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

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.