Download or read book Estimation in Generalized Linear Mixed Models Via the EM Algorithm written by Brian M. Steele and published by . This book was released on 1995 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Monte Carlo EM Algorithm for Generalized Linear Mixed Models with Flexible Random Effects Distribution written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A popular way to model correlated binary, count, or other data arising inclinical trials and epidemiological studies of cancer and other diseases is byusing generalized linear mixed models (GLMMs), which acknowledge correlationthrough incorporation of random effects. A standard model assumption is thatthe random effects follow a parametric family such as the normal distribution. However, this may be unrealistic or too restrictive to represent the data, raising concern over the validity of inferences both on fixed and random effects if it is violated. Here we use the seminonparametric (SNP) approach (Davidian and Gallant 1992,1993) to model the random effects, which relaxes the normality assumption andjust requires that the distribution of random effects belong to a class of`"smooth'' densities given by Gallant and Nychka (1987). This representation allows the density of random effects to be very flexible, including densitiesthat are skewed, multi--modal, fat-- or thin--tailed relative to the normal, andthe normal as a special case. We also provide a reparameterization of this representation to avoid numerical instability in estimating the polynomialcoefficients. Because an efficient algorithm to sample from a SNP density is available, wepropose a Monte Carlo expectation maximization (MCEM) algorithm using arejection sampling scheme (Booth and Hobert, 1999) to estimate the fixedparameters of the linear predictor, variance components and the SNP density. Astrategy of choosing the degree of flexibility required for the SNP density isalso proposed. We illustrate the methods by application to two data sets fromthe Framingham and Six Cities Studies, and present simulations demonstratingperformance of the approach.

Download or read book Estimation of Complex Generalized Linear Mixed Models for Measurement and Growth written by Minjeong Jeon and published by . This book was released on 2012 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A variety of methods have been developed for approximating the intractable likelihood functions, but there seems no method yet that is both computationally efficient and accurate in a wide range of situations. In this dissertation, I consider new estimation methods and applications of complex GLMMs for measurement and growth. The dissertation consists of three papers, 1) Variational maximization-maximization (MM) algorithm, 2) Monte Carlo local likelihood (MCLL) estimation, and 3) Autoregressive item response theory (IRT) growth model for longitudinal item analysis. In the first and second papers, I develop two ML methods for estimating GLMMs with crossed random effects. The variational MM algorithm is a modified expectation-maximization (EM) algorithm where a variational density is introduced in the expectation (E) step to approximate the true posterior density of the random effects given the data. The E-step is replaced by another maximization step that minimizes the Kullback-Leibler (KL) divergence between the posterior and the variational density, or equivalently, maximizes the lower bound of the log-likelihood with respect to the variational distribution. The MCLL algorithm uses the posterior samples of model parameters obtained from Markov chain Monte Carlo (MCMC) for likelihood inference. The posterior density is estimated by local likelihood density estimation and the likelihood function is approximated up to a constant by the local likelihood density estimate of the posterior divided by the prior. The performance of these new algorithms is evaluated using simulation and empirical studies and compared with other ML and Bayesian estimators. In the third paper, a new autoregressive IRT growth model is proposed to take into account serial correlations among responses to the same items over time. The consequences of ignoring serial dependence and the initial conditions problem are investigated using simulations. The new model is applied to longitudinal data of Korean students' self-esteem.

Download or read book A Finite Support Random effects Distribution Approach to Generalized Linear Mixed effects Model written by Kwan Moon Leung and published by . This book was released on 1994 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book The EM Algorithm and Related Statistical Models written by Michiko Watanabe and published by CRC Press. This book was released on 2003-10-15 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the application and formulation of the EM algorithm, The EM Algorithm and Related Statistical Models offers a valuable method for constructing statistical models when only incomplete information is available, and proposes specific estimation algorithms for solutions to incomplete data problems. The text covers current topics including statistical models with latent variables, as well as neural network models, and Markov Chain Monte Carlo methods. It describes software resources valuable for the processing of the EM algorithm with incomplete data and for general analysis of latent structure models of categorical data, and studies accelerated versions of the EM algorithm.

Download or read book Improved Iterative Schemes for REML Estimation of Variance Parameters in Linear Mixed Models written by Emma Jane Knight and published by . This book was released on 2008 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Residual maximum likelihood (REML) estimation is a popular method of estimation for variance parameters in linear mixed models, which typically requires an iterative scheme. The aim of this thesis is to review several popular iterative schemes and to develop an improved iterative strategy that will work for a wide class of models. The average information (AI) algorithm is a computationally convenient and efficient algorithm to use when starting values are in the neighbourhood of the REML solution. The expectation-maximisation (EM) algorithm and the parameter expanded EM (PXEM) algorithm are good alternatives in these situations but they can be very slow to converge. The formulation of these algorithms for a general linear mixed model is presented, along with their convergence properties. The direct comparison of the AI and PXEM algorithms shows that the PXEM algorithm, although an improvement over the EM algorithm, still falls well short of the AI algorithm in terms of speed of convergence. The hybrid schemes use EM-type iterations to move close enough to the REML solution to enable the AI algorithm to successfully converge. They are shown to be robust to choice of starting values like the EM and PXEM algorithms, while demonstrating fast convergence like the AI algorithm." -- from Abstract.

Download or read book Mixed Models written by Eugene Demidenko and published by John Wiley & Sons. This book was released on 2013-08-05 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Estimation for Generalized Linear Mixed Model Via Multiple Imputations written by On-Yee Tang and published by . This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Estimation for Generalized Linear Mixed Model via Multiple Imputations" by On-yee, Tang, 鄧安怡, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled ESTIMATION FOR GENERALIZED LINEAR MIXED MODEL VIA MULTIPLE IMPUTATIONS submitted by TANG On Yee for the degree of Master of Philosophy at The University of Hong Kong in February 2005 This thesis addresses the estimation of generalized linear mixed model in two par- ticular areas, namely analysis of zero-inated count data and survival analysis with long-term survivors. Analysis of count data is pervasive in many empirical applications. However, the count data encountered often exhibit a larger pro- portion of zeros than expected according to the Poisson distribution, making it inappropriateforanalysisusingastandardPoissonregressionmodel. Inthiscase, it is common to assume a mixture model which incorporates random e(R)ects into the Poisson regression model to accommodate the excessive zeros. More general random e(R)ects with the non-central chi-square distribution with zero degrees of freedom were proposed to model the extra variation induced by subject-specicheterogeneity. Theuseofthisspecialdistributionnotonlyprovidesmoreexibility on the relationship between covariates and random e(R)ects, but also demonstrates its superior merits and usefulness in analysis of clustered or multivariate count data. In practice, independence between observations cannot always be assumed. Correlated zero-inated count data are often encountered when they are collected on clusters of individuals or when repeated measurements are made on the same subject. In this case, each subject is regarded as a cluster. To further accommo- date the level of association among the zero-inated response counts within the same cluster, namely the intra-cluster correlation, the proposed model was ex- tended to incorporate a cluster-specic frailty, where the intra-cluster correlation can be measured either in terms of a correlation coecient or characterized by a dependence parameter. Multivariate zero-inated count data arise naturally when more than one rare event of interest, that are originally related, are observed simultaneously. To account for both preponderance of zeros and dependence between multivariate responses, a multivariate extension of the proposed model was suggested. In ad- dition to random e(R)ects which describe the subject-specic heterogeneity in the proposedmodel, agammafrailtywasintroducedtoaccommodatethedependence between multivariate response counts. Another topic deals with modeling the proportion of immunes or surviving fraction in a population. Recently, there has been a recurring interest in modelingsurvival data which hypothesize subpopulations of individuals highly susceptible tosometypesofadverseeventswhileotherindividualsareassumedtobeatmuch lessrisk. Itiscommontoassumeabinaryrandome(R)ecttomodelthesusceptibility ofeachindividual. Toanalyzethistypeofcensoreddatawithlong-termsurvivors, amixturemodelwasrevisited. Itcombinesabinaryregressionformulationforthe probabilityofoccurrenceofaneventandtheCox'sproportionalhazardsregression model for the time to occurrence of the event if it does. Simple multiple imputation algorithms were proposed to perform estimation for the above analyses. It is simple, easy to implement and has the merit of a straightforward variance estimation. Its computational and analytical simplicity were validated by simulation studies and illustrated by real data applications. DOI: 10.5353/th_b3068765 Subjects: Linear models (S

Download or read book The EM Algorithm and Extensions written by Geoffrey J. McLachlan and published by John Wiley & Sons. This book was released on 2007-11-09 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only single-source——now completely updated and revised——to offer a unified treatment of the theory, methodology, and applications of the EM algorithm Complete with updates that capture developments from the past decade, The EM Algorithm and Extensions, Second Edition successfully provides a basic understanding of the EM algorithm by describing its inception, implementation, and applicability in numerous statistical contexts. In conjunction with the fundamentals of the topic, the authors discuss convergence issues and computation of standard errors, and, in addition, unveil many parallels and connections between the EM algorithm and Markov chain Monte Carlo algorithms. Thorough discussions on the complexities and drawbacks that arise from the basic EM algorithm, such as slow convergence and lack of an in-built procedure to compute the covariance matrix of parameter estimates, are also presented. While the general philosophy of the First Edition has been maintained, this timely new edition has been updated, revised, and expanded to include: New chapters on Monte Carlo versions of the EM algorithm and generalizations of the EM algorithm New results on convergence, including convergence of the EM algorithm in constrained parameter spaces Expanded discussion of standard error computation methods, such as methods for categorical data and methods based on numerical differentiation Coverage of the interval EM, which locates all stationary points in a designated region of the parameter space Exploration of the EM algorithm's relationship with the Gibbs sampler and other Markov chain Monte Carlo methods Plentiful pedagogical elements—chapter introductions, lists of examples, author and subject indices, computer-drawn graphics, and a related Web site The EM Algorithm and Extensions, Second Edition serves as an excellent text for graduate-level statistics students and is also a comprehensive resource for theoreticians, practitioners, and researchers in the social and physical sciences who would like to extend their knowledge of the EM algorithm.

Download or read book Nonlinear Models for Repeated Measurement Data written by Marie Davidian and published by Routledge. This book was released on 2017-11-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear measurement data arise in a wide variety of biological and biomedical applications, such as longitudinal clinical trials, studies of drug kinetics and growth, and the analysis of assay and laboratory data. Nonlinear Models for Repeated Measurement Data provides the first unified development of methods and models for data of this type, with a detailed treatment of inference for the nonlinear mixed effects and its extensions. A particular strength of the book is the inclusion of several detailed case studies from the areas of population pharmacokinetics and pharmacodynamics, immunoassay and bioassay development and the analysis of growth curves.

Download or read book The EM Algorithm and Related Statistical Models written by Michiko Watanabe and published by CRC Press. This book was released on 2003-10-15 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the application and formulation of the EM algorithm, The EM Algorithm and Related Statistical Models offers a valuable method for constructing statistical models when only incomplete information is available, and proposes specific estimation algorithms for solutions to incomplete data problems. The text covers current topics including sta

Download or read book Foundations of Linear and Generalized Linear Models written by Alan Agresti and published by John Wiley & Sons. This book was released on 2015-02-23 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.

Download or read book Generalized Linear Mixed Models written by Charles E. McCulloch and published by IMS. This book was released on 2003 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wiley Series in Probability and Statistics A modern perspective on mixed models The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data. As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features: * A review of the basics of linear models and linear mixed models * Descriptions of models for nonnormal data, including generalized linear and nonlinear models * Analysis and illustration of techniques for a variety of real data sets * Information on the accommodation of longitudinal data using these models * Coverage of the prediction of realized values of random effects * A discussion of the impact of computing issues on mixed models

Download or read book Likelihood Estimation for Mixture Models Via the EM Algorithm written by Zhenxu Ma and published by . This book was released on 1996 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Maximum Likelihood Estimation in the Random Coefficient Regression Model Via the EM Algorithm written by Jiang-Ming Wu and published by . This book was released on 1995 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advanced Medical Statistics 2nd Edition written by Ying Lu and published by World Scientific. This book was released on 2015-06-29 with total page 1471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to provide both comprehensive reviews of the classical methods and an introduction to new developments in medical statistics. The topics range from meta analysis, clinical trial design, causal inference, personalized medicine to machine learning and next generation sequence analysis. Since the publication of the first edition, there have been tremendous advances in biostatistics and bioinformatics. The new edition tries to cover as many important emerging areas and reflect as much progress as possible. Many distinguished scholars, who greatly advanced their research areas in statistical methodology as well as practical applications, also have revised several chapters with relevant updates and written new ones from scratch.The new edition has been divided into four sections, including, Statistical Methods in Medicine and Epidemiology, Statistical Methods in Clinical Trials, Statistical Genetics, and General Methods. To reflect the rise of modern statistical genetics as one of the most fertile research areas since the publication of the first edition, the brand new section on Statistical Genetics includes entirely new chapters reflecting the state of the art in the field.Although tightly related, all the book chapters are self-contained and can be read independently. The book chapters intend to provide a convenient launch pad for readers interested in learning a specific topic, applying the related statistical methods in their scientific research and seeking the newest references for in-depth research.