Bayesian Statistical Analysis Of Generalized Linear Models With Measurement Error

In biomedical, management, economics and engineering, researchers often find that the observations is not the actual variable values. There are some errors between the observation and the actual variable values, which is so-called measurement errors problems. As we know, when we deal with the measurement error data, statistical results of ignoring measurement error always lead to a biased and inconsistent estimator. To solve this problems, measurement error model is proposed. In the last three decades, statical analysis on the measurement error model has become one of the most important issues. The classical assumption for generalized linear measurement error models (GLMEMs) is that covariates subject to measurement errors are distributed as a fully parametric distribution such as the multivariate normal distribution. However, violation of the parametric assumption on the measurement error may lead to unreasonable conclusions or even wholly misleading results. Therefore, in the paper, we propose several practicable GLMEMs based on the Bayesian method.1. This paper relaxes the fully parametric distributional assumption of covariates subject to measurement errors by specifying a centered Dirichlet process mixture model for covariates subject to measurement errors, and develops a semi-parametric Bayesian approach to simultaneously obtain Bayesian estimations of parameters and covariates subject to measurement errors by combining the stick-breaking prior and the Gibbs sampler together with the Metropolis-Hastings algorithm. A Bayesian case-deletion diagnostic is proposed to identify the potential outliers or influential observations in GLMEMs via the φ-divergence. A computationally feasible formula for evaluating Bayesian case-deletion diagnostic is presented.2. We propose a semiparametric Bayesian varying-coefficient linear measurement error model multivariate longitudinal data with multivariate normal distribution. One main feature of the model is that we relax the commonly used normality assumption for measurement error and within-subject errors by using a centered Dirichlet (CDP) process prior to specify the distribution of measurement error and using a multivariate normal distribution to specify the distribution of within-subject errors. Bayesian penalized splines are used to fitting varying-coefficient functions. Based on Bayesian penalized-splines (B-splines) technique,A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, measurement error and varying-coefficient functions by combining the Gibbs sampler and the Metropolis-Hastings algorithm.3. We assume a semiparametric Bayesian generalized varying-coefficient linear measurement error model with multivariate ignoring missing longitudinal data. A Bayesian imputation approach performs the response variable contain ignoring missing data. One main feature of the model is that we relax the commonly used normality assumption for measurement error and within-subject errors by using a centered Dirichlet (CDP) process prior to specify the distribution of measurement error and using a multivariate normal distribution to specify the distribution of within-subject errors. Bayesian penalized splines are used to fitting varying-coefficient functions. Based on Bayesian penalized-splines (B-splines) technique and Bayesian imputation methods, a Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, measurement error, parameters of missing mechanism, covariate with measurement error and varying-coefficient functions by combining the Gibbs sampler and the Metropolis-Hastings algorithm.