A Metropolis–Hastings Robbins–Monro algorithm via variational inference for estimating the multidimensional graded response model: a calculationally efficient estimation scheme to deal with complex test structures

Xue Wang, Jing Lu () and Jiwei Zhang ()
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Xue Wang: Northeast Normal University
Jing Lu: Northeast Normal University
Jiwei Zhang: Northeast Normal University

Computational Statistics, 2025, vol. 40, issue 3, No 5, 1253-1284

Abstract: Abstract This paper introduces the Metropolis–Hastings variational inference Robbins–Monro (MHVIRM) algorithm, a modification of the Metropolis–Hastings Robbins–Monro (MHRM) method, designed for estimating parameters in complex multidimensional graded response models (MGRM). By integrating a black-box variational inference (BBVI) approach, MHVIRM enhances computational efficiency and estimation accuracy, particularly for models with high-dimensional data and complex test structures. The algorithms effectiveness is demonstrated through simulations, showing improved precision over traditional MHRM, especially in scenarios with complex structures and small sample sizes. Moreover, MHVIRM is robust to initial values. The applicability is further illustrated with a real dataset analysis.

Keywords: Item response theory; Metropolis–Hastings Robbins–Monro algorithm; Variational inference; Marginal maximum likelihood estimation; Multidimensional graded response model (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-024-01533-x

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