Bayesian regression models adjusting for unidirectional covariate misclassification

Abstract

In this article we consider unidirectional covariate misclassification, meaning that the direction of classification error is known. We investigate the identifiability of Bayesian regression models when a binary covariate is subject to unidirectional misclassification. In the Bayesian framework we consider whether knowledge of the direction of error suffices, so that adjustment for misclassification can be undertaken without any source of information on the magnitude of error. Although measurement error models are generally non‐identified without such information, for the case of unidirectional misclassification, we do obtain model identifiability when the response variable is non‐binary. For the binary response model that is non‐identified we examine the extent of partial identification. The limiting posterior distributions of the parameters are obtained for this partially identified model, for two different prior distributions. We perform computational studies that illustrate statistical learning, for the three cases where the model is easily identified, weakly identified, and partially identified. A case study is performed using real data. The Canadian Journal of Statistics 44: 198–218; 2016 © 2016 Statistical Society of Canada

Bayesian inference for unidirectional misclassification of a binary response trait

“…Here, we study statistical learning based on the conditional distribution of the misclassified response given the correctly measured covariate. Since the odds ratio is symmetric in the variables V and X , the problem has a similar nature to the binary response case discussed in Xia and Gustafson . Thus, it is not surprising to obtain the partial identification of the model.…”

“…Note that the current model is similar to the binary response case studied in Xia and Gustafson in the sense that we are interested in assessing the association of a pair of binary variables with one of them subject to unidirectional misclassification. Treating the misclassified variable as a covariate, Xia and Gustafson showed that the model is partially identified when there is a binary response that is correctly measured. In the earlier paper, the identification is studied based on the conditional distribution of the correctly measured variable given the misclassified variable.…”

“…From the figure, we observe that the width of the credible interval decreases quickly with increasing sample size, particularly for the cases where the limiting credible intervals are very narrow. Contrarily to the target parameters in Xia and Gustafson, the indirect learning does not seem to stop at a small sample size, particularly for the cases where the limiting posterior distributions are narrower. This confirms the conjecture in Xia and Gustafson that at a certain sample size, how much additional sampling would improve the learning of the parameter depends on how wide the limiting posterior distribution is compared to the current finite sample posterior.…”

Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression

“…For the problem of insurance misrepresentation, Xia and Gustafson (2016) is the first paper that studied the model identification and implementation when concerning the association between a response and a binary risk factor subject to misrepresentation. The paper used the term unidirectional misclassification from Gustafson (2014) for the type of measurement such as misrepresentation where the error occurs only in one direction that favors the respondent.…”

“…For all the earlier papers except for Gustafson (2014); Hahn et al (2016), the models possessed the identifiability, which enables us to perform statistical inference on all the model parameters without prior knowledge on the severity of misrepresentation. In the most recent paper concerning the problem of misrepresentation , the model from Xia and Gustafson (2016) was expanded for the purpose of predictive analytics on the misrepresentation risk, while including multiple risk factors with some of them subject to misrepresentation.…”