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A data depth can be used to measure the \"depth\" or \"outlyingness\" of a given multivariate sample with respect to its underlying distribution. This leads to a natural center-outward ordering of the sample points. Based on this ordering, quantitative and graphical methods are introduced for analyzing multivariate distributional characteristics such as location, scale, bias, skewness and kurtosis, as well as for comparing inference methods. All graphs are one-dimensional curves in the plane and can be easily visualized and interpreted. A \"sunburst plot\" is presented as a bivariate generalization of the box-plot. DD-(depth versus depth) plots are proposed and examined as graphical inference tools. Some new diagnostic tools for checking multivariate normality are introduced. One of them monitors the exact rate of growth of the maximum deviation from the mean, while the others examine the ratio of the overall dispersion to the dispersion of a certain central region. The affine invariance property of a data depth also leads to appropriate invariance properties for the proposed statistics and methods.

[This book] reviews the basic concepts and applications of SEM using Mplus Version 6. ... The first two chapters introduce the fundamental concepts of SEM and important basics of the Mplus program. The remaining chapters focus on SEM applications and include a variety of SEM models presented within the context of three sections: Single-group analyses, Multiple-group analyses, and other important topics, the latter of which includes the multitrait-multimethod, latent growth curve, and multilevel models. (DIPF/Orig.).

A reference guide for applications of SEM using Mplus Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a flexible tool to analyze their data with an easy-to-use interface and graphical displays of data and analysis results. Key features: Presents a useful reference guide for applications of SEM whilst systematically demonstrating various advanced SEM models, such as multi-group and mixture models using Mplus. Discusses and demonstrates various SEM models using both cross-sectional and longitudinal data with both continuous and categorical outcomes. Provides step-by-step instructions of model specification and estimation, as well as detail interpretation of Mplus results. Explores different methods for sample size estimate and statistical power analysis for SEM. By following the examples provided in this book, readers will be able to build their own SEM models using Mplus. Teachers, graduate students, and researchers in social sciences and health studies will also benefit from this book.

HighlightsConsumers demand the purchase of fortified dairy products.Instrumental (color, texture) and sensorial attributes are critical tests for novel food.Almond milk has high nutritional value with unique textural and sensorial properties.Almond milk is an innovative and attractive additive in probiotic yogurt.In this study, the effect of almond milk addition on color, texture and sensory attributes of probiotic yogurt was investigated. The data generated in combination with instrumental (color and texture parameters) and sensory measurements was analysed statistically to describe a product’s attributes scientifically. Statistical analysis illustrated that almond milk rate and storage time had a significant (P < 0.05) effect on the color and textural parameters of yogurt. Compared with the sensorial parameters, generally there were statistically significant differences among samples, whereas insignificant effect was determined among storage days. The results of descriptive statistics (Principle Component and Hierarchical Cluster Analysis) indicated that the relationships among the analysed attributes were determined. In addition, statistical data has demonstrated that almond milk may be used as a novel and functional ingredient in both industrial and research areas for development, innovation, quality, and safety of dairy products.

Does land security matter in climate change adaptation strategies choice? To provide answers to this, the paper used a survey data collected from a random sample of 341 agricultural households in 2020 in Benin. Descriptive statistics and multivariate probit model were used to analyze the data. The main adaptations strategies identified are adjustment in sowing time, tree planting, crop and livestock integration, use of irrigation, use of improved variety, and endogenous beliefs, while family land, own land and rented land are the types of land tenure arrangements. Results from a multivariate probit model show that the use of family land increases the likelihood of planting tree, crop and livestock integration, use of improved variety, and endogenous beliefs. Farmers using own land are more likely to adopt tree planting and endogenous beliefs as adaptation strategies, while they are less likely to adopt irrigation. The use of rented land increases the likelihood of adjusting the sowing time, crop and livestock integration, use of irrigation, use of improved variety, and use of endogenous beliefs. These findings suggest that the choice of adaptation strategies to cope with climate change depends on the type of land tenure arrangements.

Meta-analysis is widely used to synthesize the results of multiple studies. Although meta-analysis is traditionally carried out by combining the summary statistics of relevant studies, advances in technologies and communications have made it increasingly feasible to access the original data on individual participants. In the present paper, we investigate the relative efficiency of analyzing original data versus combining summary statistics. We show that, for all commonly used parametric and semiparametric models, there is no asymptotic efficiency gain by analyzing original data if the parameter of main interest has a common value across studies, the nuisance parameters have distinct values among studies, and the summary statistics are based on maximum likelihood. We also assess the relative efficiency of the two methods when the parameter of main interest has different values among studies or when there are common nuisance parameters across studies. We conduct simulation studies to confirm the theoretical results and provide empirical comparisons from a genetic association study.

The objective of this research is to investigate whether particular occasions, such as Australia Day and Christmas Day, have a notable impact on water demand in the Greater Sydney region. By examining water demand during these events, the study aims to enhance understanding of water consumption patterns and contribute to the development of effective demand management strategies. Multivariate time series data from several water plants in the Greater Sydney region were analyzed using three methods: correlation heatmaps, t-tests, and descriptive statistics. The findings indicate that neither Australia Day nor Christmas Day has a significant impact on water demand at different water plants in the Greater Sydney region. These results suggest that public holidays may not need to be a critical factor in short-term water demand forecasting models for this area.

The study shows how the statistical approach can provide information on the factors and processes that control the geochemical distribution of elements at the surface of an abandoned tailings pond. In this regard, the case study of a waste deposit resulting from the ore processing plant of Fundu Moldovei was carried out. The facility was concentrating Cu, Pb, and Zn from the polymetallic sulfide ores of the Fundu Moldovei—Leșu Ursului mining district (Romania). The statistics indicate three types of waste, showing specific properties: (i) Waste of the beach, rich in soluble fraction (14.4%) and secondary minerals (e.g., jarosite, ferricopiapite, magnesiocopiapite, pickeringite, and clay minerals). The latter and the related high contents of Al, K, Fe, Co, Ni, Cu, Pb, and Zn are controlled by the water evaporation and subsequent transient pH (2.6–3.5) of the leachates accumulated as puddles. The lower pH and scarce soluble fraction favor a rise in the Cu and Zn contents, while Al, K, Fe, and Co are noticeable at a higher pH when the soluble fraction is abundant. (ii) Waste of the upper dam slope, marked by intense oxidation and a meager occurrence of secondary minerals precipitated from highly acidic pore leachates (average pH of 2.55), namely, jarosite, ferricopiapite, magnesiocopiapite, and coquimbite. The surface waste contains more pyrite and is coarser because of the fine particle removal during rainfall. Unlike the beach waste, in the upper dam tailings, Al, K, Fe, Co, Cu, Pb, and Zn seem to relate mainly to the primary minerals (muscovite, chlorite, and pyrite). (iii) Downslope dam waste is less acidic (average pH of 3.75) than that of the upper slope; it contains secondary minerals stable at a higher pH (e.g., gypsum, apjohnite, dietrichite, clay minerals, and schwertmannite). Calcium, Mn, and Cd are more abundant in the dam waste. They originate from both primary and secondary minerals (e.g., muscovite, chlorite, gypsum, ferricopiapite, and magnesiocopiapite) and correlate with the coarser waste.

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.

Purpose Survivors of cancer during young adulthood face multiple psychosocial challenges following treatment. This study explores psychosocial distress and unmet needs among young adult survivors treated of hematological malignancies. Methods A total of 85 young adults aged between 18 and 39 years at time of diagnosis, were invited to join the survey after the completion of treatment with curative intent. Sociodemographic data and the need for advice were gathered with a self-report questionnaire. A set of standardized questionnaires for quality of life (EORTC QLQ-C30), psychosocial stressors (PHQ-S), fear of progression (PA-F-KF), cancer-related fatigue (EORTC QLQ-FA12), and symptoms of anxiety (GAD-7) or depression (PHQ-9) was employed. Descriptive statistics and multivariate analysis were conducted. Results Forty-seven young adult cancer survivors responded. A quarter of patients (26%) reported depressive symptoms, 15% suffered from anxiety, 36% from fear of progression, and 21% reported increased psychosocial stressors. They had a lower QoL than the general population and reported poorer outcomes on all single-item and multi-symptom scales. Employment was significantly associated with lower levels of psychosocial distress, anxiety, fatigue, and better QoL. Conclusion Young adult cancer survivors exhibited a high disposition for psychosocial distress. They reported excessive demands in everyday life and resumption of work. However, a longitudinal study of young adult cancer survivors is needed to confirm the results of this pilot study. In future, psycho-oncological and social support need to become an inherent part of the aftercare of survivors of young adult cancer survivors.