Robust Mixed Model Analysis

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Robust Mixed Model Analysis

Jiang Jiming
Robust Mixed Model Analysis Book PDF

Author : Jiang Jiming
Publisher : World Scientific
Page : 268 pages
File Size : 41,5 Mb
Release : 2019-04-10
Category : Mathematics
ISBN : 9789814733854

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Robust Mixed Model Analysis by Jiang Jiming Pdf

Mixed-effects models have found broad applications in various fields. As a result, the interest in learning and using these models is rapidly growing. On the other hand, some of these models, such as the linear mixed models and generalized linear mixed models, are highly parametric, involving distributional assumptions that may not be satisfied in real-life problems. Therefore, it is important, from a practical standpoint, that the methods of inference about these models are robust to violation of model assumptions. Fortunately, there is a full scale of methods currently available that are robust in certain aspects. Learning about these methods is essential for the practice of mixed-effects models.This research monograph provides a comprehensive account of methods of mixed model analysis that are robust in various aspects, such as to violation of model assumptions, or to outliers. It is suitable as a reference book for a practitioner who uses the mixed-effects models, and a researcher who studies these models. It can also be treated as a graduate text for a course on mixed-effects models and their applications.

Mixed Effects Models for Complex Data

Lang Wu
Mixed Effects Models for Complex Data Book PDF

Author : Lang Wu
Publisher : CRC Press
Page : 431 pages
File Size : 41,9 Mb
Release : 2009-11-11
Category : Mathematics
ISBN : 1420074083

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Mixed Effects Models for Complex Data by Lang Wu Pdf

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 and Generalized Linear Mixed Models and Their Applications

Jiming Jiang
Linear and Generalized Linear Mixed Models and Their Applications Book PDF

Author : Jiming Jiang
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 55,5 Mb
Release : 2007-05-30
Category : Mathematics
ISBN : 9780387479460

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Linear and Generalized Linear Mixed Models and Their Applications by Jiming Jiang Pdf

This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.

Robust Statistics

Ricardo A. Maronna,R. Douglas Martin,Victor J. Yohai,Matías Salibián-Barrera
Robust Statistics Book PDF

Author : Ricardo A. Maronna,R. Douglas Martin,Victor J. Yohai,Matías Salibián-Barrera
Publisher : John Wiley & Sons
Page : 466 pages
File Size : 51,8 Mb
Release : 2019-01-04
Category : Mathematics
ISBN : 9781119214687

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Robust Statistics by Ricardo A. Maronna,R. Douglas Martin,Victor J. Yohai,Matías Salibián-Barrera Pdf

A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

Mixed Models

Eugene Demidenko
Mixed Models Book PDF

Author : Eugene Demidenko
Publisher : John Wiley & Sons
Page : 768 pages
File Size : 50,6 Mb
Release : 2013-08-05
Category : Mathematics
ISBN : 9781118091579

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Mixed Models by Eugene Demidenko Pdf

Praise for the First Edition “This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one’s personal library.” —Journal of the American Statistical Association Mixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. Mixed Models: Theory and Applications with R, Second Edition fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R. The new edition provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal data, modeling data with multiple sources of variation, modeling biological variety and heterogeneity, Healthy Akaike Information Criterion (HAIC), parameter multidimensionality, and statistics of image processing. Mixed Models: Theory and Applications with R, Second Edition features unique applications of mixed model methodology, as well as: Comprehensive theoretical discussions illustrated by examples and figures Over 300 exercises, end-of-section problems, updated data sets, and R subroutines Problems and extended projects requiring simulations in R intended to reinforce material Summaries of major results and general points of discussion at the end of each chapter Open problems in mixed modeling methodology, which can be used as the basis for research or PhD dissertations Ideal for graduate-level courses in mixed statistical modeling, the book is also an excellent reference for professionals in a range of fields, including cancer research, computer science, and engineering.

Doing Meta-Analysis with R

Mathias Harrer,Pim Cuijpers,Toshi A. Furukawa,David D. Ebert
Doing Meta Analysis with R Book PDF

Author : Mathias Harrer,Pim Cuijpers,Toshi A. Furukawa,David D. Ebert
Publisher : CRC Press
Page : 500 pages
File Size : 49,9 Mb
Release : 2021-09-15
Category : Mathematics
ISBN : 9781000435634

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Doing Meta-Analysis with R by Mathias Harrer,Pim Cuijpers,Toshi A. Furukawa,David D. Ebert Pdf

Doing Meta-Analysis with R: A Hands-On Guide serves as an accessible introduction on how meta-analyses can be conducted in R. Essential steps for meta-analysis are covered, including calculation and pooling of outcome measures, forest plots, heterogeneity diagnostics, subgroup analyses, meta-regression, methods to control for publication bias, risk of bias assessments and plotting tools. Advanced but highly relevant topics such as network meta-analysis, multi-three-level meta-analyses, Bayesian meta-analysis approaches and SEM meta-analysis are also covered. A companion R package, dmetar, is introduced at the beginning of the guide. It contains data sets and several helper functions for the meta and metafor package used in the guide. The programming and statistical background covered in the book are kept at a non-expert level, making the book widely accessible. Features • Contains two introductory chapters on how to set up an R environment and do basic imports/manipulations of meta-analysis data, including exercises • Describes statistical concepts clearly and concisely before applying them in R • Includes step-by-step guidance through the coding required to perform meta-analyses, and a companion R package for the book

Linear and Generalized Linear Mixed Models and Their Applications

Jiming Jiang,Thuan Nguyen
Linear and Generalized Linear Mixed Models and Their Applications Book PDF

Author : Jiming Jiang,Thuan Nguyen
Publisher : Springer Nature
Page : 343 pages
File Size : 46,6 Mb
Release : 2021-03-22
Category : Medical
ISBN : 9781071612828

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Linear and Generalized Linear Mixed Models and Their Applications by Jiming Jiang,Thuan Nguyen Pdf

This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.

Applied Mixed Model Analysis

Jos W. R. Twisk
Applied Mixed Model Analysis Book PDF

Author : Jos W. R. Twisk
Publisher : Cambridge University Press
Page : 249 pages
File Size : 50,5 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781108480574

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Applied Mixed Model Analysis by Jos W. R. Twisk Pdf

Emphasizing interpretation of results, this hands-on guide explains why, when, and how to use mixed models with your data.

Robust Methods in Biostatistics

Stephane Heritier,Eva Cantoni,Samuel Copt,Maria-Pia Victoria-Feser
Robust Methods in Biostatistics Book PDF

Author : Stephane Heritier,Eva Cantoni,Samuel Copt,Maria-Pia Victoria-Feser
Publisher : John Wiley & Sons
Page : 292 pages
File Size : 50,7 Mb
Release : 2009-05-11
Category : Medical
ISBN : 047074054X

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Robust Methods in Biostatistics by Stephane Heritier,Eva Cantoni,Samuel Copt,Maria-Pia Victoria-Feser Pdf

Robust statistics is an extension of classical statistics that specifically takes into account the concept that the underlying models used to describe data are only approximate. Its basic philosophy is to produce statistical procedures which are stable when the data do not exactly match the postulated models as it is the case for example with outliers. Robust Methods in Biostatistics proposes robust alternatives to common methods used in statistics in general and in biostatistics in particular and illustrates their use on many biomedical datasets. The methods introduced include robust estimation, testing, model selection, model check and diagnostics. They are developed for the following general classes of models: Linear regression Generalized linear models Linear mixed models Marginal longitudinal data models Cox survival analysis model The methods are introduced both at a theoretical and applied level within the framework of each general class of models, with a particular emphasis put on practical data analysis. This book is of particular use for research students,applied statisticians and practitioners in the health field interested in more stable statistical techniques. An accompanying website provides R code for computing all of the methods described, as well as for analyzing all the datasets used in the book.

Robust and Multivariate Statistical Methods

Mengxi Yi,Klaus Nordhausen
Robust and Multivariate Statistical Methods Book PDF

Author : Mengxi Yi,Klaus Nordhausen
Publisher : Springer Nature
Page : 500 pages
File Size : 55,8 Mb
Release : 2023-04-19
Category : Mathematics
ISBN : 9783031226878

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Robust and Multivariate Statistical Methods by Mengxi Yi,Klaus Nordhausen Pdf

This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler’s shape matrix.

Mixed Models

Eugene Demidenko
Mixed Models Book PDF

Author : Eugene Demidenko
Publisher : John Wiley & Sons
Page : 732 pages
File Size : 55,8 Mb
Release : 2005-01-28
Category : Mathematics
ISBN : 9780471726135

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Mixed Models by Eugene Demidenko Pdf

A rigorous, self-contained examination of mixed model theory and application Mixed modeling is one of the most promising and exciting areas of statistical analysis, enabling the analysis of nontraditional, clustered data that may come in the form of shapes or images. This book provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as applications such as the analysis of tumor regrowth, shape, and image. Paying special attention to algorithms and their implementations, the book discusses: Modeling of complex clustered or longitudinal data Modeling data with multiple sources of variation Modeling biological variety and heterogeneity Mixed model as a compromise between the frequentist and Bayesian approaches Mixed model for the penalized log-likelihood Healthy Akaike Information Criterion (HAIC) How to cope with parameter multidimensionality How to solve ill-posed problems including image reconstruction problems Modeling of ensemble shapes and images Statistics of image processing Major results and points of discussion at the end of each chapter along with "Summary Points" sections make this reference not only comprehensive but also highly accessible for professionals and students alike in a broad range of fields such as cancer research, computer science, engineering, and industry.

The Fence Methods

Jiang Jiming,Nguyen Thuan
The Fence Methods Book PDF

Author : Jiang Jiming,Nguyen Thuan
Publisher : World Scientific
Page : 248 pages
File Size : 48,9 Mb
Release : 2015-09-22
Category : Mathematics
ISBN : 9789814596084

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The Fence Methods by Jiang Jiming,Nguyen Thuan Pdf

This book is about a recently developed class of strategies, known as the fence methods, which fits particularly well in non-conventional and complex model selection problems with practical considerations. The idea involves a procedure to isolate a subgroup of what are known as correct models, of which the optimal model is a member. This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from amongst those within the fence according to a criterion which can be made flexible. In particular, the criterion of optimality can incorporate consideration of practical interest, thus making model selection a real life practice.Furthermore, this book introduces a data-driven approach, called adaptive fence, which can be used in a wide range of problems involving determination of tuning parameters, or constants. Instead of relying on asymptotic theory, the fence focuses on finite-sample performance, and computation. Such features are particularly suitable to statistics in the new era.

Generalized, Linear, and Mixed Models

Charles E. McCulloch,Shayle R. Searle,John M. Neuhaus
Generalized Linear and Mixed Models Book PDF

Author : Charles E. McCulloch,Shayle R. Searle,John M. Neuhaus
Publisher : John Wiley & Sons
Page : 281 pages
File Size : 42,7 Mb
Release : 2011-09-20
Category : Social Science
ISBN : 9781118209967

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Generalized, Linear, and Mixed Models by Charles E. McCulloch,Shayle R. Searle,John M. Neuhaus Pdf

An accessible and self-contained introduction to statistical models-now in a modernized new edition Generalized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various construction, application, and computational aspects. A clear introduction to the basic ideas of fixed effects models, random effects models, and mixed models is maintained throughout, and each chapter illustrates how these models are applicable in a wide array of contexts. In addition, a discussion of general methods for the analysis of such models is presented with an emphasis on the method of maximum likelihood for the estimation of parameters. The authors also provide comprehensive coverage of the latest statistical models for correlated, non-normally distributed data. Thoroughly updated to reflect the latest developments in the field, the Second Edition features: A new chapter that covers omitted covariates, incorrect random effects distribution, correlation of covariates and random effects, and robust variance estimation A new chapter that treats shared random effects models, latent class models, and properties of models A revised chapter on longitudinal data, which now includes a discussion of generalized linear models, modern advances in longitudinal data analysis, and the use between and within covariate decompositions Expanded coverage of marginal versus conditional models Numerous new and updated examples With its accessible style and wealth of illustrative exercises, Generalized, Linear, and Mixed Models, Second Edition is an ideal book for courses on generalized linear and mixed models at the upper-undergraduate and beginning-graduate levels. It also serves as a valuable reference for applied statisticians, industrial practitioners, and researchers.

Robust Statistics

Ricardo A. Maronna,R. Douglas Martin,Victor J. Yohai,Matías Salibián-Barrera
Robust Statistics Book PDF

Author : Ricardo A. Maronna,R. Douglas Martin,Victor J. Yohai,Matías Salibián-Barrera
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 41,9 Mb
Release : 2018-10-19
Category : Mathematics
ISBN : 9781119214663

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Robust Statistics by Ricardo A. Maronna,R. Douglas Martin,Victor J. Yohai,Matías Salibián-Barrera Pdf

A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

Methods and Applications of Longitudinal Data Analysis

Xian Liu
Methods and Applications of Longitudinal Data Analysis Book PDF

Author : Xian Liu
Publisher : Elsevier
Page : 530 pages
File Size : 46,9 Mb
Release : 2015-09-11
Category : Mathematics
ISBN : 9780128014820

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Methods and Applications of Longitudinal Data Analysis by Xian Liu Pdf

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.