Longitudinal Functional Data Analysis With Biomedical Applications
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Author | : Xian Liu |
Publisher | : Elsevier |
Total Pages | : 531 |
Release | : 2015-09-01 |
Genre | : Mathematics |
ISBN | : 0128014822 |
Methods and Applications of Longitudinal Data Analysis describes methods for the analysis of longitudinal data in the medical, biological and behavioral sciences. It introduces basic concepts and functions including a variety of regression models, and their practical applications across many areas of research. Statistical procedures featured within the text include: - descriptive methods for delineating trends over time - linear mixed regression models with both fixed and random effects - covariance pattern models on correlated errors - generalized estimating equations - nonlinear regression models for categorical repeated measurements - techniques for analyzing longitudinal data with non-ignorable missing observations Emphasis is given to applications of these methods, using substantial empirical illustrations, designed to help users of statistics better analyze and understand longitudinal data. Methods and Applications of Longitudinal Data Analysis equips both graduate students and professionals to confidently apply longitudinal data analysis to their particular discipline. It also provides a valuable reference source for applied statisticians, demographers and other quantitative methodologists. - From novice to professional: this book starts with the introduction of basic models and ends with the description of some of the most advanced models in longitudinal data analysis - Enables students to select the correct statistical methods to apply to their longitudinal data and avoid the pitfalls associated with incorrect selection - Identifies the limitations of classical repeated measures models and describes newly developed techniques, along with real-world examples.
Author | : Garrett Fitzmaurice |
Publisher | : CRC Press |
Total Pages | : 633 |
Release | : 2008-08-11 |
Genre | : Mathematics |
ISBN | : 142001157X |
Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory
Author | : James Ramsay |
Publisher | : Springer Science & Business Media |
Total Pages | : 213 |
Release | : 2009-06-29 |
Genre | : Computers |
ISBN | : 0387981853 |
The book provides an application-oriented overview of functional analysis, with extended and accessible presentations of key concepts such as spline basis functions, data smoothing, curve registration, functional linear models and dynamic systems Functional data analysis is put to work in a wide a range of applications, so that new problems are likely to find close analogues in this book The code in R and Matlab in the book has been designed to permit easy modification to adapt to new data structures and research problems
Author | : Hulin Wu |
Publisher | : John Wiley & Sons |
Total Pages | : 401 |
Release | : 2006-05-12 |
Genre | : Mathematics |
ISBN | : 0470009667 |
Incorporates mixed-effects modeling techniques for more powerful and efficient methods This book presents current and effective nonparametric regression techniques for longitudinal data analysis and systematically investigates the incorporation of mixed-effects modeling techniques into various nonparametric regression models. The authors emphasize modeling ideas and inference methodologies, although some theoretical results for the justification of the proposed methods are presented. With its logical structure and organization, beginning with basic principles, the text develops the foundation needed to master advanced principles and applications. Following a brief overview, data examples from biomedical research studies are presented and point to the need for nonparametric regression analysis approaches. Next, the authors review mixed-effects models and nonparametric regression models, which are the two key building blocks of the proposed modeling techniques. The core section of the book consists of four chapters dedicated to the major nonparametric regression methods: local polynomial, regression spline, smoothing spline, and penalized spline. The next two chapters extend these modeling techniques to semiparametric and time varying coefficient models for longitudinal data analysis. The final chapter examines discrete longitudinal data modeling and analysis. Each chapter concludes with a summary that highlights key points and also provides bibliographic notes that point to additional sources for further study. Examples of data analysis from biomedical research are used to illustrate the methodologies contained throughout the book. Technical proofs are presented in separate appendices. With its focus on solving problems, this is an excellent textbook for upper-level undergraduate and graduate courses in longitudinal data analysis. It is also recommended as a reference for biostatisticians and other theoretical and applied research statisticians with an interest in longitudinal data analysis. Not only do readers gain an understanding of the principles of various nonparametric regression methods, but they also gain a practical understanding of how to use the methods to tackle real-world problems.
Author | : Jorge Mateu |
Publisher | : John Wiley & Sons |
Total Pages | : 448 |
Release | : 2021-11-16 |
Genre | : Social Science |
ISBN | : 1119387884 |
Geostatistical Functional Data Analysis Explore the intersection between geostatistics and functional data analysis with this insightful new reference Geostatistical Functional Data Analysis presents a unified approach to modelling functional data when spatial and spatio-temporal correlations are present. The Editors link together the wide research areas of geostatistics and functional data analysis to provide the reader with a new area called geostatistical functional data analysis that will bring new insights and new open questions to researchers coming from both scientific fields. This book provides a complete and up-to-date account to deal with functional data that is spatially correlated, but also includes the most innovative developments in different open avenues in this field. Containing contributions from leading experts in the field, this practical guide provides readers with the necessary tools to employ and adapt classic statistical techniques to handle spatial regression. The book also includes: A thorough introduction to the spatial kriging methodology when working with functions A detailed exposition of more classical statistical techniques adapted to the functional case and extended to handle spatial correlations Practical discussions of ANOVA, regression, and clustering methods to explore spatial correlation in a collection of curves sampled in a region In-depth explorations of the similarities and differences between spatio-temporal data analysis and functional data analysis Aimed at mathematicians, statisticians, postgraduate students, and researchers involved in the analysis of functional and spatial data, Geostatistical Functional Data Analysis will also prove to be a powerful addition to the libraries of geoscientists, environmental scientists, and economists seeking insightful new knowledge and questions at the interface of geostatistics and functional data analysis.
Author | : Piotr Kokoszka |
Publisher | : CRC Press |
Total Pages | : 371 |
Release | : 2017-09-27 |
Genre | : Mathematics |
ISBN | : 1498746691 |
Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.
Author | : Lesa Hoffman |
Publisher | : Routledge |
Total Pages | : 655 |
Release | : 2015-01-30 |
Genre | : Psychology |
ISBN | : 1317591097 |
Longitudinal Analysis provides an accessible, application-oriented treatment of introductory and advanced linear models for within-person fluctuation and change. Organized by research design and data type, the text uses in-depth examples to provide a complete description of the model-building process. The core longitudinal models and their extensions are presented within a multilevel modeling framework, paying careful attention to the modeling concerns that are unique to longitudinal data. Written in a conversational style, the text provides verbal and visual interpretation of model equations to aid in their translation to empirical research results. Overviews and summaries, boldfaced key terms, and review questions will help readers synthesize the key concepts in each chapter. Written for non-mathematically-oriented readers, this text features: A description of the data manipulation steps required prior to model estimation so readers can more easily apply the steps to their own data An emphasis on how the terminology, interpretation, and estimation of familiar general linear models relates to those of more complex models for longitudinal data Integrated model comparisons, effect sizes, and statistical inference in each example to strengthen readers’ understanding of the overall model-building process Sample results sections for each example to provide useful templates for published reports Examples using both real and simulated data in the text, along with syntax and output for SPSS, SAS, STATA, and Mplus at www.PilesOfVariance.com to help readers apply the models to their own data The book opens with the building blocks of longitudinal analysis—general ideas, the general linear model for between-person analysis, and between- and within-person models for the variance and the options within repeated measures analysis of variance. Section 2 introduces unconditional longitudinal models including alternative covariance structure models to describe within-person fluctuation over time and random effects models for within-person change. Conditional longitudinal models are presented in section 3, including both time-invariant and time-varying predictors. Section 4 reviews advanced applications, including alternative metrics of time in accelerated longitudinal designs, three-level models for multiple dimensions of within-person time, the analysis of individuals in groups over time, and repeated measures designs not involving time. The book concludes with additional considerations and future directions, including an overview of sample size planning and other model extensions for non-normal outcomes and intensive longitudinal data. Class-tested at the University of Nebraska-Lincoln and in intensive summer workshops, this is an ideal text for graduate-level courses on longitudinal analysis or general multilevel modeling taught in psychology, human development and family studies, education, business, and other behavioral, social, and health sciences. The book’s accessible approach will also help those trying to learn on their own. Only familiarity with general linear models (regression, analysis of variance) is needed for this text.
Author | : Jason Newsom |
Publisher | : Routledge |
Total Pages | : 407 |
Release | : 2013-06-19 |
Genre | : Psychology |
ISBN | : 1136705473 |
This book provides accessible treatment to state-of-the-art approaches to analyzing longitudinal studies. Comprehensive coverage of the most popular analysis tools allows readers to pick and choose the techniques that best fit their research. The analyses are illustrated with examples from major longitudinal data sets including practical information about their content and design. Illustrations from popular software packages offer tips on how to interpret the results. Each chapter features suggested readings for additional study and a list of articles that further illustrate how to implement the analysis and report the results. Syntax examples for several software packages for each of the chapter examples are provided at www.psypress.com/longitudinal-data-analysis. Although many of the examples address health or social science questions related to aging, readers from other disciplines will find the analyses relevant to their work. In addition to demonstrating statistical analysis of longitudinal data, the book shows how to interpret and analyze the results within the context of the research design. The methods covered in this book are applicable to a range of applied problems including short- to long-term longitudinal studies using a range of sample sizes. The book provides non-technical, practical introductions to the concepts and issues relevant to longitudinal analysis. Topics include use of publicly available data sets, weighting and adjusting for complex sampling designs with longitudinal studies, missing data and attrition, measurement issues related to longitudinal research, the use of ANOVA and regression for average change over time, mediation analysis, growth curve models, basic and advanced structural equation models, and survival analysis. An ideal supplement for graduate level courses on data analysis and/or longitudinal modeling taught in psychology, gerontology, public health, human development, family studies, medicine, sociology, social work, and other behavioral, social, and health sciences, this multidisciplinary book will also appeal to researchers in these fields.
Author | : Ciprian M. Crainiceanu |
Publisher | : CRC Press |
Total Pages | : 338 |
Release | : 2024-03-11 |
Genre | : Mathematics |
ISBN | : 1003856306 |
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.
Author | : Livio Corain |
Publisher | : CRC Press |
Total Pages | : 337 |
Release | : 2017-09-20 |
Genre | : Mathematics |
ISBN | : 1315360462 |
Ranking of Multivariate Populations: A Permutation Approach with Applications presents a novel permutation-based nonparametric approach for ranking several multivariate populations. Using data collected from both experimental and observation studies, it covers some of the most useful designs widely applied in research and industry investigations, such as multivariate analysis of variance (MANOVA) and multivariate randomized complete block (MRCB) designs. The first section of the book introduces the topic of ranking multivariate populations by presenting the main theoretical ideas and an in-depth literature review. The second section discusses a large number of real case studies from four specific research areas: new product development in industry, perceived quality of the indoor environment, customer satisfaction, and cytological and histological analysis by image processing. A web-based nonparametric combination global ranking software is also described. Designed for practitioners and postgraduate students in statistics and the applied sciences, this application-oriented book offers a practical guide to the reliable global ranking of multivariate items, such as products, processes, and services, in terms of the performance of all investigated products/prototypes.