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Author : Ka-yui Wu (Karl)
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (81 download)
Download or read book On Some Extensions of Generalized Linear Models with Varying Dispersion written by Ka-yui Wu (Karl) and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ka-Yui Karl Wu
Publisher : Open Dissertation Press
ISBN 13 : 9781361279250
Total Pages : pages
Book Rating : 4.2/5 (792 download)
Download or read book On Some Extensions of Generalized Linear Models with Varying Dispersion written by Ka-Yui Karl Wu and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On Some Extensions of Generalized Linear Models With Varying Dispersion" by Ka-yui, Karl, Wu, 胡家銳, 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: When dealing with exponential family distributions, a constant dispersion is often assumed since it simplifies both model formulation and estimation. In contrast, heteroscedasticity is a common feature of almost every empirical data set. In this dissertation, the dispersion parameter is no longer considered as constant throughout the entire sample, but defined as the expected deviance of the individual response yi and its expected value _i such that it will be expressed as a linear combination of some covariates and their coefficients. At the same time, the dispersion regression is an essential part of a double Generalized Linear Model in which mean and dispersion are modelled in two interlinked and pseudo-simultaneously estimated submodels. In other words, the deviance is a function of the response mean which on the other hand depends on the dispersion. Due to the mutual dependency, the estimation algorithm will be iterated as long as the improvement of the one parameter leads to significant changes of the other until it is not the case. If appropriate covariates are chosen, the model's goodness of fit should be improved by the property that the dispersion is estimated by external information instead of being a constant. In the following, the advantage of dispersion modelling will be shown by its application on three different types of data: a) zero-inflated data, b) non-linear time series data, and c) clinical trials data. All these data follow distributions of the exponential family for which the application of the Generalized Linear Model is justified, but require certain extensions of modelling methodologies. In this dissertation, The enhanced goodness of fit given that the constant dispersion assumption is dropped will be shown in the above listed examples. In fact, by formulating and carrying out score and Wald tests on testing for the possible occurrence of varying dispersion, evidence of heterogeneous dispersion could be found to be present in the data sets considered. Furthermore, although model formulation, asymptotic properties and computational effort are more extensive when dealing with the double models, the benefits and advantages in terms of improved fitting results and more efficient parameter estimates appear to justify the additional effort not only for the types of data introduced, but also generally for empirical data analysis, on different types of data as well. DOI: 10.5353/th_b4819937 Subjects: Linear models (Statistics)
Author : Ka-yui Wu (Karl)
Publisher :
ISBN 13 :
Total Pages : 294 pages
Book Rating : 4.:/5 (81 download)
Download or read book On Some Extensions of Generalized Linear Models with Varying Dispersion written by Ka-yui Wu (Karl) and published by . This book was released on 2012 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James W. Hardin
Publisher : Stata Press
ISBN 13 : 1597180149
Total Pages : 413 pages
Book Rating : 4.5/5 (971 download)
Download or read book Generalized Linear Models and Extensions, Second Edition written by James W. Hardin and published by Stata Press. This book was released on 2007 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deftly balancing theory and application, this book stands out in its coverage of the derivation of the GLM families and their foremost links. This edition has new sections on discrete response models, including zero-truncated, zero-inflated, censored, and hurdle count models, as well as heterogeneous negative binomial, and more.
Author : Julian J. Faraway
Publisher : CRC Press
ISBN 13 : 0203492285
Total Pages : 307 pages
Book Rating : 4.2/5 (34 download)
Download or read book Extending the Linear Model with R written by Julian J. Faraway and published by CRC Press. This book was released on 2016-02-10 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author's treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the data described in the book is available at http://people.bath.ac.uk/jjf23/ELM/ Statisticians need to be familiar with a broad range of ideas and techniques. This book provides a well-stocked toolbox of methodologies, and with its unique presentation of these very modern statistical techniques, holds the potential to break new ground in the way graduate-level courses in this area are taught.
Author : P. McCullagh
Publisher : Routledge
ISBN 13 : 1351445847
Total Pages : 361 pages
Book Rating : 4.3/5 (514 download)
Download or read book Generalized Linear Models written by P. McCullagh and published by Routledge. This book was released on 2019-01-22 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and ot
Author : Michael Smithson
Publisher : SAGE Publications
ISBN 13 : 1544334524
Total Pages : 136 pages
Book Rating : 4.5/5 (443 download)
Download or read book Generalized Linear Models for Bounded and Limited Quantitative Variables written by Michael Smithson and published by SAGE Publications. This book was released on 2019-09-09 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces researchers and students to the concepts and generalized linear models for analyzing quantitative random variables that have one or more bounds. Examples of bounded variables include the percentage of a population eligible to vote (bounded from 0 to 100), or reaction time in milliseconds (bounded below by 0). The human sciences deal in many variables that are bounded. Ignoring bounds can result in misestimation and improper statistical inference. Michael Smithson and Yiyun Shou's book brings together material on the analysis of limited and bounded variables that is scattered across the literature in several disciplines, and presents it in a style that is both more accessible and up-to-date. The authors provide worked examples in each chapter using real datasets from a variety of disciplines. The software used for the examples include R, SAS, and Stata. The data, software code, and detailed explanations of the example models are available on an accompanying website.
Author : James K. Lindsey
Publisher : Springer Science & Business Media
ISBN 13 : 038722730X
Total Pages : 265 pages
Book Rating : 4.3/5 (872 download)
Download or read book Applying Generalized Linear Models written by James K. Lindsey and published by Springer Science & Business Media. This book was released on 2008-01-15 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes how generalised linear modelling procedures can be used in many different fields, without becoming entangled in problems of statistical inference. The author shows the unity of many of the commonly used models and provides readers with a taste of many different areas, such as survival models, time series, and spatial analysis, and of their unity. As such, this book will appeal to applied statisticians and to scientists having a basic grounding in modern statistics. With many exercises at the end of each chapter, it will equally constitute an excellent text for teaching applied statistics students and non- statistics majors. The reader is assumed to have knowledge of basic statistical principles, whether from a Bayesian, frequentist, or direct likelihood point of view, being familiar at least with the analysis of the simpler normal linear models, regression and ANOVA.
Author : Walter W. Stroup
Publisher : CRC Press
ISBN 13 : 1439815135
Total Pages : 547 pages
Book Rating : 4.4/5 (398 download)
Download or read book Generalized Linear Mixed Models written by Walter W. Stroup and published by CRC Press. This book was released on 2016-04-19 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: With numerous examples using SAS PROC GLIMMIX, this text presents an introduction to linear modeling using the generalized linear mixed model as an overarching conceptual framework. For readers new to linear models, the book helps them see the big picture. It shows how linear models fit with the rest of the core statistics curriculum and points out the major issues that statistical modelers must consider.
Author : Julian J. Faraway
Publisher : CRC Press
ISBN 13 : 1498720986
Total Pages : 399 pages
Book Rating : 4.4/5 (987 download)
Download or read book Extending the Linear Model with R written by Julian J. Faraway and published by CRC Press. This book was released on 2016-03-23 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Start Analyzing a Wide Range of Problems Since the publication of the bestselling, highly recommended first edition, R has considerably expanded both in popularity and in the number of packages available. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Second Edition takes advantage of the greater functionality now available in R and substantially revises and adds several topics. New to the Second Edition Expanded coverage of binary and binomial responses, including proportion responses, quasibinomial and beta regression, and applied considerations regarding these models New sections on Poisson models with dispersion, zero inflated count models, linear discriminant analysis, and sandwich and robust estimation for generalized linear models (GLMs) Revised chapters on random effects and repeated measures that reflect changes in the lme4 package and show how to perform hypothesis testing for the models using other methods New chapter on the Bayesian analysis of mixed effect models that illustrates the use of STAN and presents the approximation method of INLA Revised chapter on generalized linear mixed models to reflect the much richer choice of fitting software now available Updated coverage of splines and confidence bands in the chapter on nonparametric regression New material on random forests for regression and classification Revamped R code throughout, particularly the many plots using the ggplot2 package Revised and expanded exercises with solutions now included Demonstrates the Interplay of Theory and Practice This textbook continues to cover a range of techniques that grow from the linear regression model. It presents three extensions to the linear framework: GLMs, mixed effect models, and nonparametric regression models. The book explains data analysis using real examples and includes all the R commands necessary to reproduce the analyses.
Author : Charles E. McCulloch
Publisher : IMS
ISBN 13 : 9780940600546
Total Pages : 100 pages
Book Rating : 4.6/5 (5 download)
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
Author : Walter W. Stroup
Publisher : CRC Press
ISBN 13 : 1498755585
Total Pages : 671 pages
Book Rating : 4.4/5 (987 download)
Download or read book Generalized Linear Mixed Models written by Walter W. Stroup and published by CRC Press. This book was released on 2024-05-21 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Linear Mixed Models: Modern Concepts, Methods, and Applications (2nd edition) presents an updated introduction to linear modeling using the generalized linear mixed model (GLMM) as the overarching conceptual framework. For students new to statistical modeling, this book helps them see the big picture – linear modeling as broadly understood and its intimate connection with statistical design and mathematical statistics. For readers experienced in statistical practice, but new to GLMMs, the book provides a comprehensive introduction to GLMM methodology and its underlying theory. Unlike textbooks that focus on classical linear models or generalized linear models or mixed models, this book covers all of the above as members of a unified GLMM family of linear models. In addition to essential theory and methodology, this book features a rich collection of examples using SAS® software to illustrate GLMM practice. This second edition is updated to reflect lessons learned and experience gained regarding best practices and modeling choices faced by GLMM practitioners. New to this edition are two chapters focusing on Bayesian methods for GLMMs. Key Features: • Most statistical modeling books cover classical linear models or advanced generalized and mixed models; this book covers all members of the GLMM family – classical and advanced models. • Incorporates lessons learned from experience and on-going research to provide up-to-date examples of best practices. • Illustrates connections between statistical design and modeling: guidelines for translating study design into appropriate model and in-depth illustrations of how to implement these guidelines; use of GLMM methods to improve planning and design. • Discusses the difference between marginal and conditional models, differences in the inference space they are intended to address and when each type of model is appropriate. • In addition to likelihood-based frequentist estimation and inference, provides a brief introduction to Bayesian methods for GLMMs. Walt Stroup is an Emeritus Professor of Statistics. He served on the University of Nebraska statistics faculty for over 40 years, specializing in statistical modeling and statistical design. He is a Fellow of the American Statistical Association, winner of the University of Nebraska Outstanding Teaching and Innovative Curriculum Award and author or co-author of three books on mixed models and their extensions. Marina Ptukhina (Pa-too-he-nuh), PhD, is an Associate Professor of Statistics at Whitman College. She is interested in statistical modeling, design and analysis of research studies and their applications. Her research includes applications of statistics to economics, biostatistics and statistical education. Ptukhina earned a PhD in Statistics from the University of Nebraska-Lincoln, a Master of Science degree in Mathematics from Texas Tech University and a Specialist degree in Management from The National Technical University "Kharkiv Polytechnic Institute." Julie Garai, PhD, is a Data Scientist at Loop. She earned her PhD in Statistics from the University of Nebraska-Lincoln and a bachelor’s degree in Mathematics and Spanish from Doane College. Dr Garai actively collaborates with statisticians, psychologists, ecologists, forest scientists, software engineers, and business leaders in academia and industry. In her spare time, she enjoys leisurely walks with her dogs, dance parties with her children, and playing the trombone.
Author : James William Hardin
Publisher :
ISBN 13 : 9781597182263
Total Pages : pages
Book Rating : 4.1/5 (822 download)
Download or read book Generalized Linear Models and Extensions written by James William Hardin and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Youngjo Lee
Publisher : CRC Press
ISBN 13 : 135181155X
Total Pages : 242 pages
Book Rating : 4.3/5 (518 download)
Download or read book Data Analysis Using Hierarchical Generalized Linear Models with R written by Youngjo Lee and published by CRC Press. This book was released on 2017-07-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their introduction, hierarchical generalized linear models (HGLMs) have proven useful in various fields by allowing random effects in regression models. Interest in the topic has grown, and various practical analytical tools have been developed. This book summarizes developments within the field and, using data examples, illustrates how to analyse various kinds of data using R. It provides a likelihood approach to advanced statistical modelling including generalized linear models with random effects, survival analysis and frailty models, multivariate HGLMs, factor and structural equation models, robust modelling of random effects, models including penalty and variable selection and hypothesis testing. This example-driven book is aimed primarily at researchers and graduate students, who wish to perform data modelling beyond the frequentist framework, and especially for those searching for a bridge between Bayesian and frequentist statistics.
Author : Bent Jorgensen
Publisher : CRC Press
ISBN 13 : 9780412997112
Total Pages : 264 pages
Book Rating : 4.9/5 (971 download)
Download or read book The Theory of Dispersion Models written by Bent Jorgensen and published by CRC Press. This book was released on 1997-06-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of dispersion models straddles both statistics and probability, and involves an encyclopedic collection of tools, such as exponential families, asymptotic theory, stochastic processes, Tauber theory, infinite divisibility, and stable distributions. The Theory of Dispersion Models introduces the reader to these models, which serve as error distributions for generalized linear models, and looks at their applications within this context.
Author : Julian J. Faraway
Publisher : CRC Press
ISBN 13 : 1439887349
Total Pages : 284 pages
Book Rating : 4.4/5 (398 download)
Download or read book Linear Models with R written by Julian J. Faraway and published by CRC Press. This book was released on 2016-04-19 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models
Author : James W. Hardin
Publisher : Stata Press
ISBN 13 : 9781597181051
Total Pages : 0 pages
Book Rating : 4.1/5 (81 download)
Download or read book Generalized Linear Models and Extensions, Third Edition written by James W. Hardin and published by Stata Press. This book was released on 2012-06-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a thorough examination of generalized linear model (GLM) estimation methods as well as the derivation of all major GLM families. Examined families include Gaussian, gamma, inverse Gaussian, binomial, Poisson, geometric, and negative binomial. The text also contains various models that have been developed on the basis of GLM theory, including GAM, ordered binomial models, multinomial logit and probit models, GEE and other quasi-likelihood models, fixed and random effects models, and random intercept and random parameter models. Using Stata, the book offers numerous examples to assist you in applying the models to your own data situations.
