Open AccessBayesian Modal Estimation for the One-Parameter Logistic Ability-Based Guessing (1PL-AG) Model
Author(s) -
Shaoyang Guo,
Tong Wu,
Chanjin Zheng,
Yanlei Chen
Publication year - 2021
Publication title -
applied psychological measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.083
H-Index - 64
eISSN - 1552-3497
pISSN - 0146-6216
DOI - 10.1177/0146621621990761
Subject(s) - markov chain monte carlo , statistics , bayesian probability , maximization , marginal likelihood , mathematics , logistic regression , estimation theory , expectation–maximization algorithm , sample size determination , computer science , econometrics , maximum likelihood , mathematical optimization
The calibration of the one-parameter logistic ability-based guessing (1PL-AG) model in item response theory (IRT) with a modest sample size remains a challenge for its implausible estimates and difficulty in obtaining standard errors of estimates. This article proposes an alternative Bayesian modal estimation (BME) method, the Bayesian Expectation-Maximization-Maximization (BEMM) method, which is developed by combining an augmented variable formulation of the 1PL-AG model and a mixture model conceptualization of the three-parameter logistic model (3PLM). By comparing with marginal maximum likelihood estimation (MMLE) and Markov Chain Monte Carlo (MCMC) in JAGS, the simulation shows that BEMM can produce stable and accurate estimates in the modest sample size. A real data example and the MATLAB codes of BEMM are also provided.