Bayes Local Influence Analysis Of The Mixed-effects Models

The mixed-effects models are popular in the analysis of longitudinal data. They are frequently used in biology, medicine, and economics, sampling designs and quality control procedures, and so on. In this thesis, we focused on the local influence analysis of this model. Using Bayesian method, we obtained the Bayesian local influential formulas of parameter estimates. Our result can be applied to the local influence of a particular datum as well as the data of one individual. An example is used for illustration. More precisely, our work consists of the following three parts:(1) In chapter two, we studied the statistical diagnostics of the model from a frequentist's view-point: the leverage analysis and the case deletion model. We derived the leverage matrix of one individual which was divided into two parts : The marginal leverage of the fixed-effect and random-effect, and the Cook distance formula for the case that all the data of an individual is deleted. An example is given for illustration.(2) In chapter three, we derived the posterior distribution of the parameters based on the hierarchical model method. We proposed two types of perturbation schemes in terms of the characteristics of longitudinal data which include both individuals and individual cases. Using the posterior distribution, we analyzed the influence of a particular datum as well as the data of one individual, on the estimates of the parameters. The Bayesian local influential formulas are provided for both perturbation schemes.(3) Based on the data analysis, we got the influential individuals and the influential observations. We find that the basic result is the same to the global influence analysis. But some new cases were detected. We should emphasize that: the influential individual case and the influential individual are usually not belonged to the same individual even under the same perturbation.