Logistic Regression Measurement Error
publishersPoliciesContact Project Euclidfor Researchers Manage my accountAccessing Project EuclidAccess levelsPay-per-view and print-on-demandfor Librarians Manage my accountAccess levelsCollections, titles, and orderingLibrarian toolsfor Publishers Manage my accountYour publication in Project EuclidDiscovery service partnersPublisher tools The Annals of StatisticsInfoCurrent issueAll issuesSearch ← Previous articleTOCNext article → Ann. Statist. Volume 13, Number 4 (1985), 1335-1351.Covariate Measurement Error in Logistic RegressionLeonard A. Stefanski and Raymond J. Carroll More by Leonard A. StefanskiSearch this author in:Google ScholarProject Euclid More by Raymond J. CarrollSearch this author in:Google ScholarProject Euclid Full-text: Open access PDF File (1445 KB) AbstractArticle info and citationFirst pageAbstract In a logistic regression model when covariates are subject to measurement error the naive estimator, obtained by regressing on the observed covariates, is asymptotically biased. We introduce a bias-adjusted estimator and two estimators appropriate for normally distributed measurement errors -a functional maximum likelihood estimator and an estimator which exploits the conseq
Alerts Search this journal Advanced Journal Search » Impact Factor:0.932 | Ranking:Statistics & Probability 59 out of 123 Source:2016 Release of Journal Citation Reports with Source: 2015 Web of Science Data Correcting for covariate measurement error in logistic regression using nonparametric maximum likelihood estimation Sophia Rabe-Hesketh1, Andrew Pickles2 and Anders Skrondal3 1Department of Biostatistics and Computing, Institute of Psychiatry, King’s College London, London, UK, spaksrh{at}iop.kcl.ac.uk 2School of Epidemiology and Health Sciences and CCSR, The University of Manchester, Manchester, UK 3Division of Epidemiology, Norwegian https://projecteuclid.org/euclid.aos/1176349741 Institute of Public Health, Oslo, Norway Abstract When covariates are measured with error, inference based on conventional generalized linear models can yield biased estimates of regression parameters. This problem can potentially be rectified by using generalized linear latent and mixed models (GLLAMM), including a measurement model for the relationship between observed and true covariates. However, the models are typically estimated under http://smj.sagepub.com/content/3/3/215.short the assumption that both the true covariates and the measurement errors are normally distributed, although skewed covariate distributions are often observed in practice. In this article we relax the normality assumption for the true covariates by developing nonparametric maximum likelihood estimation (NPMLE) for GLLAMMs. The methodology is applied to estimating the effect of dietary fibre intake on coronary heart disease. We also assess the performance of estimation of regression parameters and empirical Bayes prediction of the true covariate. Normal as well as skewed covariate distributions are simulated and inference is performed based on both maximum likelihood assuming normality and NPMLE. Both estimators are unbiased and have similar root mean square errors when the true covariate is normal. With a skewed covariate, the conventional estimator is biased but has a smaller mean square error than the NPMLE. NPMLE produces substantially improved empirical Bayes predictions of the true covariate when its distribution is skewed. empirical Bayes prediction factor model generalized linear models GLLAMM logistic regression measurement error nonparametric maximum likelihood estimation CiteULike Connotea Delicious Digg Facebook Google+ LinkedIn Mendeley Reddit StumbleUpon Twitter What's this? Â
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