Mixture Models in Measurement Error Problems, with Reference to Epidemiological Studies
- 1 October 2002
- journal article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series A: Statistics in Society
- Vol. 165 (3), 549-566
- https://doi.org/10.1111/1467-985x.00252
Abstract
Summary: The paper focuses on a Bayesian treatment of measurement error problems and on the question of the specification of the prior distribution of the unknown covariates. It presents a flexible semiparametric model for this distribution based on a mixture of normal distributions with an unknown number of components. Implementation of this prior model as part of a full Bayesian analysis of measurement error problems is described in classical set-ups that are encountered in epidemiological studies: logistic regression between unknown covariates and outcome, with a normal or log-normal error model and a validation group. The feasibility of this combined model is tested and its performance is demonstrated in a simulation study that includes an assessment of the influence of misspecification of the prior distribution of the unknown covariates and a comparison with the semiparametric maximum likelihood method of Roeder, Carroll and Lindsay. Finally, the methodology is illustrated on a data set on coronary heart disease and cholesterol levels in blood.Keywords
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