Marginal Bayesian parameter estimation in the multidimensional generalized graded unfolding model

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Thompson, Vanessa Marie
Roberts, James S.
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The Multidimensional Generalized Graded Unfolding Model (MGGUM) is a proximity-based, noncompensatory item response theory (IRT) model with applications in the context of attitude, personality, and preference measurement. Model development used fully Bayesian Markov Chain Monte Carlo (MCMC) parameter estimation (Roberts, Jun, Thompson, & Shim, 2009a; Roberts & Shim, 2010). Challenges can arise while estimating MGGUM parameters using MCMC where the meaning of dimensions may switch during the estimation process and difficulties in obtaining informative starting values may lead to increased identification of local maxima. Furthermore, researchers must contend with lengthy computer processing time. It has been shown alternative estimation methods perform just as well as, if not better than, MCMC in the unidimensional Generalized Graded Unfolding Model (GGUM; Roberts & Thompson, 2011) with marginal maximum a posteriori (MMAP) item parameter estimation paired with expected a posteriori (EAP) person parameter estimation being a viable alternative. This work implements MMAP/EAP parameter estimation in the multidimensional model. Additionally, item location initial values are derived from detrended correspondence analysis (DCA) based on previous implementation of correspondence analysis in the GGUM (Polak, 2011). A parameter recovery demonstrates the accuracy of two-dimensional MGGUM MMAP/EAP parameter estimates and a comparative analysis of MMAP/EAP and MCMC demonstrates equal accuracy, yet much improved efficiency of the former method. Analysis of real attitude measurement data also provides an illustrative application of the model.
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