Guo Shaoyang, Wu Tong, Zheng Chanjin, Chen Yanlei
East China Normal University, Shanghai, China.
Purdue University, West Lafayette, IN, USA.
Appl Psychol Meas. 2021 May;45(3):195-213. doi: 10.1177/0146621621990761. Epub 2021 Feb 8.
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.
在项目反应理论（IRT）中，对于样本量适中的单参数基于逻辑能力的猜测（1PL - AG）模型进行校准，仍然是一项挑战，因为其估计值不合理且难以获得估计的标准误差。本文提出了一种替代的贝叶斯模态估计（BME）方法，即贝叶斯期望最大化 - 最大化（BEMM）方法，该方法是通过将1PL - AG模型的增广变量公式与三参数逻辑模型（3PLM）的混合模型概念相结合而开发的。通过与JAGS中的边际最大似然估计（MMLE）和马尔可夫链蒙特卡罗（MCMC）进行比较，模拟表明BEMM在样本量适中的情况下能够产生稳定且准确的估计值。本文还提供了一个实际数据示例以及BEMM的MATLAB代码。
