GMM nonparametric correction methods for logistic regression with error‐contaminated covariates and partially observed instrumental variables

• Published in: Scandinavian journal of statistics Vol. 46; no. 3; pp. 898 - 919
• Main Authors: Song, Xiao, Wang, Ching‐Yun
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.09.2019
• Subjects: Asymptotic properties; Calibration; Computer simulation; Economic models; Error analysis; Error correction; Estimating techniques; Generalized method of moments; generalized methods of moments; inverse selection probability weighting; Method of moments; missing at random; Nonparametric statistics; Statistical analysis; Variables
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/sjos.12364

We consider logistic regression with covariate measurement error. Most existing approaches require certain replicates of the error‐contaminated covariates, which may not be available in the data. We propose generalized method of moments (GMM) nonparametric correction approaches that use instrumental variables observed in a calibration subsample. The instrumental variable is related to the underlying true covariates through a general nonparametric model, and the probability of being in the calibration subsample may depend on the observed variables. We first take a simple approach adopting the inverse selection probability weighting technique using the calibration subsample. We then improve the approach based on the GMM using the whole sample. The asymptotic properties are derived, and the finite sample performance is evaluated through simulation studies and an application to a real data set.