Sparse Simultaneous Penalized Variable Selection In Hierarchical Structure Genetic Data Analysis

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Sparse Simultaneous Penalized Variable Selection in Hierarchical Structure Genetic Data Analysis

Author : Shuang Huang
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (12 download)

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Book Synopsis Sparse Simultaneous Penalized Variable Selection in Hierarchical Structure Genetic Data Analysis by : Shuang Huang

Download or read book Sparse Simultaneous Penalized Variable Selection in Hierarchical Structure Genetic Data Analysis written by Shuang Huang and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sparse simultaneous penalized variable selection method for data with hierarchical structure is proposed to identify the quantitative trait loci and expression traits that are related to certain clinical trait in genetic data analysis. This method is developed for data sets in which the dependency is linear, and among a large number of gene loci and expression traits candidates, relatively few are important to the interested clinical trait. The method focuses on identifying the candidates in genome set and expression traits that are significantly related to clinical observation via the hierarchical dependence structure. A penalized linear model is used to reduce the number of parameters, using a novel computational algorithm that can handle the unknowns simultaneously. A data-adaptive tuning procedure based on cross validation acts as a parameter selector. Simulation studies are conducted to check the performance of the proposed method, and to compare with some well developed methods, including several penalized methods and Step AIC method. The real data application is done on a data set from an obesity study. The data set contains 541 mice, and for each individual, over 1,000 expression traits and around 1,000 gene loci are recorded. We compare the finding of our method with previous studies on the same species of mice and the similarity and difference of the outcomes are discussed.

High-dimensional Variable Selection in Longitudinal and Nonlinear Gene-environment Interaction Studies

Author : Fei Zhou
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (131 download)

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Book Synopsis High-dimensional Variable Selection in Longitudinal and Nonlinear Gene-environment Interaction Studies by : Fei Zhou

Download or read book High-dimensional Variable Selection in Longitudinal and Nonlinear Gene-environment Interaction Studies written by Fei Zhou and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection from both the frequentist and Bayesian frameworks has gained increasing popularity in the analysis of high-dimensional genomic data. Despite the success of existing studies, challenges still remain as tailored methods for sparse interaction structures are not available when the response variables are repeatedly measured and/or have heavy-tailed distributions. These challenges have motivated the development of novel variable selection methods proposed in the following projects. Meanwhile, powerful software packages from these projects are publically available to facilitate fast and reliable computation, as well as reproducible research. In the first project, we have developed a novel penalized variable selection method to identify important lipid-environment interactions in a longitudinal lipidomics study, where the environment factors refer to a group of dummy variables corresponding to a four-level treatment factor. An efficient Newton-Raphson based algorithm was proposed within the generalized estimating equation (GEE) framework. Simulation studies have demonstrated the superior performance of our method over alternatives, in terms of both identification accuracy and prediction performance. Analysis of the high-dimensional lipid datasets collected using mice from the skin cancer prevention study identified meaningful markers that provide fresh insight into the underlying mechanism of cancer preventive effects. In the second project, we have proposed a sparse group penalization method for the bi-level GxE interaction study under the repeatedly measured phenotype to accommodate more general environment factors. Within the quadratic inference function (QIF) framework, the proposed method can achieve simultaneous identification of main and interaction effects on both the group and individual level. We conducted simulation studies to establish the advantage of the proposed regularization methods. In the case study, the environment factors include age, gender and treatment, which are either continuous or categorical. Our method leads to improved prediction and identification of main and interaction effects with important implications. In the third project, a sparse Bayesian quantile varying coefficient model has been developed for non-linear GxE studies. The proposed model can accommodate heavy-tailed errors and outliers from the disease phenotypes while pinpointing important non-linear interactions through Bayesian variable selection based on spike-and-slab priors. Fast computation has been facilitated by the efficient Gibbs sampler. Simulation studies and real data analysis with age as the univariate environment factor have been performed to show the superiority of the proposed method over multiple competing alternatives. The open source R packages with C++ implementations of all the methods under comparison have been provided along this dissertation. The R packages interep and springer, for the first two projects respectively, are available on CRAN. The R package for the last project on Bayesian regularized quantile varying coefficient model will be released soon to the public.

High-dimensional Variable Selection for Genomics Data, from Both Frequentist and Bayesian Perspectives

Author : Jie Ren
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (124 download)

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Book Synopsis High-dimensional Variable Selection for Genomics Data, from Both Frequentist and Bayesian Perspectives by : Jie Ren

Download or read book High-dimensional Variable Selection for Genomics Data, from Both Frequentist and Bayesian Perspectives written by Jie Ren and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection is one of the most popular tools for analyzing high-dimensional genomic data. It has been developed to accommodate complex data structures and lead to structured sparse identification of important genomics features. We focus on the network and interaction structure that commonly exist in genomic data, and develop novel variable selection methods from both frequentist and Bayesian perspectives. Network-based regularization has achieved success in variable selections for high-dimensional cancer genomic data, due to its ability to incorporate the correlations among genomic features. However, as survival time data usually follow skewed distributions, and are contaminated by outliers, network-constrained regularization that does not take the robustness into account leads to false identifications of network structure and biased estimation of patients' survival. In the first project, we develop a novel robust network-based variable selection method under the accelerated failure time (AFT) model. Extensive simulation studies show the advantage of the proposed method over the alternative methods. Promising findings are made in two case studies of lung cancer datasets with high dimensional gene expression measurements. Gene-environment (G×E) interactions are important for the elucidation of disease etiology beyond the main genetic and environmental effects. In the second project, a novel and powerful semi-parametric Bayesian variable selection model has been proposed to investigate linear and nonlinear G×E interactions simultaneously. It can further conduct structural identification by distinguishing nonlinear interactions from main-effects-only case within the Bayesian framework. The proposed method conducts Bayesian variable selection more efficiently and accurately than alternatives. Simulation shows that the proposed model outperforms competing alternatives in terms of both identification and prediction. In the case study, the proposed Bayesian method leads to the identification of effects with important implications in a high-throughput profiling study with high-dimensional SNP data. In the last project, a robust Bayesian variable selection method has been developed for G×E interaction studies. The proposed robust Bayesian method can effectively accommodate heavy-tailed errors and outliers in the response variable while conducting variable selection by accounting for structural sparsity. Spike and slab priors are incorporated on both individual and group levels to identify the sparse main and interaction effects. Extensive simulation studies and analysis of both the diabetes data with SNP measurements from the Nurses' Health Study and TCGA melanoma data with gene expression measurements demonstrate the superior performance of the proposed method over multiple competing alternatives. To facilitate reproducible research and fast computation, we have developed open source R packages for each project, which provide highly efficient C++ implementation for all the proposed and alternative approaches. The R packages regnet and spinBayes, associated with the first and second project correspondingly, are available on CRAN. For the third project, the R package robin is available from GitHub and will be submitted to CRAN soon.

Simultaneous Selection of Variables and Smoothing Parameters by Genetic Algorithms

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (836 download)

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Book Synopsis Simultaneous Selection of Variables and Smoothing Parameters by Genetic Algorithms by :

Download or read book Simultaneous Selection of Variables and Smoothing Parameters by Genetic Algorithms written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In additive models the problem of variable selection is strongly linked to the choice of the amount of smoothing used for components that represent metrical variables. Many software packages use separate toolsto solve the different tasks of variable selection and smoothing parameter choice. The combinationof these tools often leads to inappropriate results. In this paper we propose a simulataneous choice of variables and smoothing parameters based on genetic algorithms. Common genetic algorithms have to be modified since inclusion of variables and smoothing have to be coded separately but are linked in the search for optimal solutions. The basic tool for fitting the additive model is the penalized expansion in B-splines. -- Genetic algorithm ; Additive model ; Variable selection ; Penalized regression splines ; B-splines ; Improved AIC ; BIC

Big and Complex Data Analysis

Author : S. Ejaz Ahmed
Publisher : Springer
ISBN 13 : 3319415735
Total Pages : 390 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Big and Complex Data Analysis by : S. Ejaz Ahmed

Download or read book Big and Complex Data Analysis written by S. Ejaz Ahmed and published by Springer. This book was released on 2017-03-21 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume conveys some of the surprises, puzzles and success stories in high-dimensional and complex data analysis and related fields. Its peer-reviewed contributions showcase recent advances in variable selection, estimation and prediction strategies for a host of useful models, as well as essential new developments in the field. The continued and rapid advancement of modern technology now allows scientists to collect data of increasingly unprecedented size and complexity. Examples include epigenomic data, genomic data, proteomic data, high-resolution image data, high-frequency financial data, functional and longitudinal data, and network data. Simultaneous variable selection and estimation is one of the key statistical problems involved in analyzing such big and complex data. The purpose of this book is to stimulate research and foster interaction between researchers in the area of high-dimensional data analysis. More concretely, its goals are to: 1) highlight and expand the breadth of existing methods in big data and high-dimensional data analysis and their potential for the advancement of both the mathematical and statistical sciences; 2) identify important directions for future research in the theory of regularization methods, in algorithmic development, and in methodologies for different application areas; and 3) facilitate collaboration between theoretical and subject-specific researchers.

Statistical Learning with Sparsity

Author : Trevor Hastie
Publisher : CRC Press
ISBN 13 : 1498712177
Total Pages : 354 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Statistical Learning with Sparsity by : Trevor Hastie

Download or read book Statistical Learning with Sparsity written by Trevor Hastie and published by CRC Press. This book was released on 2015-05-07 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl

Data Classification

Author : Charu C. Aggarwal
Publisher : CRC Press
ISBN 13 : 1498760589
Total Pages : 710 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Data Classification by : Charu C. Aggarwal

Download or read book Data Classification written by Charu C. Aggarwal and published by CRC Press. This book was released on 2014-07-25 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive Coverage of the Entire Area of ClassificationResearch on the problem of classification tends to be fragmented across such areas as pattern recognition, database, data mining, and machine learning. Addressing the work of these different communities in a unified way, Data Classification: Algorithms and Applications explores the underlyi

Personalized Psychiatry

Author : Bernhard Baune
Publisher : Academic Press
ISBN 13 : 0128131772
Total Pages : 604 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Personalized Psychiatry by : Bernhard Baune

Download or read book Personalized Psychiatry written by Bernhard Baune and published by Academic Press. This book was released on 2019-10-16 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Personalized Psychiatry presents the first book to explore this novel field of biological psychiatry that covers both basic science research and its translational applications. The book conceptualizes personalized psychiatry and provides state-of-the-art knowledge on biological and neuroscience methodologies, all while integrating clinical phenomenology relevant to personalized psychiatry and discussing important principles and potential models. It is essential reading for advanced students and neuroscience and psychiatry researchers who are investigating the prevention and treatment of mental disorders. Combines neurobiology with basic science methodologies in genomics, epigenomics and transcriptomics Demonstrates how the statistical modeling of interacting biological and clinical information could transform the future of psychiatry Addresses fundamental questions and requirements for personalized psychiatry from a basic research and translational perspective

High-dimensional Data Analysis

Author : Tony Cai;Xiaotong Shen
Publisher :
ISBN 13 : 9787894236326
Total Pages : 318 pages
Book Rating : 4.2/5 (363 download)

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Book Synopsis High-dimensional Data Analysis by : Tony Cai;Xiaotong Shen

Download or read book High-dimensional Data Analysis written by Tony Cai;Xiaotong Shen and published by . This book was released on with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few years, significant developments have been taking place in highdimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics and signal processing. In particular, substantial advances have been made in the areas of feature selection, covariance estimation, classification and regression. This book intends to examine important issues arising from highdimensional data analysis to explore key ideas for statistical inference and prediction. It is structured around topics on multiple hypothesis testing, feature selection, regression, cla.

Statistical Foundations of Data Science

Author : Jianqing Fan
Publisher : CRC Press
ISBN 13 : 0429527616
Total Pages : 942 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis Statistical Foundations of Data Science by : Jianqing Fan

Download or read book Statistical Foundations of Data Science written by Jianqing Fan and published by CRC Press. This book was released on 2020-09-21 with total page 942 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.

High-Dimensional Covariance Estimation

Author : Mohsen Pourahmadi
Publisher : John Wiley & Sons
ISBN 13 : 1118573668
Total Pages : 204 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis High-Dimensional Covariance Estimation by : Mohsen Pourahmadi

Download or read book High-Dimensional Covariance Estimation written by Mohsen Pourahmadi and published by John Wiley & Sons. This book was released on 2013-05-28 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.

Optimization with Sparsity-Inducing Penalties

Author : Francis Bach
Publisher :
ISBN 13 : 9781601985101
Total Pages : 124 pages
Book Rating : 4.9/5 (851 download)

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Book Synopsis Optimization with Sparsity-Inducing Penalties by : Francis Bach

Download or read book Optimization with Sparsity-Inducing Penalties written by Francis Bach and published by . This book was released on 2011-12-23 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate nonsmooth norms. Optimization with Sparsity-Inducing Penalties presents optimization tools and techniques dedicated to such sparsity-inducing penalties from a general perspective. It covers proximal methods, block-coordinate descent, reweighted ?2-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provides an extensive set of experiments to compare various algorithms from a computational point of view. The presentation of Optimization with Sparsity-Inducing Penalties is essentially based on existing literature, but the process of constructing a general framework leads naturally to new results, connections and points of view. It is an ideal reference on the topic for anyone working in machine learning and related areas.

Handbook of Graphs and Networks

Author : Stefan Bornholdt
Publisher : John Wiley & Sons
ISBN 13 : 3527606335
Total Pages : 417 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Handbook of Graphs and Networks by : Stefan Bornholdt

Download or read book Handbook of Graphs and Networks written by Stefan Bornholdt and published by John Wiley & Sons. This book was released on 2006-03-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex interacting networks are observed in systems from such diverse areas as physics, biology, economics, ecology, and computer science. For example, economic or social interactions often organize themselves in complex network structures. Similar phenomena are observed in traffic flow and in communication networks as the internet. In current problems of the Biosciences, prominent examples are protein networks in the living cell, as well as molecular networks in the genome. On larger scales one finds networks of cells as in neural networks, up to the scale of organisms in ecological food webs. This book defines the field of complex interacting networks in its infancy and presents the dynamics of networks and their structure as a key concept across disciplines. The contributions present common underlying principles of network dynamics and their theoretical description and are of interest to specialists as well as to the non-specialized reader looking for an introduction to this new exciting field. Theoretical concepts include modeling networks as dynamical systems with numerical methods and new graph theoretical methods, but also focus on networks that change their topology as in morphogenesis and self-organization. The authors offer concepts to model network structures and dynamics, focussing on approaches applicable across disciplines.

Kaufman’s Atlas of Mouse Development Supplement

Author : Richard Baldock
Publisher : Academic Press
ISBN 13 : 0128009136
Total Pages : 343 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Kaufman’s Atlas of Mouse Development Supplement by : Richard Baldock

Download or read book Kaufman’s Atlas of Mouse Development Supplement written by Richard Baldock and published by Academic Press. This book was released on 2015-09-23 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kaufman's Atlas of Mouse Development: With Coronal Sections continues the stellar reputation of the original Atlas by providing updated, in-depth anatomical content and morphological views of organ systems.The publication offers written descriptions of the developmental origins of the organ systems alongside high-resolution images for needed visualization of developmental processes. Matt Kaufman himself has annotated the coronal images in the same clear, meticulous style of the original Atlas. Kaufman's Atlas of Mouse Development: With Coronal Sections follows the original Atlas as a continuation of the standard in the field for developmental biologists and researchers across biological and biomedical sciences studying mouse development. Provides high-resolution images for best visualization of key developmental processes and structures Offers in-depth anatomy and morphological views of organ systems Written descriptions convey developmental origins of the organ systems

Molecular Evolution and Phylogenetics

Author : Masatoshi Nei
Publisher : Oxford University Press
ISBN 13 : 0199881227
Total Pages : 444 pages
Book Rating : 4.1/5 (998 download)

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Book Synopsis Molecular Evolution and Phylogenetics by : Masatoshi Nei

Download or read book Molecular Evolution and Phylogenetics written by Masatoshi Nei and published by Oxford University Press. This book was released on 2000-07-27 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last ten years, remarkable progress has occurred in the study of molecular evolution. Among the most important factors that are responsible for this progress are the development of new statistical methods and advances in computational technology. In particular, phylogenetic analysis of DNA or protein sequences has become a powerful tool for studying molecular evolution. Along with this developing technology, the application of the new statistical and computational methods has become more complicated and there is no comprehensive volume that treats these methods in depth. Molecular Evolution and Phylogenetics fills this gap and present various statistical methods that are easily accessible to general biologists as well as biochemists, bioinformatists and graduate students. The text covers measurement of sequence divergence, construction of phylogenetic trees, statistical tests for detection of positive Darwinian selection, inference of ancestral amino acid sequences, construction of linearized trees, and analysis of allele frequency data. Emphasis is given to practical methods of data analysis, and methods can be learned by working through numerical examples using the computer program MEGA2 that is provided.

Multivariate Reduced-Rank Regression

Author : Raja Velu
Publisher : Springer Science & Business Media
ISBN 13 : 1475728530
Total Pages : 269 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Multivariate Reduced-Rank Regression by : Raja Velu

Download or read book Multivariate Reduced-Rank Regression written by Raja Velu and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the area of multivariate analysis, there are two broad themes that have emerged over time. The analysis typically involves exploring the variations in a set of interrelated variables or investigating the simultaneous relation ships between two or more sets of variables. In either case, the themes involve explicit modeling of the relationships or dimension-reduction of the sets of variables. The multivariate regression methodology and its variants are the preferred tools for the parametric modeling and descriptive tools such as principal components or canonical correlations are the tools used for addressing the dimension-reduction issues. Both act as complementary to each other and data analysts typically want to make use of these tools for a thorough analysis of multivariate data. A technique that combines the two broad themes in a natural fashion is the method of reduced-rank regres sion. This method starts with the classical multivariate regression model framework but recognizes the possibility for the reduction in the number of parameters through a restrietion on the rank of the regression coefficient matrix. This feature is attractive because regression methods, whether they are in the context of a single response variable or in the context of several response variables, are popular statistical tools. The technique of reduced rank regression and its encompassing features are the primary focus of this book. The book develops the method of reduced-rank regression starting from the classical multivariate linear regression model.

Mixed Effects Models for Complex Data

Author : Lang Wu
Publisher : CRC Press
ISBN 13 : 9781420074086
Total Pages : 431 pages
Book Rating : 4.0/5 (74 download)

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Book Synopsis Mixed Effects Models for Complex Data by : Lang Wu

Download or read book Mixed Effects Models for Complex Data written by Lang Wu and published by CRC Press. This book was released on 2009-11-11 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.