Abstract

Abstract
When directional data fall in the positive orthant of the unit hypersphere, a folded directional distribution is preferred over a simple directional distribution for modeling the data. Since directional data, especially axial data, can be modeled using a Watson distribution, this paper considers a folded Watson distribution for such cases. We first address the parameter estimation of this distribution using maximum likelihood, which requires a numerical algorithm to solve the likelihood equations. We use the Expectation-Maximization (EM) algorithm to obtain these estimates and to analyze the properties of the concentration estimator through simulation. Next, we propose the Bayes rule for a folded Watson distribution and evaluate its performance through simulation in various scenarios, comparing it with the Bayes rule for the Watson distribution. Finally, we present examples using both simulated and real data available in the literature.

Abstract
We propose an approach to cluster and classify compositional data. We transform the compositional data into directional data using the square root transformation. To cluster the compositional data, we apply the identification of a mixture of Watson distributions on the hypersphere and to classify the compositional data into predefined groups, we apply Bayes rules based on the Watson distribution to the directional data. We then compare our clustering results with those obtained in hierarchical clustering and in the K-means clustering using the log-ratio transformations of the data and compare our classification results with those obtained in linear discriminant analysis using log-ratio transformations of the data. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

Abstract
Introduction: School lunches are essential in promoting a sustainable, healthy diet for children. However, students’ adherence in developed countries is modest. Objectives: A cross-sectional study with the objective of evaluating school lunch participation and exploring the factors influencing participation and its associations with sociodemographic characteristics, socioeconomic status, body weight, and adherence to the Mediterranean Dietary Pattern. Methodology: Baseline results from the R23 project, collected during the first five weeks of the 2022/23 school year, were used. In total, 806 students, aged 10–16 years, from the 2nd and 3rd cycles of basic education in Portugal, Benavente, participated in this study. Using a face-to-face structured questionnaire, students’ sociodemographic data, socioeconomic status, adherence to the Mediterranean Dietary Pattern, and school lunch participation were assessed. Daily school lunch participation was obtained via the school lunch booking service. Anthropometric measurements (weight, height and waist circumference) were performed on all students with signed consent forms. Results: The school lunch participation rate was 25.3%. Overall, 39.1% of students reported never attending the school canteen. Only 27% of the students eligible for Free or Reduced-Price Meals had an effective adherence to school lunch, and the non-participation rate in this group was 31%. Key barriers included living near to school and dissatisfaction with meal quality. Students' school lunch participation was significantly associated with age, grade, eligibility for Free or Reduced-Price Meals, and adherence to Mediterranean Dietary Pattern. Younger students and students eligible for Free or Reduced-Price Meals went to the canteen more often. While school lunch participation was positively and significantly associated with higher adherence to Mediterranean Dietary Pattern, no significant relationship was observed with body mass index or waist-to-height ratio. Students with greater adherence to Mediterranean Dietary Pattern displayed healthier body mass index and waist-to-height ratio. Conclusions: School lunch participation among adolescents was low, but increased participation was associated with higher adherence to the Mediterranean Dietary Pattern. These findings highlight the importance of school lunches in promoting healthier eating habits.

Abstract
Introduction: Together with sociodemographic and clinical features, locus of control and self-efficacy may impact the processes underlying changes in eating habits. Objectives: To study the relationships of sociodemographic and clinical characteristics, locus of control, general self-efficacy and eating self-efficacy with the perception of adherence to healthy eating among patients undergoing treatment for overweight. Methodology: A convenience sample of 74 overweight (BMI = 25.0 kg/m2) individuals (77.0% females, mean age = 41 years, SD = 11) attending nutrition consultations was studied regarding sociodemographic and clinical data, stages of change towards healthy eating, health locus of control (Health Locus of Control Scale), eating self-efficacy (General Eating Self-Efficacy Scale) and general self-efficacy (Self-Concept Clinical Inventory’s self-efficacy factor). Results: Approximately two-thirds (67.6%) of participants were in the “Action/Maintenance” stage towards healthy eating. In the total locus of control scale, general self-efficacy and eating self-efficacy, participants showed average scores slightly higher than the midpoint of the respective scales. In a binary logistic regression model, sociodemographic, clinical, locus of control and self-efficacy variables significantly predicted being in the action/maintenance stage towards healthy eating (p < 0.001; Nagelkerkle’s R2 = 48.4%). A higher proportion of weight loss (adjusted Exp(ß) = 1.074, p = 0.017) and higher eating self-efficacy (adjusted Exp(ß) = 1.317, p = 0.005) were significantly associated with higher odds of being in the “Action/Maintenance” stage. Conclusions: Most participants attending nutrition consultations to treat overweight considered following a healthy diet. Higher eating self-efficacy and greater weight loss associated to being in the “Action/Maintenance” stage towards healthy eating.

Abstract
Background/Objectives: Obesity is a major contributor to cardiovascular disease, yet traditional risk assessment methods may overlook behavioral and circadian influences that modulate metabolic health. Chronotype, physical activity, sleep quality, eating speed, and breakfast habits have been increasingly associated with cardiometabolic outcomes. This study aims to evaluate the associations between these behavioral factors and both anthropometric and biochemical markers of cardiovascular risk among obese candidates for bariatric surgery. Methods: A cross-sectional study was conducted in a sample of 286 obese adults (78.3% females, mean 44.3 years, SD = 10.8, mean BMI = 42.5 kg/m2, SD = 6.2) followed at a central Portuguese hospital. Chronotype (reduced Morningness-Eveningness Questionnaire), sleep quality (Pittsburgh Sleep Quality Index), physical activity (Godin-Shephard Questionnaire), eating speed, and breakfast skipping were assessed. Cardiovascular risk markers included waist-to-hip ratio (WHR), waist-to-height ratio, A Body Shape Index (ABSI), Body Roundness Index, atherogenic index of plasma (AIP), triglyceride-glucose index (TyG), and homeostatic model assessment for insulin resistance (HOMA-IR). Results: Men exhibited significantly higher WHR, ABSI, HOMA-IR, TyG, and AIP. Eveningness was associated with higher insulin (r = -0.168, p = 0.006) and HOMA-IR (r = -0.156, p = 0.011). Poor sleep quality was associated with higher body fat mass (r = 0.151, p = 0.013), total cholesterol (r = 0.169, p = 0.005) and LDL cholesterol (r = 0.132, p = 0.030). Faster eating speed was associated with a higher waist circumference (r = 0.123, p = 0.038) and skeletal muscle mass (r = 0.160, p = 0.009). Conclusions: Male sex, evening chronotype, and poor sleep quality were associated with more adverse cardiometabolic profiles in individuals with severe obesity. These findings support the integration of behavioral and circadian factors into cardiovascular risk assessment strategies.