Bayesian Analysis Of Spatial Panel Data Models

Spatial panel data models(SPDMs)are extension and development of the panel data models which attract lots of attention in modern econometric research.They consider not only the correlation of spaces,but also the correlation of time.Among the studies of SPDMs,most of them assume that random effects and error terms follow the normal distribution,and that response variables and covariates are fully observed.However,the data may be biased or missing in its practical application.Unreasonable or wrong conclusions can be obtained if statistical inference is based on the traditional Gaussian hypothesis.So,this thesis explain the parameter estimation,variable selection and statistical diagnosis of SPDMs with random effect and missing data under the Bayesian framework.The main content of research is followed:(1)Under the assumption that both the random effects and the error terms are distributed as the skew-normal distribution,a Markov chain Monte Carl(MCMC)algorithm is developed to simultaneously evaluate Bayesian estimates of unknown parameters and random effects in the skew-normal spatial dynamic panel data models by combing the Gibbs sampler and the Metropolis-Hastings(MH)algorithm.(2)Bayesian local influence approach will be applied to the skew-normal spatial dynamic panel data models in order to employ different perturbation strategies in disturbed model of covariates,response variables,the prior and the sampling distribution.According to the theory of perturbation manifolds in differential geometry,the metric tensor and geodesic are used to measure perturbation or intrinsic correlation.The approximation formulas of the first-and second-order diagnostic statistics of the objective function including Bayes factor,(?)-divergences and the posterior mean distance are proposed based on MCMC algorithm.(3)As for the SPDM with nonignorable missing responses,the Logistic regression model is used to establish the missing data model.In order to avoid high dimensional integrals of the likelihood function,a MCMC algorithm which combines the Gibbs sampler and the MH algorithm is developed to obtain Bayesian estimates in the SPDM.Meanwhile.Deleting a data point(or data set)to estimate the unknown parameters is considered,especially for the(?)-divergence,Cooks posterior mode distance and Cooks posterior mean distance.The first-order approximation formulas of case diagnostic statistics are derived.(4)As for the SPDMs with covariates measurement error,without assuming a random effect distribution,Bayesian estimates of the unknown parameters and the random effect are studied.In order to make statistical inferences,the truncated Dirichlet process prior is used to approximate the distribution of random effect,and the linear measurement error model is used to describe covariates.A MCMC algorithm which combines Gibbs sampling and MH algorithm is obtained to estimate the unknown parameters and random effects in the model.At the same time,the Bayesian variable selection is discussed based on the assumption.