Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition, 2nd Edition (Hardback) book cover

Measurement Error in Nonlinear Models

A Modern Perspective, Second Edition, 2nd Edition

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

Chapman and Hall/CRC

484 pages | 75 B/W Illus.

Purchasing Options:$ = USD
Hardback: 9781584886334
pub: 2006-06-21
SAVE ~$28.00
eBook (VitalSource) : 9780429139635
pub: 2006-06-21
from $70.00

FREE Standard Shipping!


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.


". . . 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

Table of Contents

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


About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General