On rotating to smooth functions

Tucker has outlined an application of principal components analysis to a set of learning curves, for the purpose of identifying meaningful dimensions of individual differences in learning tasks. Since the principal components are defined in terms of a statistical criterion (maximum variance accounted for) rather than a substantive one, it is typically desirable to rotate the components to a more interpretable orientation. Simple structure is not a particularly appealing consideration for such a rotation; it is more reasonable to believe that any meaningful factor should form a (locally) smooth curve when the component loadings are plotted against trial number. Accordingly, this paper develops a procedure for transforming an arbitrary set of component reference curves to a new set which are mutually orthogonal and, subject to orthogonality, are as smooth as possible in a well defined (least squares) sense. Potential applications to learning data, electrophysiological responses, and growth data are indicated.Portions of this research were supported by the National Research Council of Canada, Grant A8615 to the second author. We thank Jagdeth Sheth for supplying his raw data.     

Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study

In order to make the parallel analysis criterion for determining the number of factors easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. The correlation matrices were derived from distributions of normally distributed random numbers. The independent variables are log (N–1) and log {[n(n–1)/2]–[(i–1)n]}, whereN is the number of observations;n, the number of variables; andi, the ordinal position of the eigenvalue. The results were excellent, with multiple correlation coefficients ranging from .9948 to .9992.This research was supported by the Office of Naval Research under Contract N00014-67-A-0305-0012, Lloyd G. Humphreys, principal investigator, and by the Department of Computer Science of which Richard G. Montanelli, Jr., is a member.     

Comments on “the measurement of factorial indeterminacy”

Guttman's index of indeterminacy (2² – 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation ² for predicting the factor from the observed variables is the average correlation _AB between independently selected alternative solutionsA andB, while var ( _AB )=(1 – ²)²/s, wheres is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, ² is the lower bound for E( _AB ); however, E( _AB ) need not be a modal value in the distribution of _AB . Guttman's index and E( _AB ) measure different aspects of the same indeterminacy problem.     

A look,by simulation,at the validity of some asymptotic distribution results for rotated loadings

In the last few years, a number of asymptotic results for the distribution of unrotated and rotated factor loadings have been given. This paper investigates the validity of some of these results based on simulation techniques. In particular, it looks at principal component extraction and quartimax rotation on a problem with 13 variables. The indication is that the asymptotic results are quite good.     

Caveats of non-ipsatization of basic values: A review of issues and a simulation study

Ipsatization, or a correction of variables by their common component, is routinely applied to measures of basic values. Although ipsatization has been criticized, the consequences of non-ipsatization are rarely discussed. We show that the ipsatization of values is intertwined with their definition. A common factor involved in ipsatization was suggested to represent a nuisance variable, a response style, social desirability, or other constructs. A simulation study illustrated that within-individual centering revealed more accurate value scores when the common factor was in the data, with exception of the situation when values were consistently and positively correlated with each other. We conclude that in different conditions both applying and failing to apply ipsatization can cause bias. Therefore, no general advice in regard to ipsatization can be provided.     

Agreeableness and the common core of dark traits are functionally different constructs

The Dark Factor of Personality (D) has been suggested as the basic disposition underlying dark traits, thereby representing their common core. However, it has also been argued that such commonalities reflect the low pole of Agreeableness. The present study (N = 729) employed five established inventories to model the Agreeableness construct and considered seven theoretically derived criterion variables, including one behavioral outcome. Results indicate that Agreeableness and D exhibit a substantial, but far from perfect, association of r = −.64. Further, D incrementally improved the prediction of all but one criterion measure. These results speak against the notion that the commonalities of dark traits can be reduced to low Agreeableness and rather support the contention to consider Agreeableness and D as functionally distinct constructs.     

A Validation of a Multicultural Competency Measure Among South Korean Counselors

The authors translated the California Brief Multicultural Competence Scale (CBMCS; Gamst et al., 2004), a measure of multicultural competence, into Korean for cross-cultural validation. An exploratory factor analysis followed by a confirmatory factor analysis on a sample of Korean counselors (N = 365) supported a 3-factor model: Multicultural Ability, Multicultural Knowledge, and Multicultural Awareness. The Korean version was deemed to possess sound psychometric properties, such as high test-retest reliability and criterion-related validity. Los autores tradujeron al idioma coreano la Escala Breve de Competencia Multicultural de California (CBMCS, por sus siglas en inglés; Gamst et al., 2004), un instrumento de medida de competencia multicultural, para su validación intercultural. Un análisis factorial exploratorio seguido de un análisis factorial confirmatorio sobre una muestra de consejeros coreanos (N = 365) respaldó un modelo de 3 factores: Habilidad Multicultural, Conocimiento Multicultural y Conciencia Multicultural. Se concluyó que la versión en coreano tenía propiedades psicométricas sólidas, como una alta fiabilidad de la repetición de las pruebas y una alta validez de criterio.     

“己之所欲”还是“成人之美”？解释水平视角下个体赠送-接受礼物的偏好不对称性

解释水平理论被广泛应用于消费研究领域。本研究以解释水平理论为理论基础,采用情境问卷调查方法,通过5个实验探讨个体赠送与接受礼物时是否存在性别和角色偏好的不对称性。结果发现,一般情境下,受性别因素影响,男生偏好赠送和接受工具性礼物,女生偏好赠送和接受表达性礼物。但随着心理距离（社会距离和空间距离）的拉近,个体的解释水平降低,更关心他人的喜好和需求,赠送者会更基于接收者的偏好进行礼物选择。     

Dimensions of fatigue in different working populations

Perceived fatigue related to work has often been measured in one dimension. The main purpose of the present study was to validate a proposed five-factor model of perceived fatigue in a new sample. 597 persons, employed in five occupations with different types of work loads, rated their fatigue after work. The ratings were subjected to analyses of linear structural equation models. The results suggest a slightly revised model for perceived fatigue, still with the five dimensions: Lack of energy, Physical exertion, Physical discomfort, Lack of motivation and Sleepiness. As expected, the rating profiles describing fatigue states differed between the five occupations. On the basis of these results, a revised version of the Swedish Occupational Fatigue Inventory (SOFI) is presented.     

A Multitrait–Multisource Confirmatory Factor Analytic Approach to the Construct Validity of ADHD and ODD Rating Scales with Malaysian Children

Confirmatory factor analysis (CFA) was used to model a multitrait by multisource matrix to determine the convergent and discriminant validity of measures of attention-deficit hyperactivity disorder (ADHD)-inattention (IN), ADHD-hyperactivity/impulsivity (HI), and oppositional defiant disorder (ODD) in 917 Malaysian elementary school children. The three trait factors were ADHD-IN, ADHD-HI, and ODD. The two source factors were parents and teachers. Similar to earlier studies with Australian and Brazilian children, the parent and teacher measures failed to show convergent and discriminant validity with Malaysian children. The study outlines the implications of such strong source effects in ADHD-IN, ADHD-HI, and ODD measures for the use of such parent and teacher scales to study the symptom dimensions.