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Summary
Summary
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.
"The effort of Professor Fuller is commendable . . . [the book] provides a complete treatment of an important and frequently ignored topic. Those who work with measurement error models will find it valuable. It is the fundamental book on the subject, and statisticians will benefit from adding this book to their collection or to university or departmental libraries."
-Biometrics
"Given the large and diverse literature on measurement error/errors-in-variables problems, Fuller's book is most welcome. Anyone with an interest in the subject should certainly have this book."
-Journal of the American Statistical Association
"The author is to be commended for providing a complete presentation of a very important topic. Statisticians working with measurement error problems will benefit from adding this book to their collection."
-Technometrics
" . . . this book is a remarkable achievement and the product of impressive top-grade scholarly work."
-Journal of Applied Econometrics
Measurement Error Models offers coverage of estimation for situations where the model variables are observed subject to measurement error. Regression models are included with errors in the variables, latent variable models, and factor models. Results from several areas of application are discussed, including recent results for nonlinear models and for models with unequal variances. The estimation of true values for the fixed model, prediction of true values under the random model, model checks, and the analysis of residuals are addressed, and in addition, procedures are illustrated with data drawn from nearly twenty real data sets.
Author Notes
Wayne A. Fuller, PhD, is Distinguished Professor Emeritus in the Department of Economics at Iowa State University
Table of Contents
| List of Examples | p. xv |
| List of Principal Results | p. xix |
| List of Figures | p. xxiii |
| 1 A Single Explanatory Variable | p. 1 |
| 1.1 Introduction | p. 1 |
| 1.1.1 Ordinary Least Squares and Measurement Error | p. 1 |
| 1.1.2 Estimation with Known Reliability Ratio | p. 5 |
| 1.1.3 Identification | p. 9 |
| 1.2 Measurement Variance Known | p. 13 |
| 1.2.1 Introduction and Estimators | p. 13 |
| 1.2.2 Sampling Properties of the Estimators | p. 15 |
| 1.2.3 Estimation of True x Values | p. 20 |
| 1.2.4 Model Checks | p. 25 |
| 1.3 Ratio of Measurement Variances Known | p. 30 |
| 1.3.1 Introduction | p. 30 |
| 1.3.2 Method of Moments Estimators | p. 30 |
| 1.3.3 Least Squares Estimation | p. 36 |
| 1.3.4 Tests of Hypotheses for the Slope | p. 44 |
| 1.4 Instrumental Variable Estimation | p. 50 |
| 1.5 Factor Analysis | p. 59 |
| 1.6 Other Methods and Models | p. 72 |
| 1.6.1 Distributional Knowledge | p. 72 |
| 1.6.2 The Method of Grouping | p. 73 |
| 1.6.3 Measurement Error and Prediction | p. 74 |
| 1.6.4 Fixed Observed X | p. 79 |
| Appendix 1.A Large Sample Approximations | p. 85 |
| Appendix 1.B Moments of the Normal Distribution | p. 88 |
| Appendix 1.C Central Limit Theorems for Sample Moments | p. 89 |
| Appendix 1.D Notes on Notation | p. 95 |
| 2 Vector Explanatory Variables | p. 100 |
| 2.1 Bounds for Coefficients | p. 100 |
| 2.2 The Model with an Error in the Equation | p. 103 |
| 2.2.1 Estimation of Slope Parameters | p. 103 |
| 2.2.2 Estimation of True Values | p. 113 |
| 2.2.3 Higher-Order Approximations for Residuals and True Values | p. 118 |
| 2.3 The Model with No Error in the Equation | p. 124 |
| 2.3.1 The Functional Model | p. 124 |
| 2.3.2 The Structural Model | p. 139 |
| 2.3.3 Higher-Order Approximations for Residuals and True Values | p. 140 |
| 2.4 Instrumental Variable Estimation | p. 148 |
| 2.5 Modifications to Improve Moment Properties | p. 163 |
| 2.5.1 An Error in the Equation | p. 164 |
| 2.5.2 No Error in the Equation | p. 173 |
| 2.5.3 Calibration | p. 177 |
| Appendix 2.A Language Evaluation Data | p. 181 |
| 3 Extensions of the Single Relation Model | p. 185 |
| 3.1 Nonnormal Errors and Unequal Error Variances | p. 185 |
| 3.1.1 Introduction and Estimators | p. 186 |
| 3.1.2 Models with an Error in the Equation | p. 193 |
| 3.1.3 Reliability Ratios Known | p. 199 |
| 3.1.4 Error Variance Functionally Related to Observations | p. 202 |
| 3.1.5 The Quadratic Model | p. 212 |
| 3.1.6 Maximum Likelihood Estimation for Known Error Covariance Matrices | p. 217 |
| 3.2 Nonlinear Models with No Error in the Equation | p. 225 |
| 3.2.1 Introduction | p. 225 |
| 3.2.2 Models Linear in x | p. 226 |
| 3.2.3 Models Nonlinear in x | p. 229 |
| 3.2.4 Modifications of the Maximum Likelihood Estimator | p. 247 |
| 3.3 The Nonlinear Model with an Error in the Equation | p. 261 |
| 3.3.1 The Structural Model | p. 261 |
| 3.3.2 General Explanatory Variables | p. 263 |
| 3.4 Measurement Error Correlated with True Value | p. 271 |
| 3.4.1 Introduction and Estimators | p. 271 |
| 3.4.2 Measurement Error Models for Multinomial Random Variables | p. 272 |
| Appendix 3.A Data for Examples | p. 281 |
| 4 Multivariate Models | p. 292 |
| 4.1 The Classical Multivariate Model | p. 292 |
| 4.1.1 Maximum Likelihood Estimation | p. 292 |
| 4.1.2 Properties of Estimators | p. 303 |
| 4.2 Least Squares Estimation of the Parameters of a Covariance Matrix | p. 321 |
| 4.2.1 Least Squares Estimation | p. 321 |
| 4.2.2 Relationships between Least Squares and Maximum Likelihood | p. 333 |
| 4.2.3 Least Squares Estimation for the Multivariate Functional Model | p. 338 |
| 4.3 Factor Analysis | p. 350 |
| 4.3.1 Introduction and Model | p. 350 |
| 4.3.2 Maximum Likelihood Estimation | p. 353 |
| 4.3.3 Limiting Distribution of Factor Estimators | p. 360 |
| Appendix 4.A Matrix-Vector Operations | p. 382 |
| Appendix 4.B Properties of Least Squares and Maximum Likelihood Estimators | p. 396 |
| Appendix 4.C Maximum Likelihood Estimation for Singular Measurement Covariance | p. 404 |
| Bibliography | p. 409 |
| Author Index | p. 433 |
| Subject Index | p. 435 |
