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Changes in key odorants of shaken black tea (SBT) during its manufacture were determined using headspace solid-phase microextraction (HS-SPME) combined with comprehensive two-dimensional gas chromatography–time-of-flight mass spectrometry (GC × GC–TOFMS) and multivariate data analysis. A total of 241 volatiles was identified, comprising 49 aldehydes, 40 esters, 29 alcohols, 34 ketones, 30 aromatics, 24 alkenes, 17 alkanes, 13 furans, and 5 other compounds. A total of 27 volatiles had average relative odor activity values (rOAVs) greater than 1, among which (E)-β-ionone, (E,Z)-2,6-nonadienal, and 1-octen-3-one exhibited the highest values. According to the criteria of variable importance in projection (VIP) > 1, p < 0.05, and |log2FC| > 1, 61 discriminatory volatile compounds were screened out, of which 26 substances were shared in the shaking stage (FL vs. S1, S1 vs. S2, S2 vs. S3). The results of the orthogonal partial least squares discriminate analysis (OPLS-DA) differentiated the influence of shaking, fermentation, and drying processes on the formation of volatile compounds in SBT. In particular, (Z)-3-hexenol, (Z)-hexanoic acid, 3-hexenyl ester, (E)-β-farnesene, and indole mainly formed in the shaking stage, which promoted the formation of the floral and fruity flavor of black tea. This study enriches the basic theory of black tea flavor quality and provide the theoretical basis for the further development of aroma quality control.

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.

Consumers are increasingly interested in the characteristics of the products they consume, including aroma, taste, and appearance, and hence, scientific research was conducted in order to develop electronic senses devices that mimic the human senses. Thanks to the utilization of electroanalytical techniques that used various sensors modified with different electroactive materials coupled with pattern recognition methods, artificial senses such as electronic tongues (ETs) are widely applied in food analysis for quality and authenticity approaches. This paper summarizes the applications of electrochemical sensors (voltammetric, amperometric, and potentiometric) coupled with unsupervised and supervised pattern recognition methods (principal components analysis (PCA), linear discriminant analysis (LDA), partial least square (PLS) regression, artificial neural network (ANN)) for wine authenticity assessments including the discrimination of varietal and geographical origins, monitoring the ageing processes, vintage year discrimination, and detection of frauds and adulterations. Different wine electrochemical authentication methodologies covering the electrochemical techniques, electrodes types, functionalization sensitive materials and multivariate statistical analysis are emphasized and the main advantages and disadvantages of using the proposed methodologies for real applications were concluded.

This paper explores the innovative path of news dissemination based on multivariate data chain network, through the design and implementation of a multivariate data chain integrated planning system, to improve the transmission efficiency and accessibility of the data chain network, and then optimize the effect of news dissemination. The study designs a multivariate data chain integrated planning system, considering the constraints of delay and transmission, and uses Poisson distribution and queuing theory to analyze the access delay of the data chain. It is found that the access delay can be effectively reduced by controlling the generation and transmission process of data packets. Secondly, the C-RTT algorithm is proposed to optimize the synchronous time slot allocation in Link16 network, which is experimentally demonstrated to improve the time slot utilization by 1.64% to 6.57% and significantly increase the network capacity. Further, the multivariate datalink dissemination model outperforms the traditional news dissemination method regarding news content perception, environmental awareness, news reliability, and environmental behavioral intention. The application of multivariate data chain network has significant advantages in news dissemination and has substantial impacts on the development of news industry.

The technological advancements of the modern era have enabled the collection of huge amounts of data in science and beyond. Extracting useful information from such massive datasets is an ongoing challenge as traditional data visualization tools typically do not scale well in high-dimensional settings. An existing visualization technique that is particularly well suited to visualizing large datasets is the heatmap. Although heatmaps are extremely popular in fields such as bioinformatics, they remain a severely underutilized visualization tool in modern data analysis. This article introduces superheat, a new R package that provides an extremely flexible and customizable platform for visualizing complex datasets. Superheat produces attractive and extendable heatmaps to which the user can add a response variable as a scatterplot, model results as boxplots, correlation information as barplots, and more. The goal of this article is two-fold: (1) to demonstrate the potential of the heatmap as a core visualization method for a range of data types, and (2) to highlight the customizability and ease of implementation of the superheat R package for creating beautiful and extendable heatmaps. The capabilities and fundamental applicability of the superheat package will be explored via three reproducible case studies, each based on publicly available data sources.

Multivariate analysis of variance (MANOVA) is a powerful and versatile method to infer and quantify main and interaction effects in metric multivariate multi-factor data. It is, however, neither robust against change in units nor meaningful for ordinal data. Thus, we propose a novel nonparametric MANOVA. Contrary to existing rank-based procedures, we infer hypotheses formulated in terms of meaningful Mann–Whitney-type effects in lieu of distribution functions. The tests are based on a quadratic form in multivariate rank effect estimators, and critical values are obtained by bootstrap techniques. The newly developed procedures provide asymptotically exact and consistent inference for general models such as the nonparametric Behrens–Fisher problem and multivariate one-, two-, and higher-way crossed layouts. Computer simulations in small samples confirm the reliability of the developed method for ordinal and metric data with covariance heterogeneity. Finally, an analysis of a real data example illustrates the applicability and correct interpretation of the results.

[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.).

This article presents biplots derived from factor analysis of correlation matrices for both continuous and ordinal data. It introduces biplots specifically designed for factor analysis, detailing the geometric interpretation for each data type and providing an algorithm to compute biplot coordinates from the factorization of correlation matrices. The theoretical developments are illustrated using a real dataset that explores the relationship between volunteering, political ideology, and civic engagement in Spain.

This work is concerned with testing the population mean vector of nonnormal high-dimensional multivariate data. Several tests for high-dimensional mean vector, based on modifying the classical Hotelling T ² test, have been proposed in the literature. Despite their usefulness, they tend to have unsatisfactory power performance for heavy-tailed multivariate data, which frequently arise in genomics and quantitative finance. This article proposes a novel high-dimensional nonparametric test for the population mean vector for a general class of multivariate distributions. With the aid of new tools in modern probability theory, we proved that the limiting null distribution of the proposed test is normal under mild conditions when p is substantially larger than n . We further study the local power of the proposed test and compare its relative efficiency with a modified Hotelling T ² test for high-dimensional data. An interesting finding is that the newly proposed test can have even more substantial power gain with large p than the traditional nonparametric multivariate test does with finite fixed p . We study the finite sample performance of the proposed test via Monte Carlo simulations. We further illustrate its application by an empirical analysis of a genomics dataset. Supplementary materials for this article are available online.

A multivariate dataset consists of n cases in d dimensions, and is often stored in an n by d data matrix. It is well-known that real data may contain outliers. Depending on the situation, outliers may be (a) undesirable errors, which can adversely affect the data analysis, or (b) valuable nuggets of unexpected information. In statistics and data analysis, the word outlier usually refers to a row of the data matrix, and the methods to detect such outliers only work when at least half the rows are clean. But often many rows have a few contaminated cell values, which may not be visible by looking at each variable (column) separately. We propose the first method to detect deviating data cells in a multivariate sample which takes the correlations between the variables into account. It has no restriction on the number of clean rows, and can deal with high dimensions. Other advantages are that it provides predicted values of the outlying cells, while imputing missing values at the same time. We illustrate the method on several real datasets, where it uncovers more structure than found by purely columnwise methods or purely rowwise methods. The proposed method can help to diagnose why a certain row is outlying, for example, in process control. It also serves as an initial step for estimating multivariate location and scatter matrices.