Buonaccorsi Measurement Error

Models, Methods, and Applications
Erscheinungsjahr 2010
ISBN: 978-1-4200-6658-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 464 Seiten

Reihe: Chapman & Hall/CRC Interdisciplinary Statistics

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.

Zielgruppe

Researchers and graduate students in biostatistics; quantitative researchers in epidemiology, public health, econometrics, ecology, and social sciences.

Autoren/Hrsg.

Buonaccorsi, John P.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Forschungsmethodik, Wissenschaftliche Ausstattung

Inhaltsverzeichnis

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

Über Autor(innen)

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