Bayesian Inference Of Nonlinear Structure Equation Models With Nonignorable Missing Data And Random Regression Coefficients From Reproductive Dispersion Models

Nonlinear structural equation models with nonignorable missing outcomes and random regression coefficients from reproductive dispersion models(MRRSEM) is a natural extension of nonlinear reproductive dispersion structural equation models. MRRSEMs are useful in various settings including modern behavioral,educational psychological, medicine,social, public health, epidemiology and econometrics.various structural equation models have been developed to explore the latent variables from the manifest variables,and to assess regression-type relationships among latent variables. Therefore, this class of models have received a lot of attention in recent years.The Bayesian estimation, Bayesian case influence analysis and local influence in MRRSEMs are discussed in this thesis,including:1. In the development of structural equation models(SEMs), it is commonly assumed that the factor are distributed as a exponential family such as normal distribution or assumed the structural coefficients are fixed paraments.But, in some practical applications, the structural factors may not follow a exponential family but belong to a reproductive dispersion family even belong to a nonparametric distribution such as the skewed and bimodal and heavy-tailed distribution,and structural coefficients are random coefficients.Therefore, it is of practical importance to consider a flexible distribution,manifest variables with missing data are follow a reproductive dispersion family,structural factor are spatial with adjacent time effects and structural coefficients are random regression coefficients. A hybrid Bayesian procedure combining the Gibbs sampler and the MH algorithm is used to simultaneously obtain the Bayesian estimates of unknown parameters, random coefficients and a procedure calculating the Bayes factor for model comparison is given via path sampling.2. Following Zhu et al.(2012) and Tang et al.(2013), this thesis presents two Bayesian case influence measures to identify the potential influential observations in MRRSEMs based on the φ-divergence, Cook’s posterior mean distance.The first order approximation formulas of three Bayesian case influence measures are proved. A hybrid Bayesian procedure combining the Gibbs sampler and the MH algorithm is used to obtain the joint Bayesian estimates of unknown parameters and random coeffiects. Compared the changing of parameters in MRRSEMs case influence in real data.3. Following Zhu et al.(2011) and Chen et al.(2013), the another research emphasis of this article is to develop a Bayesian local influence approach to assess the effect of minor perturbations to the individual observations, the prior and the sampling distribution to the MRRSEMs. We construct the Bayesian perturbation manifold for the perturbation model and the geometrical quantities associated with appropriate scheme, we also develop Bayesian local influence measures for identifying the most perturbations based on the objective functions of the Bayes factor and the φ-divergence. Some computationally feasible formulae for Bayesain influence analysis are given by using output from the MCMC algorithm.Compared the changing of parameters in MRRSEMs case influence in real data.