Data analysis is a vital part of science today, and in assessing quality, multivariate analysis is often necessary in order to avoid loss of essential information. Martens provides a powerful and versatile methodology that enables researchers to design their investigations and analyse data effectively and safely, without the need for formal statistical training. * Offers an introductory explanation of multivariate analysis by graphical 'soft modelling' * Minimises mathematics, providing all technical details in the appendix * Presents itself in an accessible style with cartoons, self-assessment questions and a wide range of practical examples * Demonstrates the methodology for various types of quality assessment, ranging from human quality perception via industrial quality monitoring to environmental quality and its molecular basis All data sets available FREE online on "Chemometrics World" (http://www.wiley.co.uk/wileychi/chemometrics)
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.
Multivariate Analysis in the Pharmaceutical Industry provides industry practitioners with guidance on multivariate data methods and their applications over the lifecycle of a pharmaceutical product, from process development, to routine manufacturing, focusing on the challenges specific to each step. It includes an overview of regulatory guidance specific to the use of these methods, along with perspectives on the applications of these methods that allow for testing, monitoring and controlling products and processes. The book seeks to put multivariate analysis into a pharmaceutical context for the benefit of pharmaceutical practitioners, potential practitioners, managers and regulators. Users will find a resources that addresses an unmet need on how pharmaceutical industry professionals can extract value from data that is routinely collected on products and processes, especially as these techniques become more widely used, and ultimately, expected by regulators. Targets pharmaceutical industry practitioners and regulatory staff by addressing industry specific challenges Includes case studies from different pharmaceutical companies and across product lifecycle of to introduce readers to the breadth of applications Contains information on the current regulatory framework which will shape how multivariate analysis (MVA) is used in years to come
Applied statisticians often need to perform analyses of multivariate data; for these they will typically use one of the statistical software packages, S-Plus or R. This book sets out how to use these packages for these analyses in a concise and easy-to-use way, and will save users having to buy two books for the job. The author is well-known for this kind of book, and so buyers will trust that he’s got it right.
Praise for the Second Edition "This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere." —IIE Transactions Filled with new and timely content, Methods of Multivariate Analysis, Third Edition provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a "methods" approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. This Third Edition continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical procedures (including t-tests, analysis of variance, and multiple regression) to analogous multivariate techniques that involve several dependent variables. The latter half of the book describes statistical tools that are uniquely multivariate in nature, including procedures for discriminating among groups, characterizing low-dimensional latent structure in high-dimensional data, identifying clusters in data, and graphically illustrating relationships in low-dimensional space. In addition, the authors explore a wealth of newly added topics, including: Confirmatory Factor Analysis Classification Trees Dynamic Graphics Transformations to Normality Prediction for Multivariate Multiple Regression Kronecker Products and Vec Notation New exercises have been added throughout the book, allowing readers to test their comprehension of the presented material. Detailed appendices provide partial solutions as well as supplemental tables, and an accompanying FTP site features the book's data sets and related SAS® code. Requiring only a basic background in statistics, Methods of Multivariate Analysis, Third Edition is an excellent book for courses on multivariate analysis and applied statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for both statisticians and researchers across a wide variety of disciplines.
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.
Using formal descriptions, graphical illustrations, practical examples, and R software tools, Introduction to Multivariate Statistical Analysis in Chemometrics presents simple yet thorough explanations of the most important multivariate statistical methods for analyzing chemical data. It includes discussions of various statistical methods, such as principal component analysis, regression analysis, classification methods, and clustering. Written by a chemometrician and a statistician, the book reflects the practical approach of chemometrics and the more formally oriented one of statistics. To enable a better understanding of the statistical methods, the authors apply them to real data examples from chemistry. They also examine results of the different methods, comparing traditional approaches with their robust counterparts. In addition, the authors use the freely available R package to implement methods, encouraging readers to go through the examples and adapt the procedures to their own problems. Focusing on the practicality of the methods and the validity of the results, this book offers concise mathematical descriptions of many multivariate methods and employs graphical schemes to visualize key concepts. It effectively imparts a basic understanding of how to apply statistical methods to multivariate scientific data.
Multivariate Calibration Harald Martens, Chemist, Norwegian Food Research Institute, Aas, Norway and Norwegian Computing Center, Oslo, Norway Tormod Naes, Statistician, Norwegian Food Research Institute, Aas, Norway The aim of this inter-disciplinary book is to present an up-to-date view of multivariate calibration of analytical instruments, for use in research, development and routine laboratory and process operation. The book is intended to show practitioners in chemistry and technology how to extract the quantitative and understandable information embedded in non-selective, overwhelming and apparently useless measurements by multivariate data analysis. Multivariate calibration is the process of learning how to combine data from several channels, in order to overcome selectivity problems, gain new insight and allow automatic outlier detection. Multivariate calibration is the basis for the present success of high-speed Near-Infrared (NIR) diffuse spectroscopy of intact samples. But the technique is very general: it has shown similar advantages in, for instance, UV, Vis, and IR spectrophotometry, (transmittance, reflectance and fluorescence), for x-ray diffraction, NMR, MS, thermal analysis, chromatography (GC, HPLC) and for electrophoresis and image analysis (tomography, microscopy), as well as other techniques. The book is written at two levels: the main level is structured as a tutorial on the practical use of multivariate calibration techniques. It is intended for university courses and self-study for chemists and technologists, giving one complete and versatile approach, based mainly on data compression methodology in self-modelling PLS regression, with considerations of experimental design, data pre-processing and model validation. A second, more methodological, level is intended for statisticians and specialists in chemometrics. It compares several alternative calibration methods, validation approaches and ways to optimize the models. The book also outlines some cognitive changes needed in analytical chemistry, and suggests ways to overcome some communication problems between statistics and chemistry and technology.
'This book is a helpful guide to reading and understanding multivariate data analysis results in social and psychological research' --C. Y. Joanne Peng, Indiana University at Bloomington 'This book serves as a resource for readers who want to have an overall view of what encompasses multivariate analyses. The author has discussed some important issues rather philosophically (e.g., theory vs. data analysis). These points are valuable even for readers who have extensive training with multivariate analyses' --Jenn-Yun Tein, Arizona State University
With its focus on the practical application of the techniques of multivariate statistics, this book shapes the powerful tools of statistics for the specific needs of ecologists and makes statistics more applicable to their course of study. It gives readers a solid conceptual understanding of the role of multivariate statistics in ecological applications and the relationships among various techniques, while avoiding detailed mathematics and the underlying theory. More importantly, the reader will gain insight into the type of research questions best handled by each technique and the important considerations in applying them. Whether used as a textbook for specialised courses or as a supplement to general statistics texts, the book emphasises those techniques that students of ecology and natural resources most need to understand and employ in their research. While targeted for upper-division and graduate students in wildlife biology, forestry, and ecology, and for professional wildlife scientists and natural resource managers, this book will also be valuable to researchers in any of the biological sciences.
This classic book provides the much needed conceptual explanations of advanced computer-based multivariate data analysis techniques: correlation and regression analysis, factor analysis, discrimination analysis, cluster analysis, multi-dimensional scaling, perceptual mapping, and more. It closes the gap between spiraling technology and its intelligent application, fulfilling the potential of both.
Since 1975, The Analysis of Time Series: An Introduction has introduced legions of statistics students and researchers to the theory and practice of time series analysis. With each successive edition, bestselling author Chris Chatfield has honed and refined his presentation, updated the material to reflect advances in the field, and presented interesting new data sets. The sixth edition is no exception. It provides an accessible, comprehensive introduction to the theory and practice of time series analysis. The treatment covers a wide range of topics, including ARIMA probability models, forecasting methods, spectral analysis, linear systems, state-space models, and the Kalman filter. It also addresses nonlinear, multivariate, and long-memory models. The author has carefully updated each chapter, added new discussions, incorporated new datasets, and made those datasets available for download from www.crcpress.com. A free online appendix on time series analysis using R can be accessed at http://people.bath.ac.uk/mascc/TSA.usingR.doc. Highlights of the Sixth Edition: A new section on handling real data New discussion on prediction intervals A completely revised and restructured chapter on more advanced topics, with new material on the aggregation of time series, analyzing time series in finance, and discrete-valued time series A new chapter of examples and practical advice Thorough updates and revisions throughout the text that reflect recent developments and dramatic changes in computing practices over the last few years The analysis of time series can be a difficult topic, but as this book has demonstrated for two-and-a-half decades, it does not have to be daunting. The accessibility, polished presentation, and broad coverage of The Analysis of Time Series make it simply the best introduction to the subject available.
Using R with Multivariate Statistics by Randall E. Schumacker is a quick guide to using R, free-access software available for Windows and Mac operating systems that allows users to customize statistical analysis. Designed to serve as a companion to a more comprehensive text on multivariate statistics, this book helps students and researchers in the social and behavioral sciences get up to speed with using R. It provides data analysis examples, R code, computer output, and explanation of results for every multivariate statistical application included. In addition, R code for some of the data set examples used in more comprehensive texts is included, so students can run examples in R and compare results to those obtained using SAS, SPSS, or STATA. A unique feature of the book is the photographs and biographies of famous persons in the field of multivariate statistics.
Multivariate Statistical Simulation Mark E. Johnson For the researcher in statistics, probability, and operations research involved in the design and execution of a computer-aided simulation study utilizing continuous multivariate distributions, this book considers the properties of such distributions from a unique perspective. With enhancing graphics (three-dimensional and contour plots), it presents generation algorithms revealing features of the distribution undisclosed in preliminary algebraic manipulations. Well-known multivariate distributions covered include normal mixtures, elliptically assymmetric, Johnson translation, Khintine, and Burr-Pareto-logistic. 1987 (0 471-82290-6) 230 pp. Aspects of Multivariate Statistical Theory Robb J. Muirhead A classical mathematical treatment of the techniques, distributions, and inferences based on the multivariate normal distributions. The main focus is on distribution theory—both exact and asymptotic. Introduces three main areas of current activity overlooked or inadequately covered in existing texts: noncentral distribution theory, decision theoretic estimation of the parameters of a multivariate normal distribution, and the uses of spherical and elliptical distributions in multivariate analysis. 1982 (0 471-09442-0) 673 pp. Multivariate Observations G. A. F. Seber This up-to-date, comprehensive sourcebook treats data-oriented techniques and classical methods. It concerns the external analysis of differences among objects, and the internal analysis of how the variables measured relate to one another within objects. The scope ranges from the practical problems of graphically representing high dimensional data to the theoretical problems relating to matrices of random variables. 1984 (0 471-88104-X) 686 pp.
An introduction to geostatistics stressing the multivariate aspects for scientists, engineers and statisticians. The book presents a brief review of statistical concepts, a detailed introduction to linear geostatistics, and an account of three basic methods of multivariate analysis. Applications from very different areas of science, as well as exercises with solutions, are provided to help convey the general ideas. In this second edition, the chapters regarding normal kriging and cokriging have been restructured and the section on non-stationary geostatistics has been entirely rewritten.
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . . the wealth of material on statistics concerning the multivariate normal distribution is quite exceptional. As such it is a very useful source of information for the general statistician and a must for anyone wanting to penetrate deeper into the multivariate field." -Mededelingen van het Wiskundig Genootschap "This book is a comprehensive and clearly written text on multivariate analysis from a theoretical point of view." -The Statistician Aspects of Multivariate Statistical Theory presents a classical mathematical treatment of the techniques, distributions, and inferences based on multivariate normal distribution. Noncentral distribution theory, decision theoretic estimation of the parameters of a multivariate normal distribution, and the uses of spherical and elliptical distributions in multivariate analysis are introduced. Advances in multivariate analysis are discussed, including decision theory and robustness. The book also includes tables of percentage points of many of the standard likelihood statistics used in multivariate statistical procedures. This definitive resource provides in-depth discussion of the multivariate field and serves admirably as both a textbook and reference.
Get up-to-speed on the latest methods of multivariate statistics Multivariate statistical methods provide a powerful tool for analyzing data when observations are taken over a period of time on the same subject. With the advent of fast and efficient computers and the availability of computer packages such as S-plus and SAS, multivariate methods once too complex to tackle are now within reach of most researchers and data analysts. With an emphasis on computing techniques in combination with a full understanding of the mathematics behind the methods, Methods of Multivariate Statistics offers an up-to-date account of multivariate methods. Focusing on the maximum likelihood method for estimation, testing of hypotheses, and "profile analysis," this book offers comprehensive discussions of commonly encountered multivariate data and also covers some practical and important problems lacking in other texts. These include: * Missing at-random observations * "Growth Curve Models" and multivariate one-sided tests applicable in pharmaceutical and medical trials * Bootstrap methods * Principal component method for predicting a multivariate response vector * Outlier detection and handling inference when covariance is singular With clear chapter introductions and numerous problem sets, Methods of Multivariate Statistics meets every statistician's need for a comprehensive investigation of the latest methods in multivariate statistics.