Stochastic Approximation of the Multidimensional Generalized Graded Unfolding Model
King, David R.
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The multidimensional generalized graded unfolding model (MGGUM; Roberts & Shim, 2010) is a distance-based, unfolding multidimensional item response theory (MIRT) model for measuring person and item characteristics from graded or binary disagree-agree responses to Thurstone or Likert style questionnaire items. The current paper examined the utility of the Metropolis-Hastings Robbins-Monro (MH-RM; Cai, 2010a; Cai, 2010b; Cai, 2010c) algorithm for estimating item parameters in the MGGUM. Initial attempts to estimate the MGGUM with the MH-RM resulted in severe misestimation of item parameters, although estimation accuracy was markedly improved through modifications to the MH-RM. Namely, the Newton-Raphson step for updating item parameters was replaced with the L-BFGS-B method for constrained optimization (Byrd, Lu, Nocedal, & Zhu, 1995). Runtime and estimation accuracy of the modified MH-RM were examined through a parameter recovery study that varied test length (10, 20, or 30 items), sample size (1000, 1500, or 2000 persons), number of response categories (2, 4, or 6), dimensional structure of items (simple or complex), and dimensionality (2 or 3 dimensions). Furthermore, the practical utility of the method was explored through a real data analysis of facial affect responses. Results indicated that the modified MH-RM is an efficient method for estimating high-dimensional MGGUMs and that estimation accuracy is comparable to other commonly used methods.