2nd Edition

Measurement Error in Nonlinear Models A Modern Perspective, Second Edition

    484 Pages 75 B/W Illustrations
    by Chapman & Hall

    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.

    Guide to Notation
    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
    Bibliographic Notes
    Linear Regression and Attenuation
    Bias Caused by Measurement Error
    Multiple and Orthogonal Regression
    Correcting for Bias
    Bias Versus Variance
    Attenuation in General Problems
    Bibliographic Notes
    Regression Calibration
    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
    Simulation Extrapolation Heuristics
    The SIMEX Algorithm
    SIMEX in Some Important Special Cases
    Extensions and Related Methods
    Bibliographic Notes
    Instrumental Variables
    Instrumental Variables in Linear Models
    Approximate Instrumental Variable Estimation
    Adjusted Score Method
    Other Methodologies
    Bibliographic Notes
    Score Function Methods
    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
    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
    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
    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
    Regression Calibration for GLMMs
    Maximum Likelihood Estimation
    Joint Modeling
    Other Models and Applications
    Example: The CHOICE Study
    Bibliographic Notes
    Nonparametric Estimation
    Nonparametric Regression
    Baseline Change Example
    Bibliographic Notes
    Semiparametric Regression
    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
    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
    Instrumental Variables
    Score Function Methods
    Likelihood and Quasilikelihood
    Bayesian Methods
    Applications and Examples Index


    Carroll, Raymond J.; Ruppert, David; Stefanski, Leonard A.; Crainiceanu, Ciprian M.

    ". . . 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