| Standard statistic analysis have been developed to analyze rectangular data sets. However, missing values often occur in multivariate datasets and deletion of incomplete observation can lead to biased results. In this thesis, we aim to develop Bayesian approaches through Gibbs sampling to analyze incomplete data for a variable measuring a count of the number of events with combination of other categorical or continuous variables. With the Gibbs sampling method, we first propose a model called Multivariate Normal/Poisson Regression model, MNPR for short, to analyze incomplete datasets containing a Poisson distributed variable along with a set of multivariate normal variables. Then we extend MNPR model to a General Location Poisson Regression model (GLPR) to further incorporate a set of categorical variables into the model. Simulation studies in this thesis suggest that the proposed models have good performance in coverages of true values, biases and precision of estimation if missing-data proporion is not severe and missing-data mechanism is missing at random. |
