Bayesian adjustment for unidirectional misclassification in ordinal covariates

A Bayesian approach for analysis of ordered categorical responses subject to misclassification

Ordinal categorical responses are frequently collected in survey studies, human medicine, and animal and plant improvement programs, just to mention a few. Errors in this type of data are neither rare nor easy to detect. These errors tend to bias the inference, reduce the statistical power and ultimately the efficiency of the decision-making process. Contrarily to the binary situation where misclassification occurs between two response classes, noise in ordinal categorical data is more complex due to the increased number of categories, diversity and asymmetry of errors. Although several approaches have been presented for dealing with misclassification in binary data, only limited practical methods have been proposed to analyze noisy categorical responses. A latent variable model implemented within a Bayesian framework was proposed to analyze ordinal categorical data subject to misclassification using simulated and real datasets. The simulated scenario consisted of a discrete response with three categories and a symmetric error rate of 5% between any two classes. The real data consisted of calving ease records of beef cows. Using real and simulated data, ignoring misclassification resulted in substantial bias in the estimation of genetic parameters and reduction of the accuracy of predicted breeding values. Using our proposed approach, a significant reduction in bias and increase in accuracy ranging from 11% to 17% was observed. Furthermore, most of the misclassified observations (in the simulated data) were identified with a substantially higher probability. Similar results were observed for a scenario with asymmetric misclassification. While the extension to traits with more categories between adjacent classes is straightforward, it could be computationally costly. For traits with high heritability, the performance of the methodology would be expected to improve.

Bayesian inference for unidirectional misclassification of a binary response trait

When assessing association between a binary trait and some covariates, the binary response may be subject to unidirectional misclassification. Unidirectional misclassification can occur when revealing a particular level of the trait is associated with a type of cost, such as a social desirability or financial cost. The feasibility of addressing misclassification is commonly obscured by model identification issues. The current paper attempts to study the efficacy of inference when the binary response variable is subject to unidirectional misclassification. From a theoretical perspective, we demonstrate that the key model parameters possess identifiability, except for the case with a single binary covariate. From a practical standpoint, the logistic model with quantitative covariates can be weakly identified, in the sense that the Fisher information matrix may be near singular. This can make learning some parameters difficult under certain parameter settings, even with quite large samples. In other cases, the stronger identification enables the model to provide more effective adjustment for unidirectional misclassification. An extension to the Poisson approximation of the binomial model reveals the identifiability of the Poisson and zero-inflated Poisson models. For fully identified models, the proposed method adjusts for misclassification based on learning from data. For binary models where there is difficulty in identification, the method is useful for sensitivity analyses on the potential impact from unidirectional misclassification.