Statistical Inference On Nonlinear Reproductive Dispersion Mixed Model With Nonignorable Missing Data

Most of the existing researches on the analysis of missing data problems assume that the missing data mechanism is ignorable.However,in some practical applications,missing data occurs as nonignorably missing(NMAR).If the ignorable missing data mechanism is still used to analyze these data,it will inevitably lead to biased or wrong statistical inference results in terms of parameter estimates.Therefore,for the nonlinear reproductive dispersion mixed effects model,under the assumption that responses and covariates subject to nonignorable missingness,this paper studies the methods of Bayesian parameter estimation,Bayesian local influence analysis and variable selection in nonlinear reproductive dispersion mixed model.The main purposes of this dissertation include:1.When responses and covariates are nonignorably missing,a Logistic regression model is specified as the missing data mechanism.Then we discuss the estimation of parameters in nonlinear reproductive dispersion mixed effects model,the covariates model and missing data mechanism model under the Bayesian framework.Combining Gibbs sampling and MH algorithm to obtain simultaneous Bayesian estimations of parameters and random effects.Finally,the effectiveness of the method is verified by simulation research.2.Based on the methodology of Bayes local influence analysis,in order to investigate local influence analysis of small disturbances,we discuss the prior distribution of parameters,the missing data mechanism model and the data model hypothesis.We choose three local influence analysis statistics for local influence analysis.Consider three different types of weighted perturbation modes.Three simulation studies show that our theoretical analysis and perturbation model settings are correct.Finally,we perform parameter estimation and local impact analysis on AIDS data.3.Based on the SCAD and ALASSO penalty functions,this dissertation considers variable selection for the NRDMM with nonignorable missing data.First,based on the MCEM algorithm,the penalty functions are used to simultaneously estimate parameters and select important covariates in NRDMM.Then the simulation analysis is used to explain the theory.