A0731
Title: Statistical modeling of combinatorial response data with application on cascading failure network
Authors: Leo Duan - University of Florida (United States) [presenting]
Abstract: In categorical data analysis, there is rich literature for modeling binary and polychotomous responses. However, existing methods are inadequate for handling combinatorial responses, where each response is an array of integers subject to additional constraints. Such data are increasingly common in modern applications, such as surveys collected under skip logic, event propagation on a network, and observed matching in ecology. Ignoring the combinatorial structure in the response data may lead to biased estimation and prediction. The fundamental challenge for modeling these integer-vector data is the lack of a link function that connects a linear or functional predictor with a probability respecting the combinatorial constraints. A novel augmented likelihood is proposed, in which a combinatorial response can be viewed as a deterministic transform of a continuous latent variable. The transform is specified as the maximizer of an integer linear program, and useful properties such as dual thresholding representation are characterized. When taking a Bayesian approach and considering a multivariate normal distribution for the latent variable, the method becomes a direct generalization to the celebrated probit data augmentation and enjoys straightforward computation via Gibbs sampler. The effectiveness of the method is demonstrated through simulation studies and a data application associated with the power delivery network.
