Generalized Estimating Equations
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Generalized Estimating Equations
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Author : James W. Hardin
language : en
Publisher: CRC Press
Release Date : 2012-12-10
Generalized Estimating Equations written by James W. Hardin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-10 with Mathematics categories.
Generalized Estimating Equations, Second Edition updates the best-selling previous edition, which has been the standard text on the subject since it was published a decade ago. Combining theory and application, the text provides readers with a comprehensive discussion of GEE and related models. Numerous examples are employed throughout the text, al
Generalized Estimating Equations
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Author : Andreas Ziegler
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-17
Generalized Estimating Equations written by Andreas Ziegler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-17 with Mathematics categories.
Generalized estimating equations have become increasingly popular in biometrical, econometrical, and psychometrical applications because they overcome the classical assumptions of statistics, i.e. independence and normality, which are too restrictive for many problems. Therefore, the main goal of this book is to give a systematic presentation of the original generalized estimating equations (GEE) and some of its further developments. Subsequently, the emphasis is put on the unification of various GEE approaches. This is done by the use of two different estimation techniques, the pseudo maximum likelihood (PML) method and the generalized method of moments (GMM). The author details the statistical foundation of the GEE approach using more general estimation techniques. The book could therefore be used as basis for a course to graduate students in statistics, biostatistics, or econometrics, and will be useful to practitioners in the same fields.
Quasi Least Squares Regression
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Author : Justine Shults
language : en
Publisher: CRC Press
Release Date : 2014-01-28
Quasi Least Squares Regression written by Justine Shults and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-28 with Mathematics categories.
Drawing on the authors’ substantial expertise in modeling longitudinal and clustered data, Quasi-Least Squares Regression provides a thorough treatment of quasi-least squares (QLS) regression—a computational approach for the estimation of correlation parameters within the framework of generalized estimating equations (GEEs). The authors present a detailed evaluation of QLS methodology, demonstrating the advantages of QLS in comparison with alternative methods. They describe how QLS can be used to extend the application of the traditional GEE approach to the analysis of unequally spaced longitudinal data, familial data, and data with multiple sources of correlation. In some settings, QLS also allows for improved analysis with an unstructured correlation matrix. Special focus is given to goodness-of-fit analysis as well as new strategies for selecting the appropriate working correlation structure for QLS and GEE. A chapter on longitudinal binary data tackles recent issues raised in the statistical literature regarding the appropriateness of semi-parametric methods, such as GEE and QLS, for the analysis of binary data; this chapter includes a comparison with the first-order Markov maximum-likelihood (MARK1ML) approach for binary data. Examples throughout the book demonstrate each topic of discussion. In particular, a fully worked out example leads readers from model building and interpretation to the planning stages for a future study (including sample size calculations). The code provided enables readers to replicate many of the examples in Stata, often with corresponding R, SAS, or MATLAB® code offered in the text or on the book’s website.
Generalized Estimating Equations
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Author : James W. Hardin
language : en
Publisher: CRC Press
Release Date : 2002-07-30
Generalized Estimating Equations written by James W. Hardin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-30 with Mathematics categories.
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in heal
Numerical Methods For Nonlinear Estimating Equations
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Author : Christopher G. Small
language : en
Publisher: OUP Oxford
Release Date : 2003-10-02
Numerical Methods For Nonlinear Estimating Equations written by Christopher G. Small and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-02 with Mathematics categories.
Nonlinearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators, and the use of root search algorithms, or one-step estimators, is a standard method of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihoods for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms, which, when started at points of nonconcavity often have very poor convergence properties, and for additional flexibility proposes a number of modifications to the standard methods for solving these algorithms. The book also extends beyond simple root search algorithms to include a discussion of the testing of roots for consistency, and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student. This is the latest in the well-established and authoritative Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. Each title has an original slant even if the material included is not specifically original. The authors are leading researchers and the topics covered will be of interest to all professional statisticians, whether they be in industry, government department or research institute. Other books in the series include 23. W.J.Krzanowski: Principles of multivariate analysis: a user's perspective updated edition 24. J.Durbin and S.J.Koopman: Time series analysis by State Space Models 25. Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e 26. J.K. Lindsey: Nonlinear Models in Medical Statistics 27. Peter J. Green, Nils L. Hjort & Sylvia Richardson: Highly Structured Stochastic Systems 28. Margaret S. Pepe: The Statistical Evaluation of Medical Tests for Classification and Prediction
Modeling Correlated Outcomes Using Extensions Of Generalized Estimating Equations And Linear Mixed Modeling
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Author : George J. Knafl
language : en
Publisher: Springer
Release Date : 2023-11-20
Modeling Correlated Outcomes Using Extensions Of Generalized Estimating Equations And Linear Mixed Modeling written by George J. Knafl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Mathematics categories.
This book formulates methods for modeling continuous and categorical correlated outcomes that extend the commonly used methods: generalized estimating equations (GEE) and linear mixed modeling. Partially modified GEE adds estimating equations for variance/dispersion parameters to the standard GEE estimating equations for the mean parameters. Fully modified GEE provides alternate estimating equations for mean parameters as well as estimating equations for variance/dispersion parameters. The new estimating equations in these two cases are generated by maximizing a "likelihood" function related to the multivariate normal density function. Partially modified GEE and fully modified GEE use the standard GEE approach to estimate correlation parameters based on the residuals. Extended linear mixed modeling (ELMM) uses the likelihood function to estimate not only mean and variance/dispersion parameters, but also correlation parameters. Formulations are provided for gradient vectors and Hessian matrices, for a multi-step algorithm for solving estimating equations, and model-based and robust empirical tests for assessing theory-based models. Standard GEE, partially modified GEE, fully modified GEE, and ELMM are demonstrated and compared using a variety of regression analyses of different types of correlated outcomes. Example analyses of correlated outcomes include linear regression for continuous outcomes, Poisson regression for count/rate outcomes, logistic regression for dichotomous outcomes, exponential regression for positive-valued continuous outcome, multinomial regression for general polytomous outcomes, ordinal regression for ordinal polytomous outcomes, and discrete regression for discrete numeric outcomes. These analyses also address nonlinearity in predictors based on adaptive search through alternative fractional polynomial models controlled by likelihood cross-validation (LCV) scores. Larger LCV scores indicate better models but not necessarily distinctly better models. LCV ratio tests are used to identify distinctly better models. A SAS macro has been developed for analyzing correlated outcomes using standard GEE, partially modified GEE, fully modified GEE, and ELMM within alternative regression contexts. This macro and code for conducting the analyses addressed in the book are available online via the book’s Springer website. Detailed descriptions of how to use this macro and interpret its output are provided in the book.
Modeling Binary Correlated Responses Using Sas Spss And R
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Author : Jeffrey R. Wilson
language : en
Publisher: Springer
Release Date : 2015-10-12
Modeling Binary Correlated Responses Using Sas Spss And R written by Jeffrey R. Wilson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-12 with Mathematics categories.
Statistical tools to analyze correlated binary data are spread out in the existing literature. This book makes these tools accessible to practitioners in a single volume. Chapters cover recently developed statistical tools and statistical packages that are tailored to analyzing correlated binary data. The authors showcase both traditional and new methods for application to health-related research. Data and computer programs will be publicly available in order for readers to replicate model development, but learning a new statistical language is not necessary with this book. The inclusion of code for R, SAS, and SPSS allows for easy implementation by readers. For readers interested in learning more about the languages, though, there are short tutorials in the appendix. Accompanying data sets are available for download through the book s website. Data analysis presented in each chapter will provide step-by-step instructions so these new methods can be readily applied to projects. Researchers and graduate students in Statistics, Epidemiology, and Public Health will find this book particularly useful.
A Graduate Course On Statistical Inference
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Author : Bing Li
language : en
Publisher: Springer
Release Date : 2019-08-02
A Graduate Course On Statistical Inference written by Bing Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-02 with Mathematics categories.
This textbook offers an accessible and comprehensive overview of statistical estimation and inference that reflects current trends in statistical research. It draws from three main themes throughout: the finite-sample theory, the asymptotic theory, and Bayesian statistics. The authors have included a chapter on estimating equations as a means to unify a range of useful methodologies, including generalized linear models, generalized estimation equations, quasi-likelihood estimation, and conditional inference. They also utilize a standardized set of assumptions and tools throughout, imposing regular conditions and resulting in a more coherent and cohesive volume. Written for the graduate-level audience, this text can be used in a one-semester or two-semester course.
Statistical Modelling
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Author : Gilg U.H. Seeber
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Statistical Modelling written by Gilg U.H. Seeber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume presents the published proceedings of the lOth International Workshop on Statistical Modelling, to be held in Innsbruck, Austria from 10 to 14 July, 1995. This workshop marks an important anniversary. The inaugural workshop in this series also took place in Innsbruck in 1986, and brought together a small but enthusiastic group of thirty European statisticians interested in statistical modelling. The workshop arose out of two G LIM conferences in the U. K. in London (1982) and Lancaster (1985), and from a num ber of short courses organised by Murray Aitkin and held at Lancaster in the early 1980s, which attracted many European statisticians interested in Generalised Linear Modelling. The inaugural workshop in Innsbruck con centrated on GLMs and was characterised by a number of features - a friendly and supportive academic atmosphere, tutorial sessions and invited speakers presenting new developments in statistical modelling, and a very well organised social programme. The academic programme allowed plenty of time for presentation and for discussion, and made available copies of all papers beforehand. Over the intervening years, the workshop has grown substantially, and now regularly attracts over 150 participants. The scope of the workshop is now much broader, reflecting the growth in the subject of statistical modelling over ten years. The elements ofthe first workshop, however, are still present, and participants always find the meetings relevant and stimulating.
Applied Longitudinal Analysis
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Author : Garrett M. Fitzmaurice
language : en
Publisher: John Wiley & Sons
Release Date : 2004-07
Applied Longitudinal Analysis written by Garrett M. Fitzmaurice and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07 with Mathematics categories.
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