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Chemometrics with R

Multivariate Data Analysis in the Natural and Life Sciences

This book offers readers an accessible introduction to the world of multivariate statistics in the life sciences, providing a comprehensive description of the general data analysis paradigm, from exploratory analysis (principal component analysis, self-organizing maps and clustering) to modeling (classification, regression) and validation (including variable selection). It also includes a special section discussing several more specific topics in the area of chemometrics, such as outlier detection, and biomarker identification. The corresponding R code is provided for all the examples in the book; and scripts, functions and data are available in a separate R package. This second revised edition features not only updates on many of the topics covered, but also several sections of new material (e.g., on handling missing values in PCA, multivariate process monitoring and batch correction).

This book offers readers an accessible introduction to the world of multivariate statistics in the life sciences, providing a comprehensive description of the general data analysis paradigm, from exploratory analysis (principal component ...

Multivariate Analysis of Ecological Data with ade4

This book introduces the ade4 package for R which provides multivariate methods for the analysis of ecological data. It is implemented around the mathematical concept of the duality diagram, and provides a unified framework for multivariate analysis. The authors offer a detailed presentation of the theoretical framework of the duality diagram and also of its application to real-world ecological problems. These two goals may seem contradictory, as they concern two separate groups of scientists, namely statisticians and ecologists. However, statistical ecology has become a scientific discipline of its own, and the good use of multivariate data analysis methods by ecologists implies a fair knowledge of the mathematical properties of these methods. The organization of the book is based on ecological questions, but these questions correspond to particular classes of data analysis methods. The first chapters present both usual and multiway data analysis methods. Further chapters are dedicated for example to the analysis of spatial data, of phylogenetic structures, and of biodiversity patterns. One chapter deals with multivariate data analysis graphs. In each chapter, the basic mathematical definitions of the methods and the outputs of the R functions available in ade4 are detailed in two different boxes. The text of the book itself can be read independently from these boxes. Thus the book offers the opportunity to find information about the ecological situation from which a question raises alongside the mathematical properties of methods that can be applied to answer this question, as well as the details of software outputs. Each example and all the graphs in this book come with executable R code.

Each example and all the graphs in this book come with executable R code. This book introduces the ade4 package for R which provides multivariate methods for the analysis of ecological data.

Discrete Multivariate Analysis

Theory and Practice

“A welcome addition to multivariate analysis. The discussion is lucid and very leisurely, excellently illustrated with applications drawn from a wide variety of fields. A good part of the book can be understood without very specialized statistical knowledge. It is a most welcome contribution to an interesting and lively subject.” -- Nature Originally published in 1974, this book is a reprint of a classic, still-valuable text.

Even a mediocre attempt to organize the extensive and widely scattered literature on discrete multivariate analysis would be welcome; happily, this is an excellent such effort, but a group of Harvard statisticians taht has contributed much ...

Multivariate Statistical Quality Control Using R

​​​​​The intensive use of automatic data acquisition system and the use of cloud computing for process monitoring have led to an increased occurrence of industrial processes that utilize statistical process control and capability analysis. These analyses are performed almost exclusively with multivariate methodologies. The aim of this Brief is to present the most important MSQC techniques developed in R language. The book is divided into two parts. The first part contains the basic R elements, an introduction to statistical procedures, and the main aspects related to Statistical Quality Control (SQC). The second part covers the construction of multivariate control charts, the calculation of Multivariate Capability Indices.

These analyses are performed almost exclusively with multivariate methodologies. The aim of this Brief is to present the most important MSQC techniques developed in R language. The book is divided into two parts.

Multivariate Statistics

Exercises and Solutions

The authors present tools and concepts of multivariate data analysis by means of exercises and their solutions. The first part is devoted to graphical techniques. The second part deals with multivariate random variables and presents the derivation of estimators and tests for various practical situations. The last part introduces a wide variety of exercises in applied multivariate data analysis. The book demonstrates the application of simple calculus and basic multivariate methods in real life situations. It contains altogether more than 250 solved exercises which can assist a university teacher in setting up a modern multivariate analysis course. All computer-based exercises are available in the R language. All data sets are included in the library SMSdata that may be downloaded via the quantlet download center www.quantlet.org. Data sets are available also via the Springer webpage. For interactive display of low-dimensional projections of a multivariate data set, we recommend GGobi.

The last part introduces a wide variety of exercises in applied multivariate data analysis. The book demonstrates the application of simple calculus and basic multivariate methods in real life situations.

Matrix-Based Introduction to Multivariate Data Analysis

This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively capture the purposes for which multivariate analysis procedures are utilized: plain explanations of the purposes with numerical examples precede mathematical descriptions in almost every chapter. This volume is appropriate for undergraduate students who already have studied introductory statistics. Graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis will also find the book useful, as it is based on modern matrix formulations with a special emphasis on singular value decomposition among theorems in matrix algebra. The book begins with an explanation of fundamental matrix operations and the matrix expressions of elementary statistics, followed by the introduction of popular multivariate procedures with advancing levels of matrix algebra chapter by chapter. This organization of the book allows readers without knowledge of matrices to deepen their understanding of multivariate data analysis.

This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms.

Multivariate Geostatistics

An Introduction with Applications

This fully revised third edition introduces geostatistics by emphasising the multivariate aspects for scientists, engineers and statisticians. Geostatistics offers a variety of models, methods and techniques for the analysis, estimation and display of multivariate data distributed in space or time. The text contains a brief review of statistical concepts, a detailed introduction to linear geostatistics, and an account of 3 basic methods of multivariate analysis. Applications from different areas of science, as well as exercises with solutions, are provided to help convey the general ideas. The introductory chapter has been divided into two separate sections for clarity. The final section deals with non-stationary geostatistics.

This book presents a brief review of statistical concepts, a detailed introduction to linear geostatistics, and an account of three methods of multivariate analysis.

Multivariate Nonparametric Methods with R

An approach based on spatial signs and ranks

This book offers a new, fairly efficient, and robust alternative to analyzing multivariate data.

Applied Multivariate Statistics with R

This book brings the power of multivariate statistics to graduate-level practitioners, making these analytical methods accessible without lengthy mathematical derivations. Using the open source, shareware program R, Professor Zelterman demonstrates the process and outcomes for a wide array of multivariate statistical applications. Chapters cover graphical displays, linear algebra, univariate, bivariate and multivariate normal distributions, factor methods, linear regression, discrimination and classification, clustering, time series models, and additional methods. Zelterman uses practical examples from diverse disciplines to welcome readers from a variety of academic specialties. Those with backgrounds in statistics will learn new methods while they review more familiar topics. Chapters include exercises, real data sets, and R implementations. The data are interesting, real-world topics, particularly from health and biology-related contexts. As an example of the approach, the text examines a sample from the Behavior Risk Factor Surveillance System, discussing both the shortcomings of the data as well as useful analyses. The text avoids theoretical derivations beyond those needed to fully appreciate the methods. Prior experience with R is not necessary.

This book brings the power of multivariate statistics to graduate-level practitioners, making these analytical methods accessible without lengthy mathematical derivations.

An Introduction to Applied Multivariate Analysis with R

The majority of data sets collected by researchers in all disciplines are multivariate, meaning that several measurements, observations, or recordings are taken on each of the units in the data set. These units might be human subjects, archaeological artifacts, countries, or a vast variety of other things. In a few cases, it may be sensible to isolate each variable and study it separately, but in most instances all the variables need to be examined simultaneously in order to fully grasp the structure and key features of the data. For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned. Multivariate analysis includes methods both for describing and exploring such data and for making formal inferences about them. The aim of all the techniques is, in general sense, to display or extract the signal in the data in the presence of noise and to find out what the data show us in the midst of their apparent chaos. An Introduction to Applied Multivariate Analysis with R explores the correct application of these methods so as to extract as much information as possible from the data at hand, particularly as some type of graphical representation, via the R software. Throughout the book, the authors give many examples of R code used to apply the multivariate techniques to multivariate data.

For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned.