Generalized Estimating Equations

  • Filename: generalized-estimating-equations.
  • ISBN: 1461404991
  • Release Date: 2011-06-17
  • Number of pages: 144
  • Author: Andreas Ziegler
  • Publisher: Springer Science & Business Media



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.

Markov Chain Marginal Bootstrap for Generalized Estimating Equations

  • Filename: markov-chain-marginal-bootstrap-for-generalized-estimating-equations.
  • ISBN: 9780549340836
  • Release Date: 2007
  • Number of pages: 90
  • Author: Di Li
  • Publisher: ProQuest



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.

Generalized Estimating Equations

  • Filename: generalized-estimating-equations.
  • ISBN: 9781420035285
  • Release Date: 2002-07-30
  • Number of pages: 240
  • Author: James W. Hardin
  • Publisher: CRC Press



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 Second Edition

  • Filename: generalized-estimating-equations-second-edition.
  • ISBN: 9781439881149
  • Release Date: 2012-12-10
  • Number of pages: 277
  • Author: James W. Hardin
  • Publisher: CRC Press



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.

Model Robust Regression Based on Generalized Estimating Equations

  • Filename: model-robust-regression-based-on-generalized-estimating-equations.
  • ISBN: 0542957612
  • Release Date: 2002
  • Number of pages: 236
  • Author:
  • Publisher: ProQuest



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

  • Filename: applied-longitudinal-data-analysis-for-epidemiology.
  • ISBN: 9781107067608
  • Release Date: 2013-05-09
  • Number of pages:
  • Author: Jos W. R. Twisk
  • Publisher: Cambridge University Press



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.

Longitudinal Data Analysis

  • Filename: longitudinal-data-analysis.
  • ISBN: 142001157X
  • Release Date: 2008-08-11
  • Number of pages: 632
  • Author: Garrett Fitzmaurice
  • Publisher: CRC Press



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.

Multilevel Analysis

  • Filename: multilevel-analysis.
  • ISBN: 9780805832181
  • Release Date: 2002
  • Number of pages: 304
  • Author: J. J. Hox
  • Publisher: Psychology Press



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.

Unconditional Estimating Equation Approaches for Missing Data

  • Filename: unconditional-estimating-equation-approaches-for-missing-data.
  • ISBN: 9780549405184
  • Release Date: 2007
  • Number of pages: 86
  • Author:
  • Publisher: ProQuest



Missing data can lead to biased and inefficient estimation if the missing mechanism is not taken into account in the analysis. In this dissertation we propose two estimators that, under fairly general conditions, are asymptotically unbiased. The first proposed estimator assume the data are missing at random (MAR) and does not require a model for the missing mechanism. The second estimator allows the missingness to be nonignorable and requires a model for the mechanism. Both proposed approaches utilize generalized estimating equations (GEE) based on unconditional models.

Governance Impact on Private Investment

  • Filename: governance-impact-on-private-investment.
  • ISBN: 0821348183
  • Release Date: 2000
  • Number of pages: 79
  • Author: Nina Bubnova
  • Publisher: World Bank Publications



During the last decade, infrastructure finance and provision graduated from traditional means to more innovative ones, primarily initiated by private companies and supported through their equity and debt. Capital markets increasingly became the main funding source for infrastructure projects worldwide, including investments in developing and transition countries where infrastructure penetration still falls considerably short of needs. Infrastructure bonds served as the most popular method of oil, gas, electricity, telecommunications, and transport project financing in these countries throughout 1990-99, thereby substituting government funding. Using an innovative methodological approach, 'Governance Impact on Private Investment' provides a thorough examination of the effect that governance frameworks, both political and regulatory, have on investors' risk perceptions and on associated costs for infrastructure financing. It identifies those political and regulatory risks that most concern investors. It offers a unique comparative analysis of developed and emerging infrastructure bond markets. The analysis demonstrates how the factors that drive infrastructure finance in the two country groups differ, which helps to identify the policy implications of these factors.

Quasi Least Squares Regression

  • Filename: quasi-least-squares-regression.
  • ISBN: 9781420099935
  • Release Date: 2014-01-28
  • Number of pages: 221
  • Author: Justine Shults
  • Publisher: CRC Press



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.

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