Generalized Estimating Equations Second Edition

Author: James W. Hardin
Publisher: CRC Press
ISBN: 1439881138
Format: PDF, ePub
Download Now
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: Andreas Ziegler
Publisher: Springer Science & Business Media
ISBN: 9781461404996
Format: PDF, ePub
Download Now
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, Docs
Download Now
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
Download Now
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
Download Now
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.

Model Robust Regression Based on Generalized Estimating Equations

Author: Seth K. Clark
Publisher:
ISBN:
Format: PDF, ePub
Download Now
One form of model robust regression (MRR) predicts mean response as a convex combination of a parametric and a nonparametric prediction. MRR is a semiparametric method by which an incompletely or an incorrectly specified parametric model can be improved through adding an appropriate amount of a nonparametric fit. The combined predictor can have less bias than the parametric model estimate alone and less variance than the nonparametric estimate alone. Additionally, as shown in previous work for uncorrelated data with linear mean function, MRR can converge faster than the nonparametric predictor alone. We extend the MRR technique to the problem of predicting mean response for clustered non-normal data. We combine a nonparametric method based on local estimation with a global, parametric generalized estimating equations (GEE) estimate through a mixing parameter on both the mean scale and the linear predictor scale. As a special case, when data are uncorrelated, this amounts to mixing a local likelihood estimate with predictions from a global generalized linear model. Cross-validation bandwidth and optimal mixing parameter selectors are developed. The global fits and the optimal and data-driven local and mixed fits are studied under no/some/substantial model misspecification via simulation. The methods are then illustrated through application to data from a longitudinal study.

Applied Longitudinal Data Analysis for Epidemiology

Author: Jos W. R. Twisk
Publisher: Cambridge University Press
ISBN: 110706760X
Format: PDF, ePub, Docs
Download Now
This book discusses the most important techniques available for longitudinal data analysis, from simple techniques such as the paired t-test and summary statistics, to more sophisticated ones such as generalized estimating of equations and mixed model analysis. A distinction is made between longitudinal analysis with continuous, dichotomous and categorical outcome variables. The emphasis of the discussion lies in the interpretation and comparison of the results of the different techniques. The second edition includes new chapters on the role of the time variable and presents new features of longitudinal data analysis. Explanations have been clarified where necessary and several chapters have been completely rewritten. The analysis of data from experimental studies and the problem of missing data in longitudinal studies are discussed. Finally, an extensive overview and comparison of different software packages is provided. This practical guide is essential for non-statisticians and researchers working with longitudinal data from epidemiological and clinical studies.

Multilevel Analysis

Author: J. J. Hox
Publisher: Psychology Press
ISBN: 0805832181
Format: PDF, Docs
Download Now
This volume provides an introduction to multilevel analysis for applied researchers. The book presents two types of multilevel models: the multilevel regression model; and a model for multilevel covariance structures.