Abstract

In this paper we introduce a novel approach to understand multivariate relationships among mixed-type variables in complex surveys utilizing a pairwise graphical model. Existing graphical model estimation methods generally assume data are simple random sample from the population. Such methods can produce incorrect graph structure estimates when data are gathered through complex informative sample designs. To address this issue, we develop a method that can handle complex informative designs and mixed-type data, both of which are frequently encountered in survey data. Theoretical results for neighborhood recovery and convergence rates are derived, and the weighted Bayesian information criterion (WBIC) is used to select the turning parameter which accounts for the design effects. Our simulation studies demonstrate that traditional methods which overlook sampling weights can result in biased estimates. We apply our approach to data from an Academic Performance Index (API) survey for illustration. This work represents the first application of a graphical model for high-dimensional data within the context of an informative survey design.