Mixture-modelling-based Bayesian MH-RM algorithm for the multidimensional 4PLM

Shaoyang Guo; Yanlei Chen; Chanjin Zheng; Guiyu Li

doi:10.1111/bmsp.12300

Mixture-modelling-based Bayesian MH-RM algorithm for the multidimensional 4PLM

Shaoyang Guo, Yanlei Chen, Chanjin Zheng, Guiyu Li

Faculty of Education

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Several recent works have tackled the estimation issue for the unidimensional four-parameter logistic model (4PLM). Despite these efforts, the issue remains a challenge for the multidimensional 4PLM (M4PLM). Fu et al. (2021) proposed a Gibbs sampler for the M4PLM, but it is time-consuming. In this paper, a mixture-modelling-based Bayesian MH-RM (MM-MH-RM) algorithm is proposed for the M4PLM to obtain the maximum a posteriori (MAP) estimates. In a comparison of the MM-MH-RM algorithm to the original MH-RM algorithm, two simulation studies and an empirical example demonstrated that the MM-MH-RM algorithm possessed the benefits of the mixture-modelling approach and could produce more robust estimates with guaranteed convergence rates and fast computation. The MATLAB codes for the MM-MH-RM algorithm are available in the online appendix.

Original language	English
Pages (from-to)	585-604
Number of pages	20
Journal	British Journal of Mathematical and Statistical Psychology
Volume	76
Issue number	3
DOIs	https://doi.org/10.1111/bmsp.12300
State	Published - Nov 2023

Keywords

MAP
MM-MH-RM
estimation
mixture modelling
multidimensional 4PL

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10.1111/bmsp.12300

Cite this

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title = "Mixture-modelling-based Bayesian MH-RM algorithm for the multidimensional 4PLM",

abstract = "Several recent works have tackled the estimation issue for the unidimensional four-parameter logistic model (4PLM). Despite these efforts, the issue remains a challenge for the multidimensional 4PLM (M4PLM). Fu et al. (2021) proposed a Gibbs sampler for the M4PLM, but it is time-consuming. In this paper, a mixture-modelling-based Bayesian MH-RM (MM-MH-RM) algorithm is proposed for the M4PLM to obtain the maximum a posteriori (MAP) estimates. In a comparison of the MM-MH-RM algorithm to the original MH-RM algorithm, two simulation studies and an empirical example demonstrated that the MM-MH-RM algorithm possessed the benefits of the mixture-modelling approach and could produce more robust estimates with guaranteed convergence rates and fast computation. The MATLAB codes for the MM-MH-RM algorithm are available in the online appendix.",

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doi = "10.1111/bmsp.12300",

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T1 - Mixture-modelling-based Bayesian MH-RM algorithm for the multidimensional 4PLM

AU - Guo, Shaoyang

AU - Chen, Yanlei

AU - Zheng, Chanjin

AU - Li, Guiyu

PY - 2023/11

Y1 - 2023/11

N2 - Several recent works have tackled the estimation issue for the unidimensional four-parameter logistic model (4PLM). Despite these efforts, the issue remains a challenge for the multidimensional 4PLM (M4PLM). Fu et al. (2021) proposed a Gibbs sampler for the M4PLM, but it is time-consuming. In this paper, a mixture-modelling-based Bayesian MH-RM (MM-MH-RM) algorithm is proposed for the M4PLM to obtain the maximum a posteriori (MAP) estimates. In a comparison of the MM-MH-RM algorithm to the original MH-RM algorithm, two simulation studies and an empirical example demonstrated that the MM-MH-RM algorithm possessed the benefits of the mixture-modelling approach and could produce more robust estimates with guaranteed convergence rates and fast computation. The MATLAB codes for the MM-MH-RM algorithm are available in the online appendix.

AB - Several recent works have tackled the estimation issue for the unidimensional four-parameter logistic model (4PLM). Despite these efforts, the issue remains a challenge for the multidimensional 4PLM (M4PLM). Fu et al. (2021) proposed a Gibbs sampler for the M4PLM, but it is time-consuming. In this paper, a mixture-modelling-based Bayesian MH-RM (MM-MH-RM) algorithm is proposed for the M4PLM to obtain the maximum a posteriori (MAP) estimates. In a comparison of the MM-MH-RM algorithm to the original MH-RM algorithm, two simulation studies and an empirical example demonstrated that the MM-MH-RM algorithm possessed the benefits of the mixture-modelling approach and could produce more robust estimates with guaranteed convergence rates and fast computation. The MATLAB codes for the MM-MH-RM algorithm are available in the online appendix.

KW - MAP

KW - MM-MH-RM

KW - estimation

KW - mixture modelling

KW - multidimensional 4PL

UR - https://www.scopus.com/pages/publications/85163065391

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ER -

Mixture-modelling-based Bayesian MH-RM algorithm for the multidimensional 4PLM

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Keywords

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