Generalized Estimating Equations Second Edition

Author: James W. Hardin
Publisher: CRC Press
ISBN: 1439881138
Format: PDF
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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, along with the software code used to create, run, and evaluate the models being examined. Stata is used as the primary software for running and displaying modeling output; associated R code is also given to allow R users to replicate Stata examples. Specific examples of SAS usage are provided in the final chapter as well as on the book’s website. This second edition incorporates comments and suggestions from a variety of sources, including the Statistics.com course on longitudinal and panel models taught by the authors. Other enhancements include an examination of GEE marginal effects; a more thorough presentation of hypothesis testing and diagnostics, covering competing hierarchical models; and a more detailed examination of previously discussed subjects. Along with doubling the number of end-of-chapter exercises, this edition expands discussion of various models associated with GEE, such as penalized GEE, cumulative and multinomial GEE, survey GEE, and quasi-least squares regression. It also offers a thoroughly new presentation of model selection procedures, including the introduction of an extension to the QIC measure that is applicable for choosing among working correlation structures. See Professor Hilbe discuss the book.

Generalized Estimating Equations

Author: James W. Hardin
Publisher: CRC Press
ISBN: 1420035282
Format: PDF
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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 health research, social science, biology, and other related fields. Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine the different varieties of generalized estimating equations and compare them with other methods, such as fixed and random effects models. The treatment then moves to residual analysis and goodness of fit, demonstrating many of the graphical and statistical techniques applicable to GEE analysis. With its careful balance of origins, applications, relationships, and interpretation, this book offers a unique opportunity to gain a full understanding of GEE methods, from their foundations to their implementation. While equally valuable to theorists, it includes the mathematical and algorithmic detail researchers need to put GEE into practice.

GENERALIZED ESTIMATING EQUATIONS FOR MIXED MODELS

Author: Lulah Alnaji
Publisher:
ISBN:
Format: PDF, ePub
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Most statistical approaches of molding the relationship between the explanatory variables and the responses assume subjects are independent. However, in clinical studies the longitudinal data are quite common. In this type of data, each subject is assessed repeatedly over a period of time. Therefore, the independence assumption is unlikely to be valid with longitudinal data due to the correlated observations of each subject. Generalized estimating equations method is a popular choice for longitudinal studies. It is an efficient method since it takes the within-subjects correlation into account by introducing a working correlation matrix. Although the generalized estimating equations' methodology considers correlation among the repeated observations on the same subject, it ignores the between-subject correlation and assumes subjects are independent. The objective of this dissertation is to provide an extension to the generalized estimating equations to take both within-subject and between-subject correlations into account by incorporating the random effect b to the model. If our interest focuses on the regression coefficients, we regard the correlation parameter as nuisance and estimate the fixed effects " using the estimating equations. If our interest focuses either on both the correlation parameter and the variance of the random effects or on the coefficient parameters and the association structure, then building an additional system of estimating equations analogous to the first estimating equations can serve to estimate either the correlation parameter and coefficients parameter, simultaneously or the variance of the random effects and the coefficient parameter, simultaneously. This estimating equations method has no closed form solution and can be solved iteratively. For example, Newton-Raphson is a popular iterative method to be used. We illustrate through simulation studies and real data applications the performance of the proposed methods in terms of bias and efficiency. Moreover, we investigate their behaviors compared to those for existing methods such as generalized estimating equations (GEE), generalized linear models (GLM) and generalized linear mixed models (GLMM). For further studying the performance of newly proposed method, the new approach is applied to the epilepsy data that was studied by many others Fitzmaurice, Laird, and Ware (2012).

Generalized Estimating Equations

Author: Andreas Ziegler
Publisher: Springer Science & Business Media
ISBN: 9781461404996
Format: PDF, Docs
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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.

Robustness of Generalized Estimating Equations in Credibility Models

Author: Danwei Huang
Publisher:
ISBN: 9781374672895
Format: PDF, Kindle
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This dissertation, "Robustness of Generalized Estimating Equations in Credibility Models" by Danwei, Huang, 黃丹薇, 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 thesis entitled ROBUSTNESS OF GENERALIZED ESTIMATING EQUATIONS IN CREDIBILITY MODELS Submitted by HUANG DAN WEI for the degree of Master of Philosophy at The University of Hong Kong in July 2007 Credibility theory is a branch of actuarial science. It provides tools to pre- dict future events or costs and helps the insurer adjust appropriately the premium charged to the policyholders. Since the insurance data can be interpreted in the context of statistical longitudinal data, there is a growing trend relating the cred- ibility theory and the generalized linear (mixed) model in parameter estimation. However, the generalized linear model (GLM) does not normally allow for serial correlation, which is a practical problem that needs to be addressed in the credi- bility context.As a supplement to the GLM in handling correlated data, a GEE (generalized estimating equations) approach has recently been proposed to estimate the struc- tural parameters in a regression credibility model which encapsulates a moving average error structure. Simulation results have shown that the GEE estimator performs well in comparison with the Buhlmann A estimator, the Buhlmann-Straub A estimatorandtheHachemeister'sestimator. ButintheGEEestimationprocedure, anormalityassumptionwasimposedandthecomparisonwasalsomadeinthenor- mal environment. When the normality assumption is violated, the performance of the GEE approach needs to be investigated. The study reported in this thesis aimed to check the robustness of the GEE es- timator in a non-normal environment. To sustain the estimation eciency, a mod- ication of the GEE estimation procedure is proposed to handle the high skewness and kurtosis of a non-normal distribution. Furthermore, diversied error structure assumptions are incorporated in the estimation procedure. The study considered the autoregressive and exchangeable error structures in addition to the moving average assumption, and estimation performances associated with these di(R)erent error structures were examined via simulation studies. In addition, the study also aimed to extend the application of the GEE method to another credibility model, the hierarchical credibility model. Derivation of the GEE estimator within the hi-erarchicalframeworkispresentedandnumericalexamplesareprovidedtofacilitate the comparison between the classical unbiased estimator and the GEE estimator. The study aimed to provide a thorough and comprehensive picture of the applica- tion of the GEE approach within the credibility context. DOI: 10.5353/th_b3884231 Subjects: Credibility theory (Insurance) Insurance - Mathematics

Markov Chain Marginal Bootstrap for Generalized Estimating Equations

Author: Di Li
Publisher: ProQuest
ISBN: 9780549340836
Format: PDF, Mobi
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Longitudinal data are characterized by repeated measures over time on each subject. The generalized estimating equations (GEE) approach (Liang and Zeger, 1996) has been widely used for the analysis of longitudinal data. The ordinary GEE approach can be robustified through the use of truncated robust estimating functions. Statistical inference on the robust GEE is often based on the asymptotic normality of the estimators, and the asymptotic variance-covariance of the regression parameter estimates can be obtained from a sandwich formula. However, this asymptotic variance-covariance matrix may depend on unknown error density functions. Direct estimation of this matrix can be difficult and unreliable since it depends quite heavily on the nonparametric density estimation. Resampling methods provide an alternative way for estimating the variance of the regression parameter estimates. In this thesis, we extend the Markov chain marginal bootstrap (MCMB) (He and Hu, 2002) to statistical inference for robust GEE estimators with longitudinal data, allowing the estimating functions to be non-smooth and the responses correlated within subjects. By decomposing the problem into one-dimensions and solving the marginal estimating equations at each step instead of solving a p--dimensional system of equations, the MCMB method renders more control to the problem and offers advantages over traditional bootstrap methods for robust GEE estimators where the estimating equation may not be easy to solve. Empirical investigations show favorable performance of the MCMB method in accuracy and reliability compared with the traditional way of inference by direct estimation of the asymptotic variance-covariance.

Longitudinal Data Analysis

Author: Garrett Fitzmaurice
Publisher: CRC Press
ISBN: 9781420011579
Format: PDF, ePub, Mobi
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Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory and applications. It also focuses on the assorted challenges that arise in analyzing longitudinal data. After discussing historical aspects, leading researchers explore four broad themes: parametric modeling, nonparametric and semiparametric methods, joint models, and incomplete data. Each of these sections begins with an introductory chapter that provides useful background material and a broad outline to set the stage for subsequent chapters. Rather than focus on a narrowly defined topic, chapters integrate important research discussions from the statistical literature. They seamlessly blend theory with applications and include examples and case studies from various disciplines. Destined to become a landmark publication in the field, this carefully edited collection emphasizes statistical models and methods likely to endure in the future. Whether involved in the development of statistical methodology or the analysis of longitudinal data, readers will gain new perspectives on the field.