Suárez-Cansino Joel, López-Morales Virgilio, Morales-Manilla Luis Roberto, Alberto-Rodríguez Adrián, Ramos-Fernández Julio César
Basic Sciences and Engineering Institute, Systems and Information Technologies Research Center, Intelligent Computing Research Group, Autonomous University of Hidalgo State, Col. Carboneras, Mineral de la Reforma 42184, Hidalgo, Mexico.
Department of Software Development, Advanced Computing and Innovation Research Group, Polytechnic University of Tulancingo, Tulancingo 43629, Hidalgo, Mexico.
Entropy (Basel). 2022 Dec 27;25(1):50. doi: 10.3390/e25010050.
To derive a latent trait (for instance ) in a computer adaptive testing (CAT) framework, the obtained results from a model must have a direct relationship to the examinees' response to a set of items presented. The set of items is previously calibrated to decide which item to present to the examinee in the next evaluation question. Some useful models are more naturally based on conditional probability in order to involve previously obtained hits/misses. In this paper, we integrate an experimental part, obtaining the information related to the examinee's academic performance, with a theoretical contribution of maximum entropy. Some academic performance index functions are built to support the experimental part and then explain under what conditions one can use constrained prior distributions. Additionally, we highlight that heuristic prior distributions might not properly work in all likely cases, and when to use personalized prior distributions instead. Finally, the inclusion of the performance index functions, arising from current experimental studies and historical records, are integrated into a theoretical part based on entropy maximization and its relationship with a CAT process.
为了在计算机自适应测试（CAT）框架中推导一个潜在特质（例如），从模型获得的结果必须与考生对一组呈现项目的回答有直接关系。这组项目事先经过校准，以决定在下一个评估问题中向考生呈现哪个项目。一些有用的模型更自然地基于条件概率，以便纳入先前获得的命中/未命中情况。在本文中，我们将获取与考生学业成绩相关信息的实验部分与最大熵的理论贡献相结合。构建了一些学业成绩指标函数来支持实验部分，然后解释在何种条件下可以使用约束先验分布。此外，我们强调启发式先验分布可能并非在所有可能情况下都能正常工作，以及何时应使用个性化先验分布取而代之。最后，将来自当前实验研究和历史记录的性能指标函数纳入基于熵最大化及其与CAT过程关系的理论部分。
