Inference problems in binary regression model with misclassified responses

TL;DR

This paper addresses bias in binary regression models caused by misclassified responses and proposes a pseudo-likelihood estimation method with asymptotic theory and bootstrap validation, improving inference accuracy.

Contribution

It introduces a bias-reducing pseudo-likelihood estimation approach for binary regression with misclassification, along with asymptotic theory and bootstrap methods for inference.

Findings

Pseudo-likelihood estimators reduce bias compared to MLE.

Asymptotic properties are rigorously established.

Bootstrap methods provide consistent inference.

Abstract

Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLE) of regression parameters. For such data, a binary regression model incorporating misclassification probabilities is extensively used by researchers in different application contexts. The model, however, suffers from a serious estimation problem because of confounding of the unknown misclassification probabilities with the regression parameters. To overcome this problem, in addition to the main sample, use of internal validation data is proposed. However, the maximum likelihood estimators (MLE) are found to be substantially biased. Investigating further, we propose a maximum pseudo-likelihood method of estimation which leads to bias reduction. For drawing inference on the regression parameters, we develop a rigorous asymptotic theory for the maximum pseudo-likelihood estimators under standard assumptions. To facilitate its easy implementation, a bootstrapped version of the estimator is proposed, and its distributional consistency is proved. Extensions of these results are also provided for more general misclassification models. The results of the simulation studies are encouraging. The methodology is illustrated with a survey data.