INFORMATION LOSS WHEN ρ IS APPLIED IN NON-NORMAL CASES

The correlation coefficient ρ of two stochastic variables underestimates the dependence between the variables, if they are not bivariately normally distributed. An information theoretical approach to the study of this underestimation is suggested. The method is applied on artificial data.     

Control and Responsibility: Taking a Closer Look at the Work of Ensuring Well-Being in Neoliberal Schools

This paper argues that the neo-liberal work of schooling includes a focus on producing subjectivities with a high level of well-being. This is done by drawing on evidence based therapeutic techniques that are adjusted to a school setting. These are termed ‘therapeutic socio-educational technologies. It is argued that these practices adhere to the neo-liberal logic of increased competition, standardization and testing, focusing on the individual child. There are a number of problems connected to these well-being enhancing technologies. These include the risk of producing passive and submissive subjectivities, that are understood as needing therapy by default; pathologizing the discomfort and struggles that are an inherent part of learning; the fragmentation of the child, focusing directly on the child rather than on the content matter at hand; producing an overly mechanic and technified pedagogy, focusing on output, as well as laying claim to much control in a risk-filled relational endeavor.     

Effects of action planning and coping planning within the theory of planned behaviour: A physical activity study of patients undergoing haemodialysis

Objective

Patients on dialysis have low physical activity levels. The aim of the study was to examine the validity of action planning and coping planning within the theory of planned behaviour framework, for predicting physical activity behaviour of patients on haemodialysis.

Design

This is a prospective study design.

Methods

One hundred and forty-four patients who were undergoing haemodialysis were selected from dialysis centres. The mean age of the patients was 56.61 (SD = 11.38) years. The patients completed a questionnaire including variables from the theory of planned behaviour, action planning and coping planning. Physical activity was prospectively assessed at 4-weeks with the validated International Physical Activity Questionnaire self-report measure. A hierarchical regression analysis was performed to examine the effects of action planning and coping planning on physical activity behaviour.

Results

There was a main effect for coping planning but not for action planning. Moreover, the analyses resulted in a significant amount of incremental variance accounted for by the interaction of coping planning and intention.

Conclusion

Results suggest the combination of high levels of coping planning and intention is associated with increases in physical activity.     

Personality in proportion: a bipolar proportional scale for personality assessments and its consequences for trait structure

Trait structures resulting from personality assessments on Likert scales are affected by the additive and multiplicative transformations implied in interval scaling and correlational analysis. The effect comes into view on selecting a plausible alternative scale. To this end, we propose a bipolar bounded scale ranging from -1 to +1 representing an underlying process in which the assessor would review and discount positive and negative behavioral instances of a trait. As an appropriate index of likeness between variables X and Y, we propose LXY = SigmaXY/N, the average of the raw scores cross products. Using this index, we carried out a raw scores principal component analysis on data consisting of 133 participants who had each been rated by 5 assessors including self on 914 items. Contrary to the Big-Five structure that was found in these data on standard analysis, the results showed a relatively large first principal component F1 and 2 very small ones, F2 and F3. The sizes LFF=SigmaF2/N, the averages of the squared component scores, were modest to small. It thus appears that the scale, bipolar proportional versus standard, has a profound impact on the size and structure of personality assessments. The dissimilarity remains on analyzing self-ratings rather than averaged (over the 5 assessors) ratings.     

Quantitative genetic analysis of latent growth curve models of cognitive abilities in adulthood

Though many cognitive abilities exhibit marked decline over the adult years, individual differences in rates of change have been observed. In the current study, biometrical latent growth models were used to examine sources of variability for ability level (intercept) and change (linear and quadratic effects) for verbal, fluid, memory, and perceptual speed abilities in the Swedish Adoption/Twin Study of Aging. Genetic influences were more important for ability level at age 65 and quadratic change than for linear slope at age 65. Expected variance components indicated decreasing genetic and increasing nonshared environmental variation over age. Exceptions included one verbal and two memory measures that showed increasing genetic and nonshared environmental variance. The present findings provide support for theories of the increasing influence of the environment with age on cognitive abilities.     

Retrieving the correlation matrix from a truncated PCA solution: The inverse principal component problem

Whenr Principal Components are available fork variables, the correlation matrix is approximated in the least squares sense by the loading matrix times its transpose. The approximation is generally not perfect unlessr =k. In the present paper it is shown that, whenr is at or above the Ledermann bound,r principal components are enough to perfectly reconstruct the correlation matrix, albeit in a way more involved than taking the loading matrix times its transpose. In certain cases just below the Ledermann bound, recovery of the correlation matrix is still possible when the set of all eigenvalues of the correlation matrix is available as additional information.     

A case of extreme simplicity of the core matrix in three-mode principal components analysis

In three-mode Principal Components Analysis, theP ×Q ×R core matrixG can be transformed to simple structure before it is interpreted. It is well-known that, whenP=QR,G can be transformed to the identity matrix, which implies that all elements become equal to values specified a priori. In the present paper it is shown that, whenP=QR − 1,G can be transformed to have nearly all elements equal to values spectified a priori. A cllsed-form solution for this transformation is offered. Theoretical and practical implications of this simple structure transformation ofG are discussed. Constructive comments from anonymous reviewers are gratefully acknowledged.     

The Genetic and Environmental Relationship Between General and Specific Cognitive Abilities in Twins Age 80 and Older

In the first twin study of the old-old, individuals 80 years old and older, we examined the relationship between general and specific cognitive abilities from a genetic perspective. That is, we examined the extent to which genetic and environmental factors influence major group factors of cognitive abilities, independent of general cognitive ability. As part of the OctoTwin project in Sweden, general and specific cognitive abilities were assessed in 52 monozygotic and 65 same-sex dizygotic twin pairs 80 years old and older using a battery of seven tests that assess verbal, spatial, speed-of-processing, and memory performance. Results suggest that genetic effects associated with general cognitive ability ( g ) account for the correlation between g and verbal, spatial, and speed-of-processing abilities. No genetic influences were found for these specific cognitive abilities separate from g . In contrast, memory ability appears to be more distinct genetically from g than are other cognitive abilities. Comparison with younger samples suggests that cognitive abilities relating to speed of processing may be genetically dedifferentiated in the old-old.     

A series of lower bounds to the reliability of a test

Two well-known lower bounds to the reliability in classical test theory, Guttman's ₂ and Cronbach's coefficient alpha, are shown to be terms of an infinite series of lower bounds. All terms of this series are equal to the reliability if and only if the test is composed of items which are essentially tau-equivalent. Some practical examples, comparing the first 7 terms of the series, are offered. It appears that the second term (₂) is generally worth-while computing as an improvement of the first term (alpha) whereas going beyond the second term is not worth the computational effort. Possibly an exception should be made for very short tests having widely spread absolute values of covariances between items. The relationship of the series and previous work on lower bound estimates for the reliability is briefly discussed.The authors are obliged to Henk Camstra for providing a computer program that was used in this study.     

Orthogonal procrustes rotation for two or more matrices

Necessary and sufficient conditions for rotating matrices to maximal agreement in the least-squares sense are discussed. A theorem by Fischer and Roppert, which solves the case of two matrices, is given a more straightforward proof. A sufficient condition for a best least-squares fit for more than two matrices is formulated and shown to be not necessary. In addition, necessary conditions suggested by Kristof and Wingersky are shown to be not sufficient. A rotation procedure that is an alternative to the one by Kristof and Wingersky is presented. Upper bounds are derived for determining the extent to which the procedure falls short of attaining the best least-squares fit. The problem of scaling matrices to maximal agreement is discussed. Modifications of Gower's method of generalized Procrustes analysis are suggested.