Paulo Gomes

Power of Tests of Uniformity Defined on the Hypersphere

Abstract In multivariate data with n individuals described by p variables it is usual to assume that the variables are fixed and the individuals are randomly selected; in the present study we assume that the individuals are fixed and the previously normalised variables are randomly selected from a population of variables. When we want to associate to the sample of variables a distribution, like the Bingham distribution, it is important to use beforehand a test of uniformity. In this article, we compare the power of Bingham and Giné tests of uniformity for some dimensions of the sphere, vs. a Bingham population or a mixture of Bingham populations.

Discriminant analysis based on the Watson distribution defined on the hypersphere

The Watson distribution defined on the hypersphere is one of the most used distributions for modelling axial data. In this paper, we consider the discriminant analysis for axial data assumed to come from a mixture of Watson distributions defined on the hypersphere. We develop an optimal classification rule, which enables us to assign a new observation into one of several Watson subpopulations defined on the hypersphere. As the probabilities of misclassification cannot be calculated in closed form, we report on a simulation study to estimate, in some cases, the probabilities of misclassification and a distance between the two Watson subpopulations defined on the hypersphere. An illustration of our approach is provided using data defined on the sphere given in the literature.

Dream Teens: Adolescents-Led Participatory Project in Portugal in the Context of the Economic Recession

This article describes the implementation process of a nationwide project to enhance young people’s participation and active citizenship in the context of Portugal’s economic recession. This project used an innovative Positive Youth Development approach that engaged Portuguese youth (aged 11-18 years) through social media tools to facilitate their civic engagement and development. Participants from all over the country were empowered (1) to design and conduct research activities on topics of their choice and about their life contexts and (2) to create ways to improve youth civic participation in their communities, while developing supportive interactions with adults and peers. Overall, youth were engaged in their activities, felt their voices were heard, and felt that they were viewed as experts of their own well-being and living contexts. Youth research actions and preliminary findings were then compiled in a set of recommendations that was formally received by a high commissioner of the Ministry of Health. The article concludes with a discussion of the next steps for the project and its limitations so far.

Impact of Alienation on Portuguese Adolescentsâ Well-being

Objective: The present work aims to analyze the influence of alienation in different areas of adolescent health. Methods: The sample used was a group of adolescents that participated in the Portuguese survey of the European study Health Behaviour in School-aged Children (HBSC). The Portuguese survey included students from grades 6, 8 and 10 within the public education system, with an average age of 14 years (SD=1.85). The total sample of the HBSC study carried out in 2010 was of 5050. For this study, only adolescents from the 8th and 10th grades were included in the sample, comprising 3494 students. Results: The results show some health risks in adolescents with higher levels of social alienation. There is a positive association between social isolation and risk behaviours to adolescents’ health, such as bullying victims. The feeling of unsatisfaction with life seems to have a lot of influence to feelings of powerlessness, while the biggest association is between normlessness and relationship with family. Be satisfied with life and have a good relationship with family is important assets in adolescent mental health. Conclusion: These findings highlight the importance of further explore the influence that social alienation may have on the health of adolescents.

Discordancy Test for the Bipolar Watson Distribution Defined on the Hypersphere

ABSTRACT As the Watson distribution is much used for modeling axial data, it is important to investigate the existence of a possible outlier in samples from this distribution. So, we generalize to the hypersphere a test of discordancy of an outlier or several outliers en bloc available for the Watson distribution defined on the sphere. We also evaluate the performance of the test for some cases with the usual types of alternatives.

Responses to positive affect, life satisfaction and self-esteem: A cross-lagged panel analysis during middle adolescence

During middle adolescence, elevated stress and a greater presence of psychological disorders have been documented. The research has paid little attention to the regulation of positive affective states. Fredricksons broaden-and-build theory suggests that cultivating positive emotions helps to build resources that boost well-being. The current research aimed to examine the longitudinal associations between responses to positive affect (emotion-focused positive rumination, self-focused positive rumination, and dampening) and psychological adjustment (self-esteem and life satisfaction) during middle adolescence. A longitudinal study with two waves separated by one year was conducted, assessing 977 adolescents (M = 13.81, SD = 0.79; 51.5% boys) with self-report measures. A cross-lagged panel analysis was performed by including within the same model the relationships between all of the variables in the two assessment points. The results indicated cross-lagged positive relationships of self-focused positive rumination with both self-esteem and life satisfaction, while dampening showed a negative cross-lagged relationship with self-esteem. Moreover, higher self-esteem predicted more emotion-focused positive rumination, and more dampening predicted lower life satisfaction. Thus, the use of adaptive responses to positive affect and a better psychological adjustment were found to be prospectively interrelated at the one-year follow-up during middle adolescence. The discussion argues for the need to implement programmes to promote more adaptive responses to positive affect to enhance psychological adjustment in the adolescent transition to adulthood.

Clustering of Variables Based on Watson Distribution on Hypersphere: A Comparison of Algorithms

We consider n individuals described by p variables, represented by points of the surface of unit hypersphere. We suppose that the individuals are fixed and the set of variables comes from a mixture of bipolar Watson distributions. For the mixture identification, we use EM and dynamic clusters algorithms, which enable us to obtain a partition of the set of variables into clusters of variables. Our aim is to evaluate the clusters obtained in these algorithms, using measures of within-groups variability and between-groups variability and compare these clusters with those obtained in other clustering approaches, by analyzing simulated and real data.