Theoretical Statistics and Mathematics Unit, ISI Delhi

Pseudo-likelihood and bootstrapped pseudo-likelihood inference in logistic regression model with misclassified responses

by A. Chatterjee, T. Bandyopadhyay and S. Adhya

Logistic regression is an extensively used regression model for binary responses. In many applications, misclassification of binary responses is not uncommon. If the misclassification is ignored, it may severely bias the maximum likelihood estimators (MLE) of regression parameters towards zero. To obviate this difficulty, we propose a pseudo-likelihood method of estimation, that uses data from internal validation study. Under minimal assumptions, we establish rigorous asymptotic results for the maximum pseudo-likelihood estimators. A bootstrapped version of the maximum pseudo likelihood estimators is proposed, and its distributional consistency is proved. It enables us to use bootstrap method for statistical inference. The results of the simulation studies clearly indicate the superiority of the maximum pseudo-likelihood estimators to the maximum full likelihood estimators, and the maximum likelihood estimators based on misclassified binary responses only. Also, inferences on the regression parameters using asymptotic distribution of maximum pseudo-likelihood estimators, and its bootstrap version, are found to be similar.

isid/ms/2016/12 [fulltext]

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