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A0172
Title: Bayesian model selection for ultrahigh-dimensional doubly-intractable distributions Authors:  Jaewoo Park - Yonsei University (Korea, South) [presenting]
Ick Hoon Jin - Yonsei University (Korea, South)
Abstract: Item response data are common, for example, cognitive-developmental stages data in educational sciences and measurements of depression of healthy controls. Although several item response theory (IRT) models have been developed for studying such data sets, each method depends on assumptions about dependence structure which are unrealistic in many settings. We propose inhomogeneous exponential random graph models (I-ERGMs) that can easily incorporate local dependence among items without any assumptions. However, in practice, I-ERGMs pose some inferential and computational challenges; likelihood functions involve intractable normalizing functions. An increasing number of items can lead to ultrahigh dimensionality in the model. To address such challenges, we develop novel Markov chain Monte Carlo methods using Bayesian variable selection methods to identify strong interactions automatically. We illustrate applying the approaches to challenging simulated, and real item response data examples for which studying local dependence is very difficult. The proposed algorithm shows significant inferential gains over existing methods in the presence of strong dependence among items.