MULTIPLE FACTOR ANALYSIS BY EXAMPLE USING R CHAPMAN HALL CRC THE R SERIES

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Multiple factor analysis (MFA) enables users to analyze tables of individuals and variables in which the variables are structured into quantitative, qualitative, or mixed groups. Written by the co-developer of this methodology, Multiple Factor Analysis by Example Using R brings together the theoretical and methodological aspects of MFA. It also includes examples of applications and details of how to implement MFA using an R package (FactoMineR). The first two chapters cover the basic factorial analysis methods of principal component analysis (PCA) and multiple correspondence analysis (MCA). The next chapter discusses factor analysis for mixed data (FAMD), a little-known method for simultaneously analyzing quantitative and qualitative variables without group distinction. Focusing on MFA, subsequent chapters examine the key points of MFA in the context of quantitative variables as well as qualitative and mixed data. The author also compares MFA and Procrustes analysis and presents a natural extension of MFA: hierarchical MFA (HMFA). The final chapter explores several elements of matrix calculation and metric spaces used in the book.

Full of real-world case studies and practical advice, Exploratory Multivariate Analysis by Example Using R, Second Edition focuses on four fundamental methods of multivariate exploratory data analysis that are most suitable for applications. It covers principal component analysis (PCA) when variables are quantitative, correspondence analysis (CA) and multiple correspondence analysis (MCA) when variables are categorical, and hierarchical cluster analysis. The authors take a geometric point of view that provides a unified vision for exploring multivariate data tables. Within this framework, they present the principles, indicators, and ways of representing and visualising objects that are common to the exploratory methods. The authors show how to use categorical variables in a PCA context in which variables are quantitative, how to handle more than two categorical variables in a CA context in which there are originally two variables, and how to add quantitative variables in an MCA context in which variables are categorical. They also illustrate the methods using examples from various fields, with related R code accessible in the FactoMineR package developed by the authors. The book has been written using minimal mathematics so as to appeal to applied statisticians, as well as researchers from various disciplines, including medical research and the social sciences. Readers can use the theory, examples, and software presented in this book in order to be fully equipped to tackle real-life multivariate data.

Author : Christopher D. Desjardins
ISBN : 9781351650304
Genre : Mathematics
File Size : 89.97 MB
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This book provides a broad overview of methods in educational and psychological measurement focusing on applications using R. It includes the key introductory topics and extends to recent research developments, such as multidimensional item response theory models. The focus is on the practical implementation of the methods, with lots of real data examples and R code integrated throughout. The book will be supplemented by an R package with all code and data available for replication. The book could be used as a supplementary text for the computing component of a course on measurement in either department.

Author : Daniel Mirman
ISBN : 9781315360331
Genre : Mathematics
File Size : 34.29 MB
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Learn How to Use Growth Curve Analysis with Your Time Course Data An increasingly prominent statistical tool in the behavioral sciences, multilevel regression offers a statistical framework for analyzing longitudinal or time course data. It also provides a way to quantify and analyze individual differences, such as developmental and neuropsychological, in the context of a model of the overall group effects. To harness the practical aspects of this useful tool, behavioral science researchers need a concise, accessible resource that explains how to implement these analysis methods. Growth Curve Analysis and Visualization Using R provides a practical, easy-to-understand guide to carrying out multilevel regression/growth curve analysis (GCA) of time course or longitudinal data in the behavioral sciences, particularly cognitive science, cognitive neuroscience, and psychology. With a minimum of statistical theory and technical jargon, the author focuses on the concrete issue of applying GCA to behavioral science data and individual differences. The book begins with discussing problems encountered when analyzing time course data, how to visualize time course data using the ggplot2 package, and how to format data for GCA and plotting. It then presents a conceptual overview of GCA and the core analysis syntax using the lme4 package and demonstrates how to plot model fits. The book describes how to deal with change over time that is not linear, how to structure random effects, how GCA and regression use categorical predictors, and how to conduct multiple simultaneous comparisons among different levels of a factor. It also compares the advantages and disadvantages of approaches to implementing logistic and quasi-logistic GCA and discusses how to use GCA to analyze individual differences as both fixed and random effects. The final chapter presents the code for all of the key examples along with samples demonstrating how to report GCA results. Throughout the book, R code illustrates how to implement the analyses and generate the graphs. Each chapter ends with exercises to test your understanding. The example datasets, code for solutions to the exercises, and supplemental code and examples are available on the author’s website.

Author : W. Holmes Finch
ISBN : 9781466515864
Genre : Mathematics
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A powerful tool for analyzing nested designs in a variety of fields, multilevel/hierarchical modeling allows researchers to account for data collected at multiple levels. Multilevel Modeling Using R provides you with a helpful guide to conducting multilevel data modeling using the R software environment. After reviewing standard linear models, the authors present the basics of multilevel models and explain how to fit these models using R. They then show how to employ multilevel modeling with longitudinal data and demonstrate the valuable graphical options in R. The book also describes models for categorical dependent variables in both single level and multilevel data. The book concludes with Bayesian fitting of multilevel models. For those new to R, the appendix provides an introduction to this system that covers basic R knowledge necessary to run the models in the book. Through the R code and detailed explanations provided, this book gives you the tools to launch your own investigations in multilevel modeling and gain insight into your research.

Author : I.T. Jolliffe
ISBN : 9781475719048
Genre : Mathematics
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Principal component analysis is probably the oldest and best known of the It was first introduced by Pearson (1901), techniques ofmultivariate analysis. and developed independently by Hotelling (1933). Like many multivariate methods, it was not widely used until the advent of electronic computers, but it is now weIl entrenched in virtually every statistical computer package. The central idea of principal component analysis is to reduce the dimen sionality of a data set in which there are a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. This reduction is achieved by transforming to a new set of variables, the principal components, which are uncorrelated, and which are ordered so that the first few retain most of the variation present in all of the original variables. Computation of the principal components reduces to the solution of an eigenvalue-eigenvector problem for a positive-semidefinite symmetrie matrix. Thus, the definition and computation of principal components are straightforward but, as will be seen, this apparently simple technique has a wide variety of different applications, as weIl as a number of different deri vations. Any feelings that principal component analysis is a narrow subject should soon be dispelled by the present book; indeed some quite broad topics which are related to principal component analysis receive no more than a brief mention in the final two chapters.

Author : Sebastien Le
ISBN : 9781466565739
Genre : Mathematics
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Choose the Proper Statistical Method for Your Sensory Data Issue Analyzing Sensory Data with R gives you the foundation to analyze and interpret sensory data. The book helps you find the most appropriate statistical method to tackle your sensory data issue. Covering quantitative, qualitative, and affective approaches, the book presents the big picture of sensory evaluation. Through an integrated approach that connects the different dimensions of sensory evaluation, you’ll understand: The reasons why sensory data are collected The ways in which the data are collected and analyzed The intrinsic meaning of the data The interpretation of the data analysis results Each chapter corresponds to one main sensory topic. The chapters start with presenting the nature of the sensory evaluation and its objectives, the sensory particularities related to the sensory evaluation, details about the data set obtained, and the statistical analyses required. Using real examples, the authors then illustrate step by step how the analyses are performed in R. The chapters conclude with variants and extensions of the methods that are related to the sensory task itself, the statistical methodology, or both.

Author : Julian J. Faraway
ISBN : 9781439887349
Genre : Mathematics
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A Hands-On Way to Learning Data Analysis Part of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition. New to the Second Edition Reorganized material on interpreting linear models, which distinguishes the main applications of prediction and explanation and introduces elementary notions of causality Additional topics, including QR decomposition, splines, additive models, Lasso, multiple imputation, and false discovery rates Extensive use of the ggplot2 graphics package in addition to base graphics Like its widely praised, best-selling predecessor, this edition combines statistics and R to seamlessly give a coherent exposition of the practice of linear modeling. The text offers up-to-date insight on essential data analysis topics, from estimation, inference, and prediction to missing data, factorial models, and block designs. Numerous examples illustrate how to apply the different methods using R.

Author : Bruno Falissard
ISBN : 9781439817674
Genre : Mathematics
File Size : 39.83 MB
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While theoretical statistics relies primarily on mathematics and hypothetical situations, statistical practice is a translation of a question formulated by a researcher into a series of variables linked by a statistical tool. As with written material, there are almost always differences between the meaning of the original text and translated text. Additionally, many versions can be suggested, each with their advantages and disadvantages. Analysis of Questionnaire Data with R translates certain classic research questions into statistical formulations. As indicated in the title, the syntax of these statistical formulations is based on the well-known R language, chosen for its popularity, simplicity, and power of its structure. Although syntax is vital, understanding the semantics is the real challenge of any good translation. In this book, the semantics of theoretical-to-practical translation emerges progressively from examples and experience, and occasionally from mathematical considerations. Sometimes the interpretation of a result is not clear, and there is no statistical tool really suited to the question at hand. Sometimes data sets contain errors, inconsistencies between answers, or missing data. More often, available statistical tools are not formally appropriate for the given situation, making it difficult to assess to what extent this slight inadequacy affects the interpretation of results. Analysis of Questionnaire Data with R tackles these and other common challenges in the practice of statistics.

Author : Kevin J Keen
ISBN : 9781584880875
Genre : Mathematics
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Graphics for Statistics and Data Analysis with R presents the basic principles of sound graphical design and applies these principles to engaging examples using the graphical functions available in R. It offers a wide array of graphical displays for the presentation of data, including modern tools for data visualization and representation. The book considers graphical displays of a single discrete variable, a single continuous variable, and then two or more of each of these. It includes displays and the R code for producing the displays for the dot chart, bar chart, pictographs, stemplot, boxplot, and variations on the quantile-quantile plot. The author discusses nonparametric and parametric density estimation, diagnostic plots for the simple linear regression model, polynomial regression, and locally weighted polynomial regression for producing a smooth curve through data on a scatterplot. The last chapter illustrates visualizing multivariate data with examples using Trellis graphics. Showing how to use graphics to display or summarize data, this text provides best practice guidelines for producing and choosing among graphical displays. It also covers the most effective graphing functions in R. R code is available for download on the book’s website.