By Hulin Wu
Accommodates mixed-effects modeling thoughts for extra robust and effective methodsThis ebook provides present and powerful nonparametric regression concepts for longitudinal information research and systematically investigates the incorporation of mixed-effects modeling suggestions into quite a few nonparametric regression versions. The authors emphasize modeling principles and inference methodologies, even supposing a few theoretical effects for the justification of the proposed tools are presented.With its logical constitution and association, starting with easy rules, the textual content develops the basis had to grasp complex rules and purposes. Following a quick evaluation, info examples from biomedical examine reports are offered and element to the necessity for nonparametric regression research ways. subsequent, the authors overview mixed-effects types and nonparametric regression versions, that are the 2 key construction blocks of the proposed modeling techniques.The center component to the publication includes 4 chapters devoted to the key nonparametric regression tools: neighborhood polynomial, regression spline, smoothing spline, and penalized spline. the subsequent chapters expand those modeling concepts to semiparametric and time various coefficient versions for longitudinal info research. the ultimate bankruptcy examines discrete longitudinal information modeling and analysis.Each bankruptcy concludes with a precis that highlights key issues and likewise offers bibliographic notes that time to extra assets for additional examine. Examples of information research from biomedical study are used to demonstrate the methodologies contained through the book.Technical proofs are provided in separate appendices.With its specialise in fixing difficulties, this is often an outstanding textbook for upper-level undergraduate and graduate classes in longitudinal information research. it's also steered as a reference for biostatisticians and different theoretical and utilized examine statisticians with an curiosity in longitudinal info research. not just do readers achieve an figuring out of the rules of assorted nonparametric regression equipment, yet additionally they achieve a pragmatic knowing of ways to take advantage of the the right way to take on real-world difficulties.
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Additional resources for Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effects Modeling Approaches
There is a vast amount of recent literature in this research area, and it is impossible for us to have an exhaustive list here. The importance of nonparametric modeling methods has been recognized in longitudinal data analysis and for practical applications, since nonparametric methods are flexible and robust against parametric assumptions. Such flexibility is useful for exploration and analysis of longitudinal data, when appropriate parametric models are unavailable. In this book, we do not intend to cover all nonparametric regression techniques.
2 Fundamental Development of the NPME Models Fundamental developments of the NPME modeling techniques will be presented in Chapters 4-7, and each chapter covers one popular nonparametric method. These are the core contents of this book and lay a good foundation for further extensions of the NPME models. Each of these chapters will also provide a review for the nonparametric population mean (NPM) model and naive smoothing methods before the mixed-effects modeling approach is introduced. In Chapter 4, we will mainly investigate local polynomial mixed-effects models after a review of the NPM model and the local polynomial kernel-based generalized estimating equations (LPK-GEE) methods.
Here y(s, t ) quantifies the bctween-subject variation while the ~ ‘ ( quantifies t) the within-subject variation. , v ( t ) GP(0, y), and t GP(0, y6). ~ - - - - SCOPE OF THE BOOK I1 Under the NPME modeling framework, we need to accomplish the following tasks: (1) to estimate the fixed-effect (population mean) function ~ ( t (2) ) ; to predict the random-effect functions v i ( t )and individual functions s i ( t ) = ~ ( t )vi(t), i = 1 , 2 , . . ,n; (3) to estimate the covariance function y(s, t ) ;and (4) to estimate the noise variance function a'(t).