Marginalized maximum a posteriori estimation for the four-parameter logistic model under a mixture modelling framework.
expectation-maximization algorithm
four-parameter logistic model
marginalized maximum a posteriori estimation
mixture model
Journal
The British journal of mathematical and statistical psychology
ISSN: 2044-8317
Titre abrégé: Br J Math Stat Psychol
Pays: England
ID NLM: 0004047
Informations de publication
Date de publication:
11 2020
11 2020
Historique:
received:
28
11
2017
revised:
17
05
2019
pubmed:
26
9
2019
medline:
28
8
2021
entrez:
26
9
2019
Statut:
ppublish
Résumé
The four-parameter logistic model (4PLM) has recently attracted much interest in various applications. Motivated by recent studies that re-express the four-parameter model as a mixture model with two levels of latent variables, this paper develops a new expectation-maximization (EM) algorithm for marginalized maximum a posteriori estimation of the 4PLM parameters. The mixture modelling framework of the 4PLM not only makes the proposed EM algorithm easier to implement in practice, but also provides a natural connection with popular cognitive diagnosis models. Simulation studies were conducted to show the good performance of the proposed estimation method and to investigate the impact of the additional upper asymptote parameter on the estimation of other parameters. Moreover, a real data set was analysed using the 4PLM to show its improved performance over the three-parameter logistic model.
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
51-82Subventions
Organisme : National Natural Science Foundation of China
ID : 11571069
Organisme : Research Program Funds of the Collaborative Innovation Center of Assessment toward Basic Education Quality
ID : 1804047
Organisme : National Science Foundation
ID : 1659328
Organisme : National Science Foundation
ID : 1712717
Organisme : Jilin Province Science and Technology Department
ID : 201705200054JH
Organisme : Fundamental Research Funds for the Central Universities, and National Science Foundation
ID : 1659328
Organisme : Fundamental Research Funds for the Central Universities, and National Science Foundation
ID : 1712717
Informations de copyright
© 2019 The British Psychological Society.
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