Handling estimating equation with nonignorably missing data based on SIR algorithm

In this paper, the estimation of parameters in estimating equation with nonignorably missing data is considered. Based on a logistic regression model for the response mechanism and an assumed parametric model for the distribution of respondents, we propose to use the sampling importance resampling (SIR) algorithm to calculate the conditional expectation for non-respondents. The proposed method can avoid the difficulty of high-dimensional kernel smoothing on calculating the conditional expectation under nonignorably missing data. Based on the SIR algorithm, we derive a modified estimating equation. To facilitate comparison, we apply the empirical likelihood method to derive the parameters estimator. Some numerical simulation results based on linear and nonlinear models show that the proposed method is robust and performs the best among the compared existing methods. So, we extend the estimation method of E[g(Y)] using SIR algorithm with nonignorably missing response to the estimation of parameters in generalized estimating equation, and obtain a new and more robust estimation method.