Presenter:  Hao Sun, PhD Candidate in Statistics

Title: Mixed Graphical Model for Surveys Under Informative Design

Abstract: We consider the problem of understanding the dependence structure of multivariate mixed-type survey response under a complex survey design using mixed graphical model. The survey variables are the nodes of the graph, which may be discrete or continuous. We specify a graphical model for the super-population. The full conditional distributions of continuous variables are assumed Gaussian, and the full conditional distributions of categorical variables are assumed multinomial. The nature of the complex sample design can cause the distribution in the sample to differ from the distribution in the population. As a result, classical edge selection procedures for simple random samples are no longer appropriate. We develop a graphical model selection procedure that appropriately accounts for the complexity of the survey design. A penalized weighted estimating equation is used for parameter estimation, where the weights are the inverses of the sample inclusion probabilities. Under suitable conditions, we provide theoretical results for neighborhood recovery and convergence speed. A weighted Bayesian information criterion (WBIC) is used to select the tuning parameter. We evaluate the procedures through a model-based simulation. Data from a California Academic Performance Index survey are used to construct a design-based simulation study to illustrate the effectiveness of our method.