A Comparison of Monte Carlo Methods for Computing Marginal Likelihoods of Item Response Theory Models.

TitleA Comparison of Monte Carlo Methods for Computing Marginal Likelihoods of Item Response Theory Models.
Publication TypeJournal Article
Year of Publication2019
AuthorsLiu, Yang, Guanyu Hu, Lei Cao, Xiaojing Wang, and Ming-Hui Chen
JournalJ Korean Stat Soc
Volume48
Issue4
Pagination503-512
Date Published2019 Dec
ISSN1226-3192
Abstract

Nowadays, Bayesian methods are routinely used for estimating parameters of item response theory (IRT) models. However, the marginal likelihoods are still rarely used for comparing IRT models due to their complexity and a relatively high dimension of the model parameters. In this paper, we review Monte Carlo (MC) methods developed in the literature in recent years and provide a detailed development of how these methods are applied to the IRT models. In particular, we focus on the "best possible" implementation of these MC methods for the IRT models. These MC methods are used to compute the marginal likelihoods under the one-parameter IRT model with the logistic link (1PL model) and the two-parameter logistic IRT model (2PL model) for a real English Examination dataset. We further use the widely applicable information criterion (WAIC) and deviance information criterion (DIC) to compare the 1PL model and the 2PL model. The 2PL model is favored by all of these three Bayesian model comparison criteria for the English Examination data.

DOI10.1016/j.jkss.2019.04.001
Alternate JournalJ Korean Stat Soc
Original PublicationA comparison of Monte Carlo methods for computing marginal likelihoods of item response theory models.
PubMed ID31929720
PubMed Central IDPMC6953617
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
R01 CA074015 / CA / NCI NIH HHS / United States
R01 GM070335 / GM / NIGMS NIH HHS / United States
Project: