Statistical Modelling 19 (4) (2019), 412–443
Repeated responses in misclassification binary regression: A Bayesian approach
Magda Carvalho Pires
Department of Statistics
Universidade Federal de Minas Gerais,
Belo Horizonte,
Brazil.
e-mail: magda@est.ufmg.br
Roberto da Costa Quinino
Department of Statistics
Universidade Federal de Minas Gerais,
Belo Horizonte,
Brazil.
Abstract:
Binary regression models generally assume that the response variable is measured perfectly. However, in some situations, the outcome is subject to misclassification: a success may be erroneously classified as a failure or vice versa. Many methods, described in existing literature, have been developed to deal with misclassification, but we demonstrate that these methods may lead to serious inferential problems when only a single evaluation of the individual is taken. Thus, this study proposes to incorporate repeated and independent responses in misclassification binary regression models, considering the total number of successes obtained or even the simple majority classification. We use subjective prior distributions, as our conditional means prior, to evaluate and compare models. A data augmentation approach, Gibbs sampling, and Adaptive Rejection Metropolis Sampling are used for posterior inferences. Simulation studies suggested that repeated measures significantly improve the posterior estimates, in that these estimates are closer to those obtained in a case with no misclassifications with a lower standard deviation. Finally, we illustrate the usefulness of the new methodology with the analysis about defects in eyeglass lenses.
Keywords:
Bayesian analysis; Data augmentation; logistic regression; misclassification; repeated responses.
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