Consistency measures for pairwise comparison matrices

We propose new measures of consistency of additive and multiplicative pairwise comparison matrices. These measures, the relative consistency and relative error, are easy to compute and have clear and simple algebraic and geometric meaning, interpretation and properties. The correspondence between these measures in the additive and multiplicative cases reflects the same correspondence which underpins the algebraic structure of the problem and relates naturally to the corresponding optimization models and axiom systems. The relative consistency and relative error are related to one another by the theorem of Pythagoras through the decomposition of comparison matrices into their consistent and error components. One of the conclusions of our analysis is that inconsistency is not a sufficient reason for revision of judgements. © 1998 John Wiley & Sons, Ltd.     

Flourishing students: A longitudinal study on positive emotions,personal resources,and study engagement

The aim of this two-wave questionnaire study with a 4-week interval among 391 Dutch university students was to test a gain cycle of positive emotions, personal resources, and study engagement. As a theoretical basis, this study drew on the broaden-and-build (B&B) theory and the conservation of resources (COR) theory. More specifically, it was hypothesized that the experience of positive emotions predicts students’ future personal resources and study engagement. Moreover, it was expected that there is a longitudinal relationship between personal resources and study engagement. Furthermore, we hypothesized that positive emotions, personal resources, and study engagement are reciprocally related. Results, obtained by means of structural equation modeling, confirmed both causal (except for the positive relationship between positive emotions and study engagement) and reciprocal hypotheses, thereby successfully integrating the B&B theory with the COR theory.     

Evoking children's spirituality in the reciprocal relationships of a learning community

Findings from my doctoral research suggest that the reciprocal relationships within a learning community can evoke and nurture children's spirituality. The study investigated the development of a community of learners in four primary school classrooms in Aotearoa New Zealand. A key finding of this study showed that when teachers and children learned together, shared decisions, and respected and trusted one another, changes were observed in some children that could not be explained in intellectual, social or emotional terms. Further analyses of these data revealed qualities that pointed to a spiritual essence. This paper presents these spiritually themed results and explores the argument that the caring, responsive and reciprocal relationships of a community of learners can provide opportunities for spiritual development.     

Savouring and perceived job performance in positive psychology: Moderating role of positive affectivity

Building on the research in positive psychology, the current study examines the impact of employee savouring on building perceived job performance and tested the extent to which an individual positive affectivity moderated the relationship of savouring and job performance. Using survey responses from 357 salespeople in six Taiwanese insurance companies, the results of hierarchical regression analyses show that savouring is positively related to perceived job performance. In addition, the relationship between savouring and perceived job performance was moderated by employees' positive affectivity. The implications of these results and the limitations of the research are discussed.     

Piecewise method of reciprocal averages for dual scaling of multiple-choice data

The proposed method handles the classical method of reciprocal averages (MRA) in a piecewise (item-by-item) mode, whereby one can deal with smaller matrices and attain faster convergence to a solution than the MRA. A new concept the principle of constant proportionality is introduced to provide an interesting interpretation for scaling multiple-choice data a la Guttman. A small example is presented for discussion of the technique.This study was supported by the Natural Sciences and Engineering Research Council Canada Grant (No. A4581) to S. Nishisato. The authors are indebted to reviewers for valuable comments.     

Computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis

In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.The authors are obliged to Charles Lewis and Dirk Knol for helpful comments, and to Frank Brokken and Henk Camstra for developing computer programs.     

Processing fluency,positive affect,and judgments of meaning in life

This study examined the effects of processing ease on judgments of meaning in life (MIL), employing a common manipulation of fluency, font styles. One hundred and three adults completed a questionnaire assessing MIL with items printed in one of four fonts that differed in readability. We predicted that those who rated MIL items printed in easy-to-read fonts would report higher MIL than those who rated items presented in difficult-to-read fonts. Participants also completed a measure of the proposed mechanism for these effects, positive affect (PA). Results showed that, as predicted, easy reading led to higher MIL than difficult reading and these effects were explained by PA. Results not only extend the influence of processing fluency to such profound judgments as life’s meaningfulness, but also lend further support to the very strong role of PA in judgments of MIL.     

Gender differences in the person-activity fit for positive psychology interventions

Research on positive psychology interventions (PPIs) has established the value of activities such as acts of kindness, gratitude, and savoring life’s joys, for increasing individuals’ sense of well-being. Critical to the efficacy of PPIs is person-activity fit – the degree activities stem from intrinsic motivation. Although person-activity fit effects are well documented, gaps remain in our understanding of how sociodemographic variables, particularly age and gender, play a role. We investigated how gender may affect self-reported person-activity fit across three PPIs: A gratitude journal; Acts of Kindness; and Savoring life’s joys. Age was explored since the subject sample ranged widely, from 18 to 51?years. Twenty-eight men and 82 women completed person-activity fit questionnaires. A multiple analysis of variance resulted in a main effect for gender, with women showing greater person-activity fit for all three PPIs. Among women only, age correlated significantly with person-activity fit for all three PPIs, suggesting greater maturational variability among men.     

In search of durable positive psychology interventions: Predictors and consequences of long-term positive behavior change

A number of positive psychology interventions have successfully helped people learn skills for improving mood and building personal resources (e.g., psychological resilience and social support). However, little is known about whether intervention activities remain effective in the long term, or whether new resources are maintained after the intervention ends. We address these issues in a 15-month follow-up survey of participants from a loving-kindness meditation intervention. Many participants continued to practice meditation, and they reported more positive emotions (PEs) than those who had stopped meditating or had never meditated. All participants maintained gains in resources made during the initial intervention, whether or not they continued meditating. Continuing meditators did not differ on resources at baseline, but they did show more PE and a more rapid PE response to the intervention. Overall, our results suggest that positive psychology interventions are not just efficacious but of significant value in participants’ real lives.     

New developments in emotion regulation with an emphasis on the positive spectrum of human functioning

There is converging evidence from several psychological fields on the ways in which individuals engage in specific strategies to modify, alter, or accept their emotional experiences to obtain more desirable outcomes. The current Special Issue is dedicated to a series of examinations on how these self-regulatory strategies can promote resilience, create and sustain positive moods and intrinsic motivation, and aid in the repair of different negative emotions. The content of these articles are briefly reviewed in the context of additional ideas for scientific advancements in understanding and developing positive health.     

Happy thoughts: Enhancing well-being in the classroom with a positive events diary

Positive psychology interventions (PPIs) are effective in increasing well-being across the population. Whilst educators are recognising the importance of well-being in the classroom and of its long-term impact on life trajectory, the transformative potential of PPIs in educational settings is yet to be fully realised. This study investigates, for the first time, the effects of a PPI in school children by means of a daily dairy. Self-report questionnaires were used to measure well-being in school children aged 8–11 years. Across two studies, children kept a positive events diary, recording three experiences every day for a week. The intervention led to an increase in happiness and a decrease in depressive symptoms immediately following the intervention and at a three-month follow-up. Children who had unhappier baseline scores benefitted more from the intervention. This study demonstrates significant scope, in school settings, for targeted light-touch interventions to promote well-being in those with the greatest need.     

Concurrent disjoint and reciprocal classification by Cebus apella in seriation tasks: evidence for hierarchical organization

We report the results of a 4-year-long study of capuchin monkeys (Cebus apella ) on concurrent three-way classification and linear size seriation tasks using explicit ordering procedures, requiring subjects to select icons displayed on touch screens rather than manipulate and sort actual objects into groups. The results indicate that C. apella is competent to classify nine items concurrently, first into three disjoint classes where class exemplars are identical to one another, then into three reciprocal classes which share common exemplar (size) features. In the final phase we compare the relative efficiency of executive control under conditions where both hierarchical and/or linear organization can be utilized. Whilst this shows a superiority of categorical based size seriation for a nine item test set suggesting an adaptive advantage for hierarchical over linear organization, Cebus nevertheless achieved high levels of principled linear size seriation with sequence lengths not normally achieved by children below the age of six years.     

The rowwise correlation between two proximity matrices and the partial rowwise correlation

This paper discusses rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, which may both be square (symmetric or asymmetric) or rectangular. Using the correlation coefficients usually associated with Pearson, Spearman, and Kendall, three different rowwise test statistics and their normalized coefficients are discussed, and subsequently compared with their nonrowwise alternatives like Mantel'sZ. It is shown that the rowwise matrix correlation coefficient between two matricesX andY is the partial correlation between the entries ofX andY controlled for the nominal variable that has the row objects as categories. Given this fact, partial rowwise correlations (as well as multiple regression extensions in the case of Pearson's approach) can be easily developed.The author wishes to thank the Editor, two referees, Jan van Hooff, and Ruud Derix for their useful comments, and E. J. Dietz for a copy of the algorithm of the Mantel permutation test.     

The approximation of two-mode proximity matrices by sums of order-constrained matrices

A least-squares strategy is proposed for representing a two-mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries. The primary class of constraints considered define Q-forms (or anti-Q-forms) for a two-mode matrix, where after suitable and separate row and column reorderings, the entries within each row and within each column are nondecreasing (or nonincreasing) to a maximum (or minimum) and thereafter nonincreasing (or nondecreasing). Several other types of order constraints are also mentioned to show how alternative structures can be considered using the same computational strategy.     

Complaining about a compliment: Evaluating attributions of positive outcomes to discrimination

People evaluate stigmatized group members negatively when they attribute negative personal outcomes to discrimination, even when discrimination is the likely cause. The present studies examined whether similar interpersonal costs exist for attributing a positive personal outcome to discrimination in the context of positive stereotypes. In Study 1, 129 participants read an excerpt written by an Asian student who attributed an unexpectedly high essay grade to discrimination, writing quality, or easy grading. Participants evaluated the student least favourably when he attributed the positive outcome to discrimination. In Study 2, 140 participants evaluated a successful Asian job applicant less favourably than a successful, white applicant, although both applicants attributed the positive outcome to group membership. The implications for how stigmatized group members perceive and respond to prejudice and discrimination are discussed.     

The time course of positive and negative emotion in dysphoria

Prior research has demonstrated attenuated reactivity to positive stimuli among depressed and dysphoric individuals, and inconsistent evidence regarding attenuated reactivity to negative stimuli. However, such research has measured experiential reactivity to emotion stimuli in one static moment, which may obscure important information regarding the time course and dynamics of emotion. The current study employed continuous measurement of experiential emotion during and following the presentation of emotion eliciting film clips. Results revealed that dysphoric individuals (n = 16), as compared to nondysphoric controls (n = 31), were equally responsive to positive and negative film clips in terms of peak reactivity during and following the clip. The most striking difference between groups was that dysphoric individuals showed a shortened time course of positive emotion. These emotion dynamics suggest that perhaps the most important aspect of positive emotion regulation in the context of depressed mood is not the inability to initially react to a positive experience, but rather the inability to maintain positive emotion. Possible underlying mechanisms of positive emotion regulation are discussed, and implications for intervention are highlighted.     

The independence of positive and negative affect depends on the affect measure

This study examined the degree of independence between Positive Affect (PA) and Negative Affect (NA) within a given situation. The affective state was measured before and after an experimentally induced success or failure experience in an anagram task. Two types of affect measures were used to assess PA and NA: the Positive and Negative Affect Schedule (PANAS) and a Pleasantness-Unpleasantness scale. Consistent with our hypotheses, results show that PA and NA are independent when measured with the PANAS but are correlated when assessed with the other scale. These PA-NA correlations differed significantly from each other before and after emotion induction, respectively. Additional analyses indicate that both PA scales are differentially sensitive to the mood induction procedure. The findings are discussed with respect to circumplex models of emotion.     

An evaluation of positive psychology intervention effectiveness trials using the re-aim framework: A practice-friendly review

Meta-analyses indicate the efficacy of positive psychology interventions in promoting well-being. But, despite accumulating empirical and anecdotal evidence of these interventions’ implementation in real-world settings, no review of effectiveness research exists. Accordingly, we identified 40 positive psychology intervention effectiveness trials targeting adults, and scored their reporting using the practice-friendly RE-AIM tool which assesses five dimensions of intervention utility: Reach, Efficacy, Adoption, Implementation and Maintenance. Reporting levels varied substantially: reporting on Reach scored 64%; Efficacy scored 73%; Adoption scored 84%; Implementation scored 58%; and Maintenance scored 16%. Within these five dimensions, reporting on participation rates, methods to select delivery agents, differences between participants and non-participants, programme maintenance and costs, was particularly sparse. The studies involved 10,664 participants, approximately half required specialist delivery, and 12 were researcher delivered. To maximize the potential of PPIs for population health promotion, expanded reporting on effectiveness trials is required. Recommendations to assist this process are offered.     

Sensitivity analysis in factor analysis: Difference between using covariance and correlation matrices

Influence curves of some parameters under various methods of factor analysis have been given in the literature. These influence curves depend on the influence curves for either the covariance or the correlation matrix used in the analysis. The differences between the influence curves based on the covariance and the correlation matrices are derived in this paper. Simple formulas for the differences of the influence curves, based on the two matrices, for the unique variance matrix, factor loadings and some other parameter are obtained under scale-invariant estimation methods, though the influence curves themselves are in complex forms.The authors are most grateful to the referees, the Associate Editor, the Editor and Raymond Lam for helpful suggestions for improving the clarity of the paper.