Measurement Error ─ Models, Methods and Applications

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.

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

IntroductionWhat is measurement error? Some examples The main ingredients Some terminologyA look ahead
Misclassification in Estimating a Proportion Motivating examplesA model for the true values Misclassification models and naive analyses Correcting for misclassificationFinite populations Multiple measures with no direct validation The multinomial caseMathematical developments
Misclassification in Two-Way Tables Introduction Models for true values Misclassification models and naive estimators Behavior of naive analysesCorrecting using external validation dataCorrecting using internal validation dataGeneral two-way tablesMathematical developments
Simple Linear RegressionIntroduction The additive Berkson model and consequences The additive measurement error model The behavior of naive analyses Correcting for additive measurement errorExamplesResidual analysis PredictionMathematical developments
Multiple Linear RegressionIntroduction Model for true values Models and bias in naive estimators Correcting for measurement errorWeighted and other estimators ExamplesInstrumental variablesMathematical developments
Measurement Error in Regression: A General Overview Introduction Models for true values Analyses without measurement error Measurement error modelsExtra dataAssessing bias in naive estimatorsAssessing bias using induced modelsAssessing bias via estimating equationsMoment based and direct bias corrections Regression calibration and quasi-likelihood methods Simulation extrapolation (SIMEX) Correcting using likelihood methodsModified estimating equation approachesCorrecting for misclassification Overview on use of validation dataBootstrappingMathematical developments
Binary Regression Introduction Additive measurement errorUsing validation dataMisclassification of predictors
Linear Models with Nonadditive Error Introduction Quadratic regressionFirst-order models with interactionGeneral nonlinear functions of the predictorsLinear measurement error with validation dataMisclassification of a categorical predictorMiscellaneous
Nonlinear Regression Poisson regression: Cigarettes and cancer rates General nonlinear models
Error in the Response Introduction Additive error in a single sampleLinear measurement error in the one-way settingMeasurement error in the response in linear models
Mixed/Longitudinal Models Introduction, overview, and some examples Berkson error in designed repeated measuresAdditive error in the linear mixed model
Time SeriesIntroduction Random walk/population viability modelsLinear autoregressive models
Background Material Notation for vectors, covariance matrices, etc. Double expectations Approximate Wald inferences The delta-method: approximate moments of nonlinear functionsFieller’s method for ratios
References
Author Index
Subject Index