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.

项目响应理论 (IRT) 中基于单参数逻辑能力的猜测 (1PL-AG) 模型的校准具有适度的样本量，这仍然是其不合理的估计和难以获得估计的标准误差的挑战。本文提出了另一种贝叶斯模态估计 (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 模型的增强变量公式和三参数的混合模型概念化相结合而开发的逻辑模型（3PLM）。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，仿真表明 BEMM 可以在适度的样本量下产生稳定准确的估计。还提供了一个真实的数据示例和 BEMM 的 MATLAB 代码。