@article{419c1ff9aab247eea761ba26bb006598,
title = "Fast Bayesian Estimation for the Four-Parameter Logistic Model (4PLM)",
abstract = "There is a rekindled interest in the four-parameter logistic item response model (4PLM) after three decades of neglect among the psychometrics community. Recent breakthroughs in item calibration include the Gibbs sampler specially made for 4PLM and the Bayes modal estimation (BME) method as implemented in the R package mirt. Unfortunately, the MCMC is often time-consuming, while the BME method suffers from instability due to the prior settings. This paper proposes an alternative BME method, the Bayesian Expectation-Maximization-Maximization-Maximization (BE3M) method, which is developed from by combining an augmented variable formulation of the 4PLM and a mixture model conceptualization of the 3PLM. The simulation shows that the BE3M can produce estimates as accurately as the Gibbs sampling method and as fast as the EM algorithm. A real data example is also provided.",
keywords = "4PLM, BE3M, BME, Gibbs sampler, mixture modeling",
author = "Chanjin Zheng and Shaoyang Guo and Kern, {Justin L.}",
note = "The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was partially supported by the Flower of Happiness Project in social science of East China Normal University (2020ECNU-XFZH007, 2019ECNU-XFZH015) and the Peak Discipline Construction Project of Education at East China Normal University. The 4PLM is applied to bullying items collected as part of the 2005 to 2006 Health Behavior in School-Aged Children study () funded by the National Institute of Child Health and Human Development. This real data example was chosen to replicate previous results (), and to demonstrate comparability between BE3M and the MCMC approaches (fourPNO package and “bayesmh” module in Stata) in terms of estimation accuracy and BE3M{\textquoteright}s advantage in terms of estimation time. The prior settings for the “bayesmh” module in Stata are the same as those for BE3M and BME in the simulation studies. To further compare BE3M with BME, items were also calibrated with BME in the mirt package. In addition, as we have discussed in the introduction, there is no available SEs for all item parameters in the mirt package because the Beta priors (“expbeta” in mirt) were imposed on the guessing and slipping parameters in this example.",
year = "2021",
doi = "10.1177/21582440211052556",
language = "English (US)",
volume = "11",
journal = "SAGE Open",
issn = "2158-2440",
publisher = "SAGE Publications Inc.",
number = "4",
}