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A0568
Title: Bayesian inference of the number of classes in restricted latent class models Authors:  Yinghan Chen - University of Nevada, Reno (United States) [presenting]
Yuguo Chen - University of Illinois at Urbana-Champaign (United States)
Abstract: Cognitive diagnosis models (CDMs) are structured latent class models widely used to classify a multidimensional collection of latent attributes. The applications of CDMs rely on the specification of the $Q$ matrix, a binary matrix representing the requirement of each attribute in the test items. Estimation of the $Q$ matrix is an important question for the correct classification of attribute profiles. Many existing exploratory methods for estimation of $Q$ must pre-specify the number of attributes, $K$. We present a Bayesian framework for general CDMs to jointly infer the number of attributes $K$ and the elements of $Q$. Using stick-breaking construction of priors and a Bayesian variable selection technique, we propose a constrained Gibbs sampling algorithm to estimate the underlying Q and model parameters of varying dimensions. The proposed method can also enforce model identifiability constraints.