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Measurement Error in Nonlinear Models
A Modern Perspective, Second Edition




ISBN 9781584886334
Published June 21, 2006 by Chapman and Hall/CRC
484 Pages - 75 B/W Illustrations

 
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Book Description

It’s been over a decade since the first edition of Measurement Error in Nonlinear Models splashed onto the scene, and research in the field has certainly not cooled in the interim. In fact, quite the opposite has occurred. As a result, Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition has been revamped and extensively updated to offer the most comprehensive and up-to-date survey of measurement error models currently available.

What’s new in the Second Edition?

·         Greatly expanded discussion and applications of Bayesian computation via Markov Chain Monte Carlo techniques

·         A new chapter on longitudinal data and mixed models

·         A thoroughly revised chapter on nonparametric regression and density estimation

·         A totally new chapter on semiparametric regression

·         Survival analysis expanded into its own separate chapter

·         Completely rewritten chapter on score functions

·         Many more examples and illustrative graphs

·         Unique data sets compiled and made available online

In addition, the authors expanded the background material in Appendix A and integrated the technical material from chapter appendices into a new Appendix B for convenient navigation. Regardless of your field, if you’re looking for the most extensive discussion and review of measurement error models, then Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition is your ideal source.

Table of Contents

Guide to Notation
Introduction
The Double/Triple-Whammy of Measurement Error
Classical Measurement Error A Nutrition Example
Measurement Error Examples
Radiation Epidemiology and Berkson Errors
Classical Measurement Error Model Extensions
Other Examples of Measurement Error Models
Checking The Classical Error Model
Loss of Power
A Brief Tour
Bibliographic Notes
Important Concepts
Functional and Structural Models
Models for Measurement Error
Sources of Data
Is There an “Exact" Predictor? What is Truth?
Differential and Nondifferential Error
Prediction
Bibliographic Notes
Linear Regression and Attenuation
Introduction
Bias Caused by Measurement Error
Multiple and Orthogonal Regression
Correcting for Bias
Bias Versus Variance
Attenuation in General Problems
Bibliographic Notes
Regression Calibration
Overview
The Regression Calibration Algorithm
NHANES Example
Estimating the Calibration Function Parameters
Multiplicative Measurement Error
Standard Errors
Expanded Regression Calibration Models
Examples of the Approximations
Theoretical Examples
Bibliographic Notes and Software
Simulation Extrapolation
Overview
Simulation Extrapolation Heuristics
The SIMEX Algorithm
Applications
SIMEX in Some Important Special Cases
Extensions and Related Methods
Bibliographic Notes
Instrumental Variables
Overview
Instrumental Variables in Linear Models
Approximate Instrumental Variable Estimation
Adjusted Score Method
Examples
Other Methodologies
Bibliographic Notes
Score Function Methods
Overview
Linear and Logistic Regression
Conditional Score Functions
Corrected Score Functions
Computation and Asymptotic Approximations
Comparison of Conditional and Corrected Scores
Bibliographic Notes
Likelihood and Quasilikelihood
Introduction
Steps 2 and 3: Constructing Likelihoods
Step 4: Numerical Computation of Likelihoods
Cervical Cancer and Herpes
Framingham Data
Nevada Test Site Reanalysis
Bronchitis Example
Quasilikelihood and Variance Function Models
Bibliographic Notes
Bayesian Methods
Overview
The Gibbs Sampler
Metropolis-Hastings Algorithm
Linear Regression
Nonlinear Models
Logistic Regression
Berkson Errors
Automatic implementation
Cervical Cancer and Herpes
Framingham Data
OPEN Data: A Variance Components Model
Bibliographic Notes
Hypothesis Testing
Overview
The Regression Calibration Approximation
Illustration: OPEN Data
Hypotheses about Sub-Vectors of βx and βz
Efficient Score Tests of H0 : βx = 0
Bibliographic Notes
Longitudinal Data and Mixed Models
Mixed Models for Longitudinal Data
Mixed Measurement Error Models
A Bias Corrected Estimator
SIMEX for GLMMEMs
Regression Calibration for GLMMs
Maximum Likelihood Estimation
Joint Modeling
Other Models and Applications
Example: The CHOICE Study
Bibliographic Notes
Nonparametric Estimation
Deconvolution
Nonparametric Regression
Baseline Change Example
Bibliographic Notes
Semiparametric Regression
Overview
Additive Models
MCMC for Additive Spline Models
Monte-Carlo EM-Algorithm
Simulation with Classical Errors
Simulation with Berkson Errors
Semiparametrics: X Modeled Parametrically
Parametric Models: No Assumptions on X
Bibliographic Notes
Survival Data
Notation and Assumptions
Induced Hazard Function
Regression Calibration for Survival Analysis
SIMEX for Survival Analysis
Chronic Kidney Disease Progression
Semi and Nonparametric Methods
Likelihood Inference for Frailty Models
Bibliographic Notes
Response Variable Error
Response Error and Linear Regression
Other Forms of Additive Response Error
Logistic Regression with Response Error
Likelihood Methods
Use of Complete Data Only
Semiparametric Methods for Validation Data
Bibliographic Notes
Appendix A: Background Material
Overview
Normal and Lognormal Distributions
Gamma and Inverse Gamma Distributions
Best and Best Linear Prediction and Regression
Likelihood Methods
Unbiased Estimating Equations
Quasilikelihood and Variance Function Models (QVF)
Generalized Linear Models
Bootstrap Methods
Appendix B: Technical Details
Appendix to Chapter 1: Power in Berkson and Classical Error Models
Appendix to Chapter 3: Linear Regression and Attenuation
Regression Calibration
SIMEX
Instrumental Variables
Score Function Methods
Likelihood and Quasilikelihood
Bayesian Methods
References
Applications and Examples Index
Index

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Reviews

". . . they are to be congratulated for producing a first-rate book that will be an indispensible resource for researchers and other serious students of the statistics of measurement error."

– Daniel B. Hall, University of Georgia, in Journal of the American Statistical Association, March 2008, Vol. 103, No. 481

“…This book is a successful attempt at collecting, organizing, and presenting the scattered literature in one place. The authors have already successfully accomplished this task in the first edition of this book. The second edition is an extensively revised, enlarged, and improved version of this earlier edition. The updated coverage of techniques and methodologies and the updated bibliography are of great help to those working on the theoretical and applied aspects of the nonlinear measurement error models. This book is a must for all who want to start working in this area. The style of writing and the sequence of topics in the chapters are excellent [and] easily understandable … . Most of the topics are accompanied by illustrated examples, which make understanding of the topics easy. Every chapter concludes with bibliographic notes. Wherever possible, the authors have given an account of the available software … . The derivations of the results are presented separately in an appendix. … This monograph should be of interest and immense help to those interested in the theoretical as well as applied aspects of nonlinear measurement error models. It can also be used as a textbook for a specialized graduate-level course. …”
Statistical Papers, Vol. 49, 2008

". . . has made an important contribution to the modern perspective of measurement error models. The book would be a valuable addition to any statistical researcher’s library."

– Eugenia Stoimenova, Institute of Mathematics and Informatics, in Journal of Applied Statistics, September 2007, Vol. 34, No. 4


“This is the second edition of a research-level monograph … about modeling with predictors that are subject to measurement error … . The text describes a variety of approaches to handling such data and illustrates the models and methods with numerous examples. The early chapters set the scene with a clear description of the problem through many examples, a discussion of the different types of error, and the distinction between functional and structural models. These two types of models form the basis of the second and third parts … with the final part devoted to more specialized material including generalized linear structure with an unknown link function, hypothesis testing, and nonparametric regression. … this edition has been expanded by the inclusion of much more detailed sections, even completely new chapters, on Bayesian MCMC techniques, longitudinal data and mixed models, score functions, and survival analysis. The end result is an up-to-date rigorous treatment of the general ideas and methods of estimation and inference in difficult problems involving nonlinear measurement error models.”
—P. Prescott (University of Southampton, UK), Short Book Reviews, December 2006