Bayesian Statistical Inference For Mixed Linear Model With Nonignorable Missing Data

Missing data are commonly encountered in various fields such as life sciences, agricultural, social economical and environmental studies. However, in classical statistical studies, most statistical analysis are conducted on the basis of complete data set. Therefore, it is of great importance to study missing data especially nonignorable missing data. Mixed effects linear model is natural extension and development of linear regression model and it has great advantages in analyzing repeated data (e.g., panel data and longitudinal data) categorical data and spatial data. Compared to the linear regression model, less assumptions such as independence and homogeneity for the responses are needed when analyzing the abovementioned data. Furthermore, in mixed effects linear models, covariance can be determined by the real data. To this end, this paper mainly focus on Bayesian analysis in mixed effects linear models with nonignorable missing responses and covariates. In order to obtain Bayesian estimates of parameters of interest, the Gibbs sampler and Metropolis-Hasting sampling methods are used to sample missing responses and random effects from their posterior distributions. Three simulation studies and a real example are presented to illustrate the proposed methodologies. The results indicated that, the methodologies proposed in this paper performed well in mixed effects linear models and can be extended to generalized mixed effects linear models as well.