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

被引：0

作者：

Wang, Xue ^{[1
]}

Lu, Jing ^{[1
]}

Zhang, Jiwei ^{[2
]}

机构：

[1] Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat MOE, Changchun, Jilin, Peoples R China

[2] Northeast Normal Univ, Fac Educ, Key Lab Appl Stat MOE, Changchun, Jilin, Peoples R China

来源：

COMPUTATIONAL STATISTICS | 2025年 / 40卷 / 03期

关键词：

Item response theory; Metropolis-Hastings Robbins-Monro algorithm; Variational inference; Marginal maximum likelihood estimation; Multidimensional graded response model; MAXIMUM-LIKELIHOOD; ITEM; INFORMATION;

D O I：

10.1007/s00180-024-01533-x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：1253 / 1284

页数：32