Measurement Error

Measurement Error: Models, Methods, and Applications

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Features

  • Covers a wide array of statistical models, including misclassification in one- and two-way categorical tables, measurement error of various types in linear and nonlinear regression, measurement error in responses, mixed models, and time series
  • Describes common methods to correct for measurement error, such as SIMEX, regression calibration, likelihood-based techniques, and corrected estimating equations
  • Includes numerous worked examples using real-world data from epidemiology, ecology, and other disciplines

Summary

Over the last 20 years, comprehensive strategies for treating measurement error in complex models and accounting for the use of extra data to estimate measurement error parameters have emerged. Focusing on both established and novel approaches, Measurement Error: Models, Methods, and Applications provides an overview of the main techniques and illustrates their application in various models. It describes the impacts of measurement errors on naive analyses that ignore them and presents ways to correct for them across a variety of statistical models, from simple one-sample problems to regression models to more complex mixed and time series models.

The book covers correction methods based on known measurement error parameters, replication, internal or external validation data, and, for some models, instrumental variables. It emphasizes the use of several relatively simple methods, moment corrections, regression calibration, simulation extrapolation (SIMEX), modified estimating equation methods, and likelihood techniques. The author uses SAS-IML and Stata to implement many of the techniques in the examples.

Accessible to a broad audience, this book explains how to model measurement error, the effects of ignoring it, and how to correct for it. More applied than most books on measurement error, it describes basic models and methods, their uses in a range of application areas, and the associated terminology.

Table of Contents

Introduction
What is measurement error?
Some examples
The main ingredients
Some terminology
A look ahead

Misclassification in Estimating a Proportion
Motivating examples
A model for the true values
Misclassification models and naive analyses
Correcting for misclassification
Finite populations
Multiple measures with no direct validation
The multinomial case
Mathematical developments

Misclassification in Two-Way Tables
Introduction
Models for true values
Misclassification models and naive estimators
Behavior of naive analyses
Correcting using external validation data
Correcting using internal validation data
General two-way tables
Mathematical developments

Simple Linear Regression
Introduction
The additive Berkson model and consequences
The additive measurement error model
The behavior of naive analyses
Correcting for additive measurement error
Examples
Residual analysis
Prediction
Mathematical developments

Multiple Linear Regression
Introduction
Model for true values
Models and bias in naive estimators
Correcting for measurement error
Weighted and other estimators
Examples
Instrumental variables
Mathematical developments

Measurement Error in Regression: A General Overview
Introduction
Models for true values
Analyses without measurement error
Measurement error models
Extra data
Assessing bias in naive estimators
Assessing bias using induced models
Assessing bias via estimating equations
Moment based and direct bias corrections
Regression calibration and quasi-likelihood methods
Simulation extrapolation (SIMEX)
Correcting using likelihood methods
Modified estimating equation approaches
Correcting for misclassification
Overview on use of validation data
Bootstrapping
Mathematical developments

Binary Regression
Introduction
Additive measurement error
Using validation data
Misclassification of predictors

Linear Models with Nonadditive Error
Introduction
Quadratic regression
First-order models with interaction
General nonlinear functions of the predictors
Linear measurement error with validation data
Misclassification of a categorical predictor
Miscellaneous

Nonlinear Regression
Poisson regression: Cigarettes and cancer rates
General nonlinear models

Error in the Response
Introduction
Additive error in a single sample
Linear measurement error in the one-way setting
Measurement error in the response in linear models

Mixed/Longitudinal Models
Introduction, overview, and some examples
Berkson error in designed repeated measures
Additive error in the linear mixed model

Time Series
Introduction
Random walk/population viability models
Linear autoregressive models

Background Material
Notation for vectors, covariance matrices, etc.
Double expectations
Approximate Wald inferences
The delta-method: approximate moments of nonlinear functions
Fieller’s method for ratios

References

Author Index

Subject Index

Author Bio(s)

John P. Buonaccorsi is a professor in the Department of Mathematics and Statistics at the University of Massachusetts, Amherst.

Editorial Reviews

The author has written a praiseworthy summary of available results on measurement errors in a wide variety of statistical models. The author also covers results described in very recent papers, which have not been previously published in any other book. … The book brings a big help for theoretical researchers as well as applied statisticians who deal with data contaminated by measurement errors. The author demonstrates a very deep understanding for the theory and does not hesitate to discuss many specific theoretical problems. He succeeds very well in illustrating the methods on real examples and explaining the ideas to applied statisticians. Although not primarily intended for biostatisticians, I would say the book is suitable exactly for epidemiological and biostatistical applications. … very clearly and systematically organized. … the book offers an excellent and remarkable overview of available methods for incorporating measurement errors to statistical analysis.
—Jan Kalina, ISCB News, 52, December 2011

… we think Buonaccorsi’s book would be a great textbook … The book also contains many interesting data examples, which are useful for those concerned with applications. Overall, the book is also a good reference resource … We would recommend this book to people who are interested in statistical methods for measurement error.
—C.Y. Wang and X. Song, The American Statistician, August 2011

This book is a successful attempt to collect, organize and present the literature over the newly developed and earlier existing topics of measurement error models in one place. …The material that is presented in chapters [11 and 12] is, to my knowledge, not available in any other book on this area. … This book should be of immense help to those who are interested in the theoretical as well as applied aspects of measurement error models. … Some topics in the book may be used to teach advanced graduate courses. … The book is overall well written, presents updated developments in the area of measurement error models and is an excellent guide to applications. I am sure that it will stimulate researchers in and newcomers to this area.
Journal of the Royal Statistical Society, Series A, April 2011

There are plenty of illustrations and worked examples throughout … The book is very readable and clearly demonstrates the importance of recognizing measurement error, which is often ignored as a bit of a nuisance to be swept under the carpet. Together with easily accessible software, in the future, the problem is likely to be more commonly addressed and dealt with properly.
International Statistical Review (2010), 78, 3

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