simplifying the presentation and interpretation of normative data. To ease interpretation of scores on the PRMQ, tables are presented for conversion of raw scores on the Total scale and Prospective and Retrospective scales to T scores (confidence limits on scores are also provided). In addition, tables are provided to allow users to assess the reliability and abnormality of differences between an individual's scores on the Prospective and Retrospective scales.     

Bifactor Modeling and the Estimation of Model-Based Reliability in the WAIS-IV

Previous confirmatory factor analytic research that has examined the factor structure of the Wechsler Adult Intelligence Scale–Fourth Edition (WAIS-IV) has endorsed either higher order models or oblique factor models that tend to amalgamate both general factor and index factor sources of systematic variance. An alternative model that has not yet been examined for the WAIS-IV is the bifactor model. Bifactor models allow all subtests to load onto both the general factor and their respective index factor directly. Bifactor models are also particularly amenable to the estimation of model-based reliabilities for both global composite scores (ω _h ) and subscale/index scores (ω _s ). Based on the WAIS-IV normative sample correlation matrices, a bifactor model that did not include any index factor cross loadings or correlated residuals was found to be better fitting than the conventional higher order and oblique factor models. Although the ω _h estimate associated with the full scale intelligence quotient (FSIQ) scores was respectably high (.86), the ω _s estimates associated with the WAIS-IV index scores were very low (.13 to .47). The results are interpreted in the context of the benefits of a bifactor modeling approach. Additionally, in light of the very low levels of unique internal consistency reliabilities associated with the index scores, it is contended that clinical index score interpretations are probably not justifiable.     

The Personal Disturbance Scale (sAD): normative data and latent structure in a large non-clinical sample

The Personal Disturbance Scale [sAD; Bedford & Foulds (1978) Delusions–Symptoms–States Inventory State of Anxiety and Depression. Windsor: NFER-Nelson] is widely used in diverse settings and yet there are unresolved issues concerning its psychometric properties and normative data for the English speaking version are limited. The sAD was administered to a large sample of the general adult population (N=758). Demographic variables (gender, age, years of education and occupational status) had only very modest influences on sAD scores. Tables are presented for conversion of raw scores on the Anxiety, Depression and Total scales to percentiles. The sAD scales possessed adequate convergent and discriminant validity, as demonstrated by their pattern of correlations with two other measures of depression and anxiety (the DASS and the HADS). Ten competing models of the latent structure of the sAD were derived from theoretical and empirical sources. These models were evaluated using confirmatory factor analysis. The best fitting model (CFI=0.96) had a tripartite structure, and consisted of a general factor of psychological distress/negative affectivity (all items loaded on this factor) plus orthogonal specific factors of anxiety and depression. Correlated errors specified according to previous empirical findings were permitted. The theoretical and practical implications of this latent structure are discussed.     

Evaluating fit of the Prospective and Retrospective Memory Questionnaire (PRMQ) in a Nigerian adult population

This study aimed to evaluate the latent structure of the Prospective and Retrospective Memory Questionnaire (PRMQ) and to estimate the reliability and validity of scores from the measure in a Nigerian adult population (N = 758; age range = 18 - 63 years; females = 52.24%). Respondents also completed the Cognitive Failures Questionnaire (CFQ). The data were analysed utilising confirmatory factor analysis (CFA). The results suggest the PRMQ to have a tripartite structure characterised by the following features: general memory, plus eight prospective and eight retrospective memory items. Scores from the PRMQ had evidence of convergent validity with the CFQ. The reliability of scores from the PRMQ was of acceptable magnitude for the research purposes investigated in the study.     

Test anxiety in UK schoolchildren: Prevalence and demographic patterns

Background. Despite a large body of international literature concerning the antecedents, correlates of and treatments for test anxiety, there has been little research until recently using samples of students drawn from the UK. There is a need to establish some basic normative data for test anxiety scores in this population of students, in order to establish whether international research findings may generalize to UK schoolchildren. Aim. To collect some exploratory data regarding test anxiety scores in a sample of UK schoolchildren, along with socio‐demographic variables identified in the existing literature as theoretically significant sources of individual and group differences in test anxiety scores. Sample. Key Stage 4 students (1348): 690 students in the Year 10 cohort and 658 students in the Year 11 cohort, drawn from seven secondary schools in the North of the UK. Method. Data on test anxiety were collected using a self‐report questionnaire, the Test Anxiety Inventory ( Spielberger, 1980 ) and additional demographic variables through the Student Profile Questionnaire. The factor structure of the Test Anxiety Inventory was explored using principal components analysis and multiple regression analysis used to predict variance in self‐reported test anxiety scores from individual and group variables. Results. The principal components analysis extracted two factors, worry and emotionality, in line with theoretical predictions. Gender, ethnic and socio‐economic background were identified as significant predictors of variance in test anxiety scores in this dataset. Whether English was an additional, or native, language of students did not predict variance in test anxiety scores and year group was identified as a predictor of emotionality scores only. Conclusion. Variance in the test anxiety scores of Key Stage 4 students can be predicted from a number of socio‐demographic variables. Further research is now required to assess the implications for assessment performance, examination arrangements and appropriateness of using a North American measure of test anxiety in a UK context.     

Multiple rectilinear prediction and the resolution into components

It is assumed that a battery ofn tests has been resolved into components in a common factor space ofr dimensions and a unique factor space of at mostn dimensions, wherer is much less thann. Simplified formulas for ordinary multiple and partial correlation of tests are derived directly in terms of the components. The best (in the sense of least squares) linear regression equations for predicting factor scores from test scores are derived also in terms of the components. Spearman's single factor prediction formulas emerge as special cases. The last part of the paper shows how the communality is an upper bound for multiple correlation. A necessary and sufficient condition is established for the square of the multiple correlation coefficient of testj on the remainingn—1 tests to approach the communality of testj as a limit asn increases indefinitely whiler remains constant. Limits are established for partial correlation and regression coefficients and for the prediction of factor scores.I am indebted to Professor Dunham Jackson for helpful criticism of most of this paper.     

Personality for free: Psychometric properties of a public domain Australian measure of the five‐factor model

Fifty items from Goldberg's International Personality Item Pool were compiled to form a public‐domain measure of personality, the Australian Personality Inventory (API). Data from a random community sample (N = 7615) and a university‐based sample (N = 271) were used to explore psychometric properties of this 50‐item measure of the five‐factor model of personality (FFM). In both samples, internal reliabilities were adequate. In the university‐based sample an appropriate pattern of convergent and divergent relationship was found between scale scores and domain scores from the NEO Five‐Factor Inventory. After adjusting for an apparent response set (mean response across items), exploratory factor analyses clearly retrieved the FFM in both samples. It is provisionally concluded that raw scale scores from the API provide reliable estimates of the FFM, but adjustment for mean response across the 50 items might clarify the five‐factor structure, especially in less educated samples.     

Assessing Emotional Reactivity: Psychometric Properties of the Perth Emotional Reactivity Scale and the Development of a Short Form

The Perth Emotional Reactivity Scale (PERS) is a 30-item self-report measure of trait levels of emotional reactivity. In this article, we examine the psychometric properties of the PERS subscale and composite scores in an adult community sample (N = 428), and develop an 18-item short form of the measure (PERS–S). The PERS and PERS–S are designed to assess the typical ease of activation, intensity, and duration of one's emotional responses, and do so for positive and negative emotions separately. Our confirmatory factor analyses supported that the PERS and PERS–S both had the same theoretically congruent factor structure, and that all subscale and composite scores displayed high internal consistency reliability. Correlations with scores from established measures of psychopathology and emotion regulation also supported the validity of PERS and PERS–S scores. Our data therefore suggest that the PERS–S subscale and composite scores retain the psychometric strengths of their longer PERS counterparts. We conclude that both forms of the measure have good utility. Clinical and research applications are discussed.     

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.     

The contribution of anxiety and depression to fatigue among a sample of Australian university students: suggestions for university counsellors

Responses to the Zung Self-Rating Anxiety Scale (SAS: Zung, W. (1971). A rating instrument for anxiety disorders. Psychosomatics, 12, 371–379), the Self-Rating Depression Scale (SDS: Zung, W. (1973). From art to science: The diagnosis and treatment of depression. Archives of General Psychiatry, 29, 328–337) and the Fatigue Severity Scale (FSS) developed by Krupp and colleagues (Krupp, L.B., LaRocca, N.G., Muir-Nash, J., & Steinberg, A.D. (1989). The fatigue severity scale: Application to patients with multiple sclerosis and systemic lupus erythematosus. Archives of Neurology, 46, 1121–1123) were collected from 200 Australian university students to explore the links between these three disorders. Reliability data were satisfactory for all three scales and there were no significant gender or age-related differences between total scale scores. Factor analyses revealed a 5-factor solution for the SAS, a 6-factor solution for the SDS and a single factor for the FSS. There were 8 major and meaningful correlations found and these were entered into a regression of the SAS and SDS factor scores upon the single factor of the FSS. Fatigue factor scores were most powerfully predicted by psychomotor agitation, pain and resultant fatigue and cognitive and emotional arousal factor scores from the SAS and SDS. These data argue for an arousal/anxiety-fatigue-depression progression in disease that may be developmental or accumulative, with extreme levels of psychomotor arousal, resultant muscle fatigue and pain, plus concurrent elevated emotional state and cognitive arousal contributing to an eventual depletion of physical resources, leaving the individual in extreme fatigue. Implications for diagnosis and treatment by counsellors are discussed.     

WISC-R Subtest But No Overall VIQ–PIQ Difference in Dutch Children with PDD-NOS

VIQ–PIQ differences have been studied in children with autism and Asperger syndrome but have not been studied in a separate group of children with PDD-NO, although, PDD-NOS has a much higher prevalence rate than autism and deficits in communication and social interaction are severe. The Wechsler Intelligence Scale for Children-Revised (WISC-R) was administered to 100 children, aged 6–12 years, with PDD-NOS (n = 76), autism (n = 13), and Asperger syndrome (n = 11). PDD-NOS was diagnosed using explicit research criteria. No overall differences between VIQ and PIQ were found in PDD-NOS and autism. Peaks in the subtest scores on Information, Similarities, Picture Arrangement, and Mazes, and troughs in the subtest scores on Comprehension, Digit Span, and Coding were demonstrated in children with PDD-NOS. Their score on the Freedom from Distractibility factor was lower than the scores on the Verbal Comprehension factor and the Perceptual Organization factor. Children with PDD-NOS seemed to have a similar VIQ–PIQ profile as children with autism, and on the subtest level children with PDD-NOS showed some similarities to children with Asperger syndrome or autism. It was not possible to distinguish PDD-NOS from autism or Asperger syndrome by using IQ scores.     

Factor Structure of the Illness Intrusiveness Rating Scale in Patients Diagnosed with Anxiety Disorders

The Illness Intrusiveness Rating Scale (IIRS) is a measure designed to assess the impact of illness on various domains of functioning (G. M. Devins, 1994). In anxiety disordered patients, illness intrusiveness ratings are higher than those of chronically ill medical patients, suggesting that the IIRS may have a different underlying structure in a sample of individuals with anxiety disorders. To examine this possibility, IIRS items were submitted to an exploratory and confirmatory factor analysis in 2 samples (total N = 294). These solutions were compared to solutions in chronically ill populations from a previous study. In the exploratory analysis, both a one-factor and a three-factor solution were identified, accounting for 42 and 61% of the variance, respectively. Confirmatory analyses showed adequate similarity between the three-factor structure of the IIRS from a medically ill population and the current three-factor structure, suggesting that elevated IIRS scores in anxiety disordered samples cannot be explained simply by a different structure of the instrument.     

The geometry of factorial indeterminancy

TheN-dimensional geometry of a Spearman-Thurstone factor solution reveals two sources for the indeterminancy of factor scores: indeterminancy of total factor space and a rotational indeterminancy within a given total factor space. The analytical papers of Ledermann [4] and Guttman [2] on indeterminancy of factor scores are related to these findings and a simple vector model is developed to reveal the properties of rotational indeterminancy. The significance of factor-score indeterminancy is discussed in light of these findings.     

Osgood and Suci's measure of pattern similarity andQ-technique factor analysis

The purpose of this article is to show that a relationship can be established between Osgood and Suci'sD based on raw scores and scores obtained from factor analysis data without equalizing the means and variances of each individual's set of scores.     

A comparison of three methods for scoring figure drawings

Figure drawings obtained from 758 white male medical students were scored using three different methods. Method I involved 16 different physical size measurements; Method II involved six separate sophistication of body concept ratings; and Method III involved 42 separate aspects of the drawings weighted in direct proportion to their relative frequency of occurrence in the sample studied (conventionality scoring). Separate factor analyses of the scores derived from each method revealed that Methods I and II each reflect only a single underlying factor, and that these factors are uncorrelated in the population studied. Method III yielded eight meaningful factors, each of which may be construed as an independent area of conventionality/deviancy. An overall conventionality/deviancy score was also derived. It is believed that these three methods of scoring capture most of the variance inherent in existing figure drawing scoring systems, but that use of all three is necessary for a comprehensive analysis.