Jian Xiaozhu, Buyun Dai, Yuanping Deng
Educational Department, Guangxi Normal University, Guilin, Guangxi Zhuang Autonomous Region, China.
School of Educational, Jinggangshan University, Ji'an, Jiangxi Province, China.
PLoS One. 2021 Apr 29;16(4):e0250268. doi: 10.1371/journal.pone.0250268. eCollection 2021.
The three-parameter Logistic model (3PLM) and the four-parameter Logistic model (4PLM) have been proposed to reduce biases in cases of response disturbances, including random guessing and carelessness. However, they could also influence the examinees who do not guess or make careless errors. This paper proposes a new approach to solve this problem, which is a robust estimation based on the 4PLM (4PLM-Robust), involving a critical-probability guessing parameter and a carelessness parameter. This approach is compared with the 2PLM-MLE(two-parameter Logistic model and a maximum likelihood estimator), the 3PLM-MLE, the 4PLM-MLE, the Biweight estimation and the Huber estimation in terms of bias using an example and three simulation studies. The results show that the 4PLM-Robust is an effective method for robust estimation, and its calculation is simpler than the Biweight estimation and the Huber estimation.
为减少包括随机猜测和粗心大意在内的反应干扰情况下的偏差，人们提出了三参数逻辑模型（3PLM）和四参数逻辑模型（4PLM）。然而，它们也可能会影响那些不猜测或不犯粗心错误的考生。本文提出了一种新的方法来解决这个问题，即基于4PLM的稳健估计（4PLM-Robust），其中涉及一个临界概率猜测参数和一个粗心参数。通过一个示例和三项模拟研究，将该方法与两参数逻辑模型和最大似然估计器（2PLM-MLE）、3PLM-MLE、4PLM-MLE、双权估计和休伯估计在偏差方面进行了比较。结果表明，4PLM-Robust是一种有效的稳健估计方法，其计算比双权估计和休伯估计更简单。
