Regression Calibration And Maximum Likelihood Inference For Measurement Error Models

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Regression Calibration and Maximum Likelihood Inference for Measurement Error Models

Author : Vicente J. Monleon-Moscardo
Publisher :
ISBN 13 :
Total Pages : 252 pages
Book Rating : 4.:/5 (635 download)

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Book Synopsis Regression Calibration and Maximum Likelihood Inference for Measurement Error Models by : Vicente J. Monleon-Moscardo

Download or read book Regression Calibration and Maximum Likelihood Inference for Measurement Error Models written by Vicente J. Monleon-Moscardo and published by . This book was released on 2005 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression calibration inference seeks to estimate regression models with measurement error in explanatory variables by replacing the mismeasured variable by its conditional expectation, given a surrogate variable, in an estimation procedure that would have been used if the true variable were available. This study examines the effect of the uncertainty in the estimation of the required conditional expectation on inference about regression parameters, when the true explanatory variable and its surrogate are observed in a calibration dataset and related through a normal linear model. The exact sampling distribution of the regression calibration estimator is derived for normal linear regression when independent calibration data are available. The sampling distribution is skewed and its moments are not defined, but its median is the parameter of interest. It is shown that, when all random variables are normally distributed, the regression calibration estimator is equivalent to maximum likelihood provided a natural estimate of variance is non-negative. A check for this equivalence is useful in practice for judging the suitability of regression calibration. Results about relative efficiency are provided for both external and internal calibration data. In some cases maximum likelihood is substantially more efficient than regression calibration. In general, though, a more important concern when the necessary conditional expectation is uncertain, is that inferences based on approximate normality and estimated standard errors may be misleading. Bootstrap and likelihood-ratio inferences are preferable.

Measurement Error in Nonlinear Models

Author : Raymond J. Carroll
Publisher : CRC Press
ISBN 13 : 9780412047213
Total Pages : 334 pages
Book Rating : 4.0/5 (472 download)

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Book Synopsis Measurement Error in Nonlinear Models by : Raymond J. Carroll

Download or read book Measurement Error in Nonlinear Models written by Raymond J. Carroll and published by CRC Press. This book was released on 1995-07-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an up-to-date discussion of analysis strategies for regression problems in which predictor variables are measured with errors. The analysis of nonlinear regression models includes generalized linear models, transform-both-sides models and quasilikelihood and variance function problems. The text concentrates on the general ideas and strategies of estimation and inference rather than being concerned with a specific problem. Measurement error occurs in many fields, such as biometry, epidemiology and economics. In particular, the book contains a large number of epidemiological examples. An outline of strategies for handling progressively more difficult problems is also provided.

Statistical Analysis of Measurement Error Models and Applications

Author : Philip J. Brown
Publisher : American Mathematical Soc.
ISBN 13 : 9780821854457
Total Pages : 264 pages
Book Rating : 4.8/5 (544 download)

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Book Synopsis Statistical Analysis of Measurement Error Models and Applications by : Philip J. Brown

Download or read book Statistical Analysis of Measurement Error Models and Applications written by Philip J. Brown and published by American Mathematical Soc.. This book was released on 1990-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measurement error models describe functional relationships among variables observed, subject to random errors of measurement. Examples include linear and nonlinear errors-in-variables regression models, calibration and inverse regression models, factor analysis models, latent structure models, and simultaneous equations models. Such models are used in a wide variety of areas, including medicine, the life sciences, econometrics, chemometrics, geology, sample surveys, and time series. Although the problem of estimating the parameters of such models exists in most scientific fields, there is a need for more sources that treat measurement error models as an area of statistical methodology. This volume is designed to address that need. This book contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Statistical Analysis of Measurement Error Models and Applications. The conference was held at Humboldt State University in Arcata, California in June 1989. The papers in this volume fall into four broad groups. The first group treats general aspects of the measurement problem and features a discussion of the history of measurement error models. The second group focuses on inference for the nonlinear measurement error model, an active area of research which generated considerable interest at the conference. The third group of papers examines computational aspects of estimation, while the final set studies estimators possessing robustness properties against deviations from common model assumptions.

Semiparametric Maximum Likelihood for Regression with Measurement Error

Author : Eun-Young Suh
Publisher :
ISBN 13 :
Total Pages : 202 pages
Book Rating : 4.:/5 (482 download)

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Book Synopsis Semiparametric Maximum Likelihood for Regression with Measurement Error by : Eun-Young Suh

Download or read book Semiparametric Maximum Likelihood for Regression with Measurement Error written by Eun-Young Suh and published by . This book was released on 2001 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semiparametric maximum likelihood analysis allows inference in errors-invariables models with small loss of efficiency relative to full likelihood analysis but with significantly weakened assumptions. In addition, since no distributional assumptions are made for the nuisance parameters, the analysis more nearly parallels that for usual regression. These highly desirable features and the high degree of modelling flexibility permitted warrant the development of the approach for routine use. This thesis does so for the special cases of linear and nonlinear regression with measurement errors in one explanatory variable. A transparent and flexible computational approach is developed, the analysis is exhibited on some examples, and finite sample properties of estimates, approximate standard errors, and likelihood ratio inference are clarified with simulation.

Measurement Error in Nonlinear Models

Author : Raymond J. Carroll
Publisher : CRC Press
ISBN 13 : 1420010131
Total Pages : 484 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Measurement Error in Nonlinear Models by : Raymond J. Carroll

Download or read book Measurement Error in Nonlinear Models written by Raymond J. Carroll and published by CRC Press. This book was released on 2006-06-21 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ex

Measurement Error

Author : John P. Buonaccorsi
Publisher : CRC Press
ISBN 13 : 1420066587
Total Pages : 465 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Measurement Error by : John P. Buonaccorsi

Download or read book Measurement Error written by John P. Buonaccorsi and published by CRC Press. This book was released on 2010-03-02 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 illu

Handbook of Measurement Error Models

Author : Grace Y. Yi
Publisher : CRC Press
ISBN 13 : 1351588591
Total Pages : 648 pages
Book Rating : 4.3/5 (515 download)

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Book Synopsis Handbook of Measurement Error Models by : Grace Y. Yi

Download or read book Handbook of Measurement Error Models written by Grace Y. Yi and published by CRC Press. This book was released on 2021-09-28 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measurement error arises ubiquitously in applications and has been of long-standing concern in a variety of fields, including medical research, epidemiological studies, economics, environmental studies, and survey research. While several research monographs are available to summarize methods and strategies of handling different measurement error problems, research in this area continues to attract extensive attention. The Handbook of Measurement Error Models provides overviews of various topics on measurement error problems. It collects carefully edited chapters concerning issues of measurement error and evolving statistical methods, with a good balance of methodology and applications. It is prepared for readers who wish to start research and gain insights into challenges, methods, and applications related to error-prone data. It also serves as a reference text on statistical methods and applications pertinent to measurement error models, for researchers and data analysts alike. Features: Provides an account of past development and modern advancement concerning measurement error problems Highlights the challenges induced by error-contaminated data Introduces off-the-shelf methods for mitigating deleterious impacts of measurement error Describes state-of-the-art strategies for conducting in-depth research

Application and Computation of Likelihood Methods for Regression with Measurement Error

Author : Roger Higdon
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.:/5 (41 download)

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Book Synopsis Application and Computation of Likelihood Methods for Regression with Measurement Error by : Roger Higdon

Download or read book Application and Computation of Likelihood Methods for Regression with Measurement Error written by Roger Higdon and published by . This book was released on 1998 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis advocates the use of maximum likelihood analysis for generalized regression models with measurement error in a single explanatory variable. This will be done first by presenting a computational algorithm and the numerical details for carrying out this algorithm on a wide variety of models. The computational methods will be based on the EM algorithm in conjunction with the use of Gauss-Hermite quadrature to approximate integrals in the E-step. Second, this thesis will demonstrate the relative superiority of likelihood-ratio tests and confidence intervals over those based on asymptotic normality of estimates and standard errors, and that likelihood methods may be more robust in these situations than previously thought. The ability to carry out likelihood analysis under a wide range of distributional assumptions, along with the advantages of likelihood ratio inference and the encouraging robustness results make likelihood analysis a practical option worth considering in regression problems with explanatory variable measurement error.

Maximum Likelihood Computations for Regression with Measurement Error

Author : Roger Higdon
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Maximum Likelihood Computations for Regression with Measurement Error by : Roger Higdon

Download or read book Maximum Likelihood Computations for Regression with Measurement Error written by Roger Higdon and published by . This book was released on 1998 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Measurement Error and Misclassification in Statistics and Epidemiology

Author : Paul Gustafson
Publisher : CRC Press
ISBN 13 : 0203502760
Total Pages : 213 pages
Book Rating : 4.2/5 (35 download)

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Book Synopsis Measurement Error and Misclassification in Statistics and Epidemiology by : Paul Gustafson

Download or read book Measurement Error and Misclassification in Statistics and Epidemiology written by Paul Gustafson and published by CRC Press. This book was released on 2003-09-25 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mismeasurement of explanatory variables is a common hazard when using statistical modeling techniques, and particularly so in fields such as biostatistics and epidemiology where perceived risk factors cannot always be measured accurately. With this perspective and a focus on both continuous and categorical variables, Measurement Error and Misclassi

Mixed Effects Models for Complex Data

Author : Lang Wu
Publisher : CRC Press
ISBN 13 : 9781420074086
Total Pages : 431 pages
Book Rating : 4.0/5 (74 download)

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Book Synopsis Mixed Effects Models for Complex Data by : Lang Wu

Download or read book Mixed Effects Models for Complex Data written by Lang Wu and published by CRC Press. This book was released on 2009-11-11 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.

Parameter Estimation in Nonlinear Regression with Covariate Measurement Error

Author : Mary Margaret Dowling
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Parameter Estimation in Nonlinear Regression with Covariate Measurement Error by : Mary Margaret Dowling

Download or read book Parameter Estimation in Nonlinear Regression with Covariate Measurement Error written by Mary Margaret Dowling and published by . This book was released on 1991 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Convenient Methods for Estimation of Linear Regression Models with MA(1) Errors

Author : Glenn M. MacDonald
Publisher : Kingston, Ont. : Institute for Economic Research, Queen's University
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.2/5 (557 download)

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Book Synopsis Convenient Methods for Estimation of Linear Regression Models with MA(1) Errors by : Glenn M. MacDonald

Download or read book Convenient Methods for Estimation of Linear Regression Models with MA(1) Errors written by Glenn M. MacDonald and published by Kingston, Ont. : Institute for Economic Research, Queen's University. This book was released on 1983 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Statistical Regression with Measurement Error

Author : Chi-Lun Cheng
Publisher : Wiley
ISBN 13 : 9780470711064
Total Pages : 0 pages
Book Rating : 4.7/5 (11 download)

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Book Synopsis Statistical Regression with Measurement Error by : Chi-Lun Cheng

Download or read book Statistical Regression with Measurement Error written by Chi-Lun Cheng and published by Wiley. This book was released on 2010-06-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a general survey of the theory of measurement error models, including the functional, structural, and ultrastructural models, this book is written in the of the Kendall and Stuart Advanced Theory of Statistics set and, like that series, includes exercises at the end of the chapters. The goal is to emphasize the ideas and practical implications of the theory in a style that does not concentrate on the theorem-proof format.

Bayesian Data Analysis, Third Edition

Author : Andrew Gelman
Publisher : CRC Press
ISBN 13 : 1439840954
Total Pages : 677 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Bayesian Data Analysis, Third Edition by : Andrew Gelman

Download or read book Bayesian Data Analysis, Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Statistical Analysis with Measurement Error or Misclassification

Author : Grace Y. Yi
Publisher : Springer
ISBN 13 : 1493966405
Total Pages : 497 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Statistical Analysis with Measurement Error or Misclassification by : Grace Y. Yi

Download or read book Statistical Analysis with Measurement Error or Misclassification written by Grace Y. Yi and published by Springer. This book was released on 2017-08-02 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph on measurement error and misclassification covers a broad range of problems and emphasizes unique features in modeling and analyzing problems arising from medical research and epidemiological studies. Many measurement error and misclassification problems have been addressed in various fields over the years as well as with a wide spectrum of data, including event history data (such as survival data and recurrent event data), correlated data (such as longitudinal data and clustered data), multi-state event data, and data arising from case-control studies. Statistical Analysis with Measurement Error or Misclassification: Strategy, Method and Application brings together assorted methods in a single text and provides an update of recent developments for a variety of settings. Measurement error effects and strategies of handling mismeasurement for different models are closely examined in combination with applications to specific problems. Readers with diverse backgrounds and objectives can utilize this text. Familiarity with inference methods—such as likelihood and estimating function theory—or modeling schemes in varying settings—such as survival analysis and longitudinal data analysis—can result in a full appreciation of the material, but it is not essential since each chapter provides basic inference frameworks and background information on an individual topic to ease the access of the material. The text is presented in a coherent and self-contained manner and highlights the essence of commonly used modeling and inference methods. This text can serve as a reference book for researchers interested in statistical methodology for handling data with measurement error or misclassification; as a textbook for graduate students, especially for those majoring in statistics and biostatistics; or as a book for applied statisticians whose interest focuses on analysis of error-contaminated data. Grace Y. Yi is Professor of Statistics and University Research Chair at the University of Waterloo. She is the 2010 winner of the CRM-SSC Prize, an honor awarded in recognition of a statistical scientist's professional accomplishments in research during the first 15 years after having received a doctorate. She is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute.

In All Likelihood

Author : Yudi Pawitan
Publisher : OUP Oxford
ISBN 13 : 0191650587
Total Pages : 626 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis In All Likelihood by : Yudi Pawitan

Download or read book In All Likelihood written by Yudi Pawitan and published by OUP Oxford. This book was released on 2013-01-17 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood.