1st Edition
Functional Data Analysis with R
Emerging technologies generate data sets of increased size and complexity that require new or updated statistical inferential methods and scalable, reproducible software. These data sets often involve measurements of a continuous underlying process, and benefit from a functional data perspective. Functional Data Analysis with R presents many ideas for handling functional data including dimension reduction techniques, smoothing, functional regression, structured decompositions of curves, and clustering. The idea is for the reader to be able to immediately reproduce the results in the book, implement these methods, and potentially design new methods and software that may be inspired by these approaches.
Features:
- Functional regression models receive a modern treatment that allows extensions to many practical scenarios and development of state-of-the-art software.
- The connection between functional regression, penalized smoothing, and mixed effects models is used as the cornerstone for inference.
- Multilevel, longitudinal, and structured functional data are discussed with emphasis on emerging functional data structures.
- Methods for clustering functional data before and after smoothing are discussed.
- Multiple new functional data sets with dense and sparse sampling designs from various application areas are presented, including the NHANES linked accelerometry and mortality data, COVID-19 mortality data, CD4 counts data, and the CONTENT child growth study.
- Step-by-step software implementations are included, along with a supplementary website (www.FunctionalDataAnalysis.com) featuring software, data, and tutorials.
- More than 100 plots for visualization of functional data are presented.
Functional Data Analysis with R is primarily aimed at undergraduate, master's, and PhD students, as well as data scientists and researchers working on functional data analysis. The book can be read at different levels and combines state-of-the-art software, methods, and inference. It can be used for self-learning, teaching, and research, and will particularly appeal to anyone who is interested in practical methods for hands-on, problem-forward functional data analysis. The reader should have some basic coding experience, but expertise in R is not required.
1. Basic Concepts
2. Key Methodological Concepts
3. Functional Principal Components Analysis
4. Scalar-on-Function Regression
5. Function-on-Scalar Regression
6. Function-on-Function Regression
7. Survival Analysis with Functional Predictors
8. Multilevel Functional Data Analysis
9. Clustering of Functional Data
Biography
Ciprian M. Crainiceanu is Professor of Biostatistics at Johns Hopkins University working on wearable and implantable technology (WIT), signal processing, and clinical neuroimaging. He has extensive experience in mixed effects modeling, semiparametric regression, and functional data analysis with application to data generated by emerging technologies.
Jeff Goldsmith is Associate Dean for Data Science and Associate Professor of Biostatistics at the Columbia University Mailman School of Public Health. His work in functional data analysis includes methodological and computational advances with applications in reaching kinematics, wearable devices, and neuroimaging.
Andrew Leroux is an Assistant Professor of Biostatistics and Informatics at the University of Colorado. His interests include the development of methodology in functional data analysis, particularly related to wearable technologies and intensive longitudinal data.
Erjia Cui is an Assistant Professor of Biostatistics at the University of Minnesota. His research interests include developing functional data analysis methods and semiparametric regression models with reproducible software, with applications in wearable devices, mobile health, and imaging.
“The book provides a modern treatment of Functional Data Analysis (FDA). It is written by accomplished experts who have published a large number of influential papers and have first-hand experience of analyzing complex data sets. It will be most useful for researchers and students wishing to focus on practical and correct application of FDA techniques. All methods are explained using nontrivial data sets a practitioner may encounter. Plentiful graphs are provided to facilitate understanding. The book contains useful treatments of subjects not covered in any other textbooks, including survival analysis with functional predictors, multilevel functional data and a self-contained, modern treatment of clustering methods. I highly recommend it to all researchers wishing to master state-of-the-art FDA methods, especially with a view toward applications in health sciences.”
~Piotr S. Kokoszka, Professor of Statistics, Colorado State University"This excellent monograph is firmly attached to the three pillars for progress in data analysis: (1) the mathematical framework, (2) data that are both interesting and abundant, and (3) the challenging task of developing the software that connects the math to the data. The historical material in the preface and bibliography is invaluable for appreciating the great advances in functional data analysis since the 2005 edition of the founding volume. A functional version linear regression analysis is the main focus of; and for a first read I would suggest, after visiting the four data sets in Chapter 1, then skipping to the scalar on function material in Chapter 4 and the function on function applications in Chapter 6. The book is indispensable for researchers and practitioners who work with functions as data objects."
~Jim Ramsay, McGill University"This book provides a good conceptual understanding of the various tools that are available for the analysis of functional data. At the same time, it is careful not to neglect the practical aspects of performing such analyses in practice. Without sacrificing mathematical rigor, the authors provide a comprehensive overview of the state of the art by taking the readers along with them on a pleasant walk through a series of applications to interesting and relevant data. The examples are accompanied by R code (with ample comments!) and plenty of informative graphical displays throughout. The pace is good and the topics are well organized. This would be a good comprehensive introduction for somebody new to functional data and a good reference for those already working in the area."
~Todd Ogden, Columbia University"Functional data, i.e., curves and surfaces indexed by continuous parameters, are increasingly common due to technological advances such as accelerometers and blood pressure monitors. This is a noteworthy book by authors who have contributed to the methodology of functional data analysis (FDA) and who have extensive experience with its applications. It is a valuable resource for statisticians, engineers, and data scientists working with functional data and an excellent introduction to R’s refund package. The book can serve as an excellent textbook for master’s courses in biostatistics and statistics departments. Data scientists will appreciate the numerous examples, many of them new and due to the authors. There are close connections between FDA and nonparametric function estimation, e.g., splines and other smoothing methods, and the book is also a valuable introduction to that topic. Readers should have a background in statistics including regression and multivariate analysis, e.g., principal components."
~David Ruppert, Cornell University
