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Parameter Estimation In Generalized Linear Mixed Models Using Quasi Monte Carlo Methods
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Book Synopsis Parameter estimation in generalized linear mixed models using quasi-Monte Carlo methods by : Eid M. O. Al-Eid
Download or read book Parameter estimation in generalized linear mixed models using quasi-Monte Carlo methods written by Eid M. O. Al-Eid and published by . This book was released on 2007 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quasi-Monte Carlo Methods in Generalized Linear Mixed Model with Correlated and Non-normal Random Effects by : Yin Chen
Download or read book Quasi-Monte Carlo Methods in Generalized Linear Mixed Model with Correlated and Non-normal Random Effects written by Yin Chen and published by . This book was released on 2009 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Generalized Linear Mixed Models by : Charles E. McCulloch
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
Book Synopsis Monte-Carlo Simulation-Based Statistical Modeling by : Ding-Geng (Din) Chen
Download or read book Monte-Carlo Simulation-Based Statistical Modeling written by Ding-Geng (Din) Chen and published by Springer. This book was released on 2017-02-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together expert researchers engaged in Monte-Carlo simulation-based statistical modeling, offering them a forum to present and discuss recent issues in methodological development as well as public health applications. It is divided into three parts, with the first providing an overview of Monte-Carlo techniques, the second focusing on missing data Monte-Carlo methods, and the third addressing Bayesian and general statistical modeling using Monte-Carlo simulations. The data and computer programs used here will also be made publicly available, allowing readers to replicate the model development and data analysis presented in each chapter, and to readily apply them in their own research. Featuring highly topical content, the book has the potential to impact model development and data analyses across a wide spectrum of fields, and to spark further research in this direction.
Book Synopsis The Choice of Monte Carlo Algorithm in the Estimation of the Generalized Linear Mixed Model by : Haiyue Song
Download or read book The Choice of Monte Carlo Algorithm in the Estimation of the Generalized Linear Mixed Model written by Haiyue Song and published by . This book was released on 2000 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parametric Estimates by the Monte Carlo Method by : G. A. Mikhailov
Download or read book Parametric Estimates by the Monte Carlo Method written by G. A. Mikhailov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Parametric Estimates by the Monte Carlo Method".
Book Synopsis A Monte Carlo EM Algorithm for Generalized Linear Mixed Models with Flexible Random Effects Distribution by :
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.
Book Synopsis Analysis of Generalized Linear Mixed Models in the Agricultural and Natural Resources Sciences by : Edward E. Gbur
Download or read book Analysis of Generalized Linear Mixed Models in the Agricultural and Natural Resources Sciences written by Edward E. Gbur and published by John Wiley & Sons. This book was released on 2020-01-22 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Linear Mixed Models in the Agricultural and Natural Resources Sciences provides readers with an understanding and appreciation for the design and analysis of mixed models for non-normally distributed data. It is the only publication of its kind directed specifically toward the agricultural and natural resources sciences audience. Readers will especially benefit from the numerous worked examples based on actual experimental data and the discussion of pitfalls associated with incorrect analyses.
Book Synopsis Bayesian Filtering and Smoothing by : Simo Särkkä
Download or read book Bayesian Filtering and Smoothing written by Simo Särkkä and published by Cambridge University Press. This book was released on 2013-09-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
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.
Book Synopsis Monte Carlo and Quasi-Monte Carlo Sampling by : Christiane Lemieux
Download or read book Monte Carlo and Quasi-Monte Carlo Sampling written by Christiane Lemieux and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute. This book presents essential tools for using quasi–Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods—uniform and non-uniform random number generation, variance reduction techniques—but the material is presented to prepare the readers for the next step, which is to replace the random sampling inherent to Monte Carlo by quasi–random sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions, randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book is devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequential Monte Carlo, with a discussion of their quasi–Monte Carlo counterpart. The prerequisites for reading this book are a basic knowledge of statistics and enough mathematical maturity to follow through the various techniques used throughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about Monte Carlo and quasi–Monte Carlo methods and researchers interested in an up-to-date guide to these methods.
Book Synopsis Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods by : Giray Okten
Download or read book Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods written by Giray Okten and published by Universal-Publishers. This book was released on 1999 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi-Monte Carlo methods, which are often described as deterministic versions of Monte Carlo methods, were introduced in the 1950s by number theoreticians. They improve several deficiencies of Monte Carlo methods; such as providing estimates with deterministic bounds and avoiding the paradoxical difficulty of generating random numbers in a computer. However, they have their own drawbacks. First, although they provide faster convergence than Monte Carlo methods asymptotically, the advantage may not be practical to obtain in "high" dimensional problems. Second, there is not a practical way to measure the error of a quasi-Monte Carlo simulation. Finally, unlike Monte Carlo methods, there is a scarcity of error reduction techniques for these methods. In this dissertation, we attempt to provide remedies for the disadvantages of quasi-Monte Carlo methods mentioned above. In the first part of the dissertation, a hybrid-Monte Carlo sequence designed to obtain error reduction in high dimensions is studied. Probabilistic results on the discrepancy of this sequence as well as results obtained by applying the sequence to problems from numerical integration and mathematical finance are presented. In the second part of the dissertation, a new hybrid-Monte Carlo method is introduced, in an attempt to obtain a practical statistical error analysis using low-discrepancy sequences. It is applied to problems from mathematical finance and particle transport theory to compare its effectiveness with the conventional methods. In the last part of the dissertation, a generalized quasi-Monte Carlo integration rule is introduced. A Koksma-Hlawka type inequality for the rule is proved, using a new concept for the variation of a function. As a consequence of the rule, error reduction techniques and in particular an "importance sampling" type statement are derived. Problems from different disciplines are used as practical tests for our methods. The numerical results obtained in favor of the methods suggest the practical advantages that can be realized by their use in a wide variety of applications.
Book Synopsis Generalized Latent Variable Modeling by : Anders Skrondal
Download or read book Generalized Latent Variable Modeling written by Anders Skrondal and published by CRC Press. This book was released on 2004-05-11 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models. Following a gentle introduction to latent variable modeling, the authors clearly explain and contrast a wi
Book Synopsis Monte Carlo Methods for Missing Data in Generalized Linear and Generalized Linear Mixed Models by : Christian Heumann
Download or read book Monte Carlo Methods for Missing Data in Generalized Linear and Generalized Linear Mixed Models written by Christian Heumann and published by . This book was released on 2004 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quasi-Likelihood And Its Application by : Christopher C. Heyde
Download or read book Quasi-Likelihood And Its Application written by Christopher C. Heyde and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first account in book form of all the essential features of the quasi-likelihood methodology, stressing its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential principles rather than detailed proofs, and readers are assumed to have a firm grounding in probability and statistics at the graduate level. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided.
Book Synopsis Generalized Linear Mixed Models with Applications in Agriculture and Biology by : Josafhat Salinas Ruíz
Download or read book Generalized Linear Mixed Models with Applications in Agriculture and Biology written by Josafhat Salinas Ruíz and published by Springer Nature. This book was released on 2023-08-16 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book offers an introduction to mixed generalized linear models with applications to the biological sciences, basically approached from an applications perspective, without neglecting the rigor of the theory. For this reason, the theory that supports each of the studied methods is addressed and later - through examples - its application is illustrated. In addition, some of the assumptions and shortcomings of linear statistical models in general are also discussed. An alternative to analyse non-normal distributed response variables is the use of generalized linear models (GLM) to describe the response data with an exponential family distribution that perfectly fits the real response. Extending this idea to models with random effects allows the use of Generalized Linear Mixed Models (GLMMs). The use of these complex models was not computationally feasible until the recent past, when computational advances and improvements to statistical analysis programs allowed users to easily, quickly, and accurately apply GLMM to data sets. GLMMs have attracted considerable attention in recent years. The word "Generalized" refers to non-normal distributions for the response variable and the word "Mixed" refers to random effects, in addition to the fixed effects typical of analysis of variance (or regression). With the development of modern statistical packages such as Statistical Analysis System (SAS), R, ASReml, among others, a wide variety of statistical analyzes are available to a wider audience. However, to be able to handle and master more sophisticated models requires proper training and great responsibility on the part of the practitioner to understand how these advanced tools work. GMLM is an analysis methodology used in agriculture and biology that can accommodate complex correlation structures and types of response variables.
Book Synopsis Foundations of Linear and Generalized Linear Models by : Alan Agresti
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.
