Asymptotic Analysis Of Mixed Effects Models
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Asymptotic Analysis Of Mixed Effects Models
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Author : Jiming Jiang
language : en
Publisher: CRC Press
Release Date : 2017-09-19
Asymptotic Analysis Of Mixed Effects Models written by Jiming Jiang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with Mathematics categories.
Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis.
Mixed Effects Models For Complex Data
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Author : Lang Wu
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2009-11-11
Mixed Effects Models For Complex Data written by Lang Wu and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-11 with Mathematics categories.
Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.
Linear Mixed Effects Models Using R
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Author : Andrzej Gałecki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-05
Linear Mixed Effects Models Using R written by Andrzej Gałecki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-05 with Mathematics categories.
Linear mixed-effects models (LMMs) are an important class of statistical models that can be used to analyze correlated data. Such data are encountered in a variety of fields including biostatistics, public health, psychometrics, educational measurement, and sociology. This book aims to support a wide range of uses for the models by applied researchers in those and other fields by providing state-of-the-art descriptions of the implementation of LMMs in R. To help readers to get familiar with the features of the models and the details of carrying them out in R, the book includes a review of the most important theoretical concepts of the models. The presentation connects theory, software and applications. It is built up incrementally, starting with a summary of the concepts underlying simpler classes of linear models like the classical regression model, and carrying them forward to LMMs. A similar step-by-step approach is used to describe the R tools for LMMs. All the classes of linear models presented in the book are illustrated using real-life data. The book also introduces several novel R tools for LMMs, including new class of variance-covariance structure for random-effects, methods for influence diagnostics and for power calculations. They are included into an R package that should assist the readers in applying these and other methods presented in this text.
Robust Small Area Estimation
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Author : Jiming Jiang
language : en
Publisher: CRC Press
Release Date : 2025-08-20
Robust Small Area Estimation written by Jiming Jiang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-20 with Mathematics categories.
In recent years there has been substantial and growing interest in small area estimation (SAE) that is largely driven by practical demands. Here, the term "small area" typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain. Keywords in SAE are “borrowing strength”. Because there are insufficient samples from the small areas to produce reliable direct estimates, statistical methods are sought to utilize other sources of information to do better than the direct estimates. A typical way of borrowing strength is via statistical modelling. On the other hand, there is no “free lunch”. Yes, one can do better by borrowing strength, but there is a cost. This is the main topic discussed in this text. Features A comprehensive account of methods, applications, as well as some open problems related to robust SAE Methods illustrated by worked examples and case studies using real data Discusses some advanced topics including benchmarking, Bayesian approaches, machine learning methods, missing data, and classified mixed model prediction Supplemented with code and data via a website Robust Small Area Estimation: Methods, Applications, and Open Problems is primarily aimed at researchers and graduate students of statistics and data science and would also be suitable for geography and survey methodology researchers. The practical approach should help persuade practitioners, such as those in government agencies, to more readily adopt robust SAE methods. It could be used to teach a graduate-level course to students with a background in mathematical statistics.
Linear And Generalized Linear Mixed Models And Their Applications
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Author : Jiming Jiang
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-30
Linear And Generalized Linear Mixed Models And Their Applications written by Jiming Jiang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-30 with Mathematics categories.
Over the past decade there has been an explosion of developments in mixed e?ects models and their applications. This book concentrates on two major classes of mixed e?ects models, linear mixed models and generalized linear mixed models, with the intention of o?ering an up-to-date account of theory and methods in the analysis of these models as well as their applications in various ?elds. The ?rst two chapters are devoted to linear mixed models. We classify l- ear mixed models as Gaussian (linear) mixed models and non-Gaussian linear mixed models. There have been extensive studies in estimation in Gaussian mixed models as well as tests and con?dence intervals. On the other hand, the literature on non-Gaussian linear mixed models is much less extensive, partially because of the di?culties in inference about these models. However, non-Gaussian linear mixed models are important because, in practice, one is never certain that normality holds. This book o?ers a systematic approach to inference about non-Gaussian linear mixed models. In particular, it has included recently developed methods, such as partially observed information, iterative weighted least squares, and jackknife in the context of mixed models. Other new methods introduced in this book include goodness-of-?t tests, p- diction intervals, and mixed model selection. These are, of course, in addition to traditional topics such as maximum likelihood and restricted maximum likelihood in Gaussian mixed models.
Statistical Methods In Health Disparity Research
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Author : J. Sunil Rao
language : en
Publisher: CRC Press
Release Date : 2023-07-11
Statistical Methods In Health Disparity Research written by J. Sunil Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-11 with Medical categories.
A health disparity refers to a higher burden of illness, injury, disability, or mortality experienced by one group relative to others attributable to multiple factors including socioeconomic status, environmental factors, insufficient access to health care, individual risk factors, and behaviors and inequalities in education. These disparities may be due to many factors including age, income, and race. Statistical Methods in Health Disparity Research will focus on their estimation, ranging from classical approaches including the quantification of a disparity, to more formal modeling, to modern approaches involving more flexible computational approaches. Features: Presents an overview of methods and applications of health disparity estimation First book to synthesize research in this field in a unified statistical framework Covers classical approaches, and builds to more modern computational techniques Includes many worked examples and case studies using real data Discusses available software for estimation The book is designed primarily for researchers and graduate students in biostatistics, data science, and computer science. It will also be useful to many quantitative modelers in genetics, biology, sociology, and epidemiology.
Nonparametric Models For Longitudinal Data
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Author : Colin O. Wu
language : en
Publisher: CRC Press
Release Date : 2018-05-23
Nonparametric Models For Longitudinal Data written by Colin O. Wu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-23 with Mathematics categories.
Nonparametric Models for Longitudinal Data with Implementations in R presents a comprehensive summary of major advances in nonparametric models and smoothing methods with longitudinal data. It covers methods, theories, and applications that are particularly useful for biomedical studies in the era of big data and precision medicine. It also provides flexible tools to describe the temporal trends, covariate effects and correlation structures of repeated measurements in longitudinal data. This book is intended for graduate students in statistics, data scientists and statisticians in biomedical sciences and public health. As experts in this area, the authors present extensive materials that are balanced between theoretical and practical topics. The statistical applications in real-life examples lead into meaningful interpretations and inferences. Features: • Provides an overview of parametric and semiparametric methods • Shows smoothing methods for unstructured nonparametric models • Covers structured nonparametric models with time-varying coefficients • Discusses nonparametric shared-parameter and mixed-effects models • Presents nonparametric models for conditional distributions and functionals • Illustrates implementations using R software packages • Includes datasets and code in the authors’ website • Contains asymptotic results and theoretical derivations
Missing And Modified Data In Nonparametric Estimation
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Author : Sam Efromovich
language : en
Publisher: CRC Press
Release Date : 2018-03-12
Missing And Modified Data In Nonparametric Estimation written by Sam Efromovich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-12 with Mathematics categories.
This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.
Mixed Effects Models For The Population Approach
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Author : Marc Lavielle
language : en
Publisher: CRC Press
Release Date : 2014-07-14
Mixed Effects Models For The Population Approach written by Marc Lavielle and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
Wide-Ranging Coverage of Parametric Modeling in Linear and Nonlinear Mixed Effects Models Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools presents a rigorous framework for describing, implementing, and using mixed effects models. With these models, readers can perform parameter estimation and modeling across a whole population of individuals at the same time. Easy-to-Use Techniques and Tools for Real-World Data Modeling The book first shows how the framework allows model representation for different data types, including continuous, categorical, count, and time-to-event data. This leads to the use of generic methods, such as the stochastic approximation of the EM algorithm (SAEM), for modeling these diverse data types. The book also covers other essential methods, including Markov chain Monte Carlo (MCMC) and importance sampling techniques. The author uses publicly available software tools to illustrate modeling tasks. Methods are implemented in Monolix, and models are visually explored using Mlxplore and simulated using Simulx. Careful Balance of Mathematical Representation and Practical Implementation This book takes readers through the whole modeling process, from defining/creating a parametric model to performing tasks on the model using various mathematical methods. Statisticians and mathematicians will appreciate the rigorous representation of the models and theoretical properties of the methods while modelers will welcome the practical capabilities of the tools. The book is also useful for training and teaching in any field where population modeling occurs.
Multivariate Kernel Smoothing And Its Applications
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Author : José E. Chacón
language : en
Publisher: CRC Press
Release Date : 2018-05-08
Multivariate Kernel Smoothing And Its Applications written by José E. Chacón and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-08 with Mathematics categories.
Kernel smoothing has greatly evolved since its inception to become an essential methodology in the data science tool kit for the 21st century. Its widespread adoption is due to its fundamental role for multivariate exploratory data analysis, as well as the crucial role it plays in composite solutions to complex data challenges. Multivariate Kernel Smoothing and Its Applications offers a comprehensive overview of both aspects. It begins with a thorough exposition of the approaches to achieve the two basic goals of estimating probability density functions and their derivatives. The focus then turns to the applications of these approaches to more complex data analysis goals, many with a geometric/topological flavour, such as level set estimation, clustering (unsupervised learning), principal curves, and feature significance. Other topics, while not direct applications of density (derivative) estimation but sharing many commonalities with the previous settings, include classification (supervised learning), nearest neighbour estimation, and deconvolution for data observed with error. For a data scientist, each chapter contains illustrative Open data examples that are analysed by the most appropriate kernel smoothing method. The emphasis is always placed on an intuitive understanding of the data provided by the accompanying statistical visualisations. For a reader wishing to investigate further the details of their underlying statistical reasoning, a graduated exposition to a unified theoretical framework is provided. The algorithms for efficient software implementation are also discussed. José E. Chacón is an associate professor at the Department of Mathematics of the Universidad de Extremadura in Spain. Tarn Duong is a Senior Data Scientist for a start-up which provides short distance carpooling services in France. Both authors have made important contributions to kernel smoothing research over the last couple of decades.