Iterated imputation estimation for generalized linear models with missing response and covariate values

A new approach named as the iterated imputation estimation is proposed for parameter estimation in generalized linear models with missing values in both response and covariates and data are missing at random. The proposed approach is much faster and easier to implement than the method of maximum likelihood or weighted estimating equation. It can be applied by directly using any existing software package for generalized linear models and treating the imputed values as observed in each iteration, which brings great convenience in programming. Theoretical results for the algorithm convergence of the iterated imputation estimation and the asymptotic distribution of the proposed estimator are obtained. Simulation studies and an illustrative example show that the iterated imputation estimation works quite well considering the trade-off between computational burden and estimation efficiency compared with the maximum likelihood estimation.