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Bias Reduction in Logistic Regression with Missing Responses When the Missing Data Mechanism is Nonignorable

Authors :
Vivek Pradhan
Ujjwal Das
Arnab Maity
Source :
The American Statistician. 73:340-349
Publication Year :
2018
Publisher :
Informa UK Limited, 2018.

Abstract

In logistic regression with nonignorable missing responses, Ibrahim and Lipsitz (1996)) proposed a method for estimating regression parameters. It is known that the regression estimates obtained by using this method are biased when the sample size is small. Also, another complexity arises when the iterative estimation process encounters separation in estimating regression coefficients. In this article we propose a method to improve the estimation of regression coefficients. In our likelihood based method, we penalize the likelihood by multiplying it by a non-informative Jeffreys prior as a penalty term. The proposed method reduces bias and is able to handle the issue of separation. Simulation results show substantial bias reduction for the proposed method as compared to the existing method. Analyses using real world data also support the simulation findings. An R package called brlrmr is developed implementing the proposed method and the Ibrahim and Lipsitz method.

Details

ISSN :
15372731 and 00031305
Volume :
73
Database :
OpenAIRE
Journal :
The American Statistician
Accession number :
edsair.doi.dedup.....3bc7d7254d00c80e9a3861c2ff09abb0
Full Text :
https://doi.org/10.1080/00031305.2017.1407359