Statistics and Its Interface

Volume 11 (2018)

Number 2

Analysis of longitudinal data under nonignorable nonmonotone nonresponse

Pages: 265 – 279



Puying Zhao (Department of Statistics and Actuarial Science, University of Waterloo, Ontario, Canada)

Lei Wang (LPMC and Institute of Statistics, Nankai University, Tianjin, China; and Department of Statistics, University of Wisconsin, Madison, Wisc., U.S.A.)

Jun Shao (Department of Statistics, University of Wisconsin, Madison, Wisc., U.S.A.)


We consider identification and estimation in a longitudinal study with nonignorable nonmonotone nonresponse in responses. To handle the identifiability issue, we use a baseline covariates named as nonresponse instrument that can be excluded from the nonresponse propensity conditional on other observed covariates and the variables subject to nonresponse. The generalized method of moments is applied to estimate the parameters in the nonresponse propensity. Marginal response means and the parameters defined via regression models between responses and baseline covariates can be estimated by inverse probability weighting using the estimated propensity. Alternatively, we derive an augmented inverse probability weighting estimator and apply the importance sampling technique for its computation. Consistency and asymptotic normality of the proposed estimators are established under possibly misspecified models. Simulations are performed to evaluate the finite sample performance of the estimators. Also, a real data example is presented to demonstrate the proposed methodology.


generalized method of moments, identifiability, instrument, misspecified models, nonignorable nonmonotone nonresponse, robustness

2010 Mathematics Subject Classification

Primary 62G05, 62H12. Secondary 62G20.

Received 15 December 2016

Published 7 March 2018