Yigit Hulya D, Douglas Jeffrey A
University of Illinois at Urbana-Champaign, USA.
Appl Psychol Meas. 2021 May;45(3):143-158. doi: 10.1177/0146621621990746. Epub 2021 Feb 15.
In learning environments, understanding the longitudinal path of learning is one of the main goals. Cognitive diagnostic models (CDMs) for measurement combined with a transition model for mastery may be beneficial for providing fine-grained information about students' knowledge profiles over time. An efficient algorithm to estimate model parameters would augment the practicality of this combination. In this study, the Expectation-Maximization (EM) algorithm is presented for the estimation of student learning trajectories with the GDINA (generalized deterministic inputs, noisy, "and" gate) and some of its submodels for the measurement component, and a first-order Markov model for learning transitions is implemented. A simulation study is conducted to investigate the efficiency of the algorithm in estimation accuracy of student and model parameters under several factors-sample size, number of attributes, number of time points in a test, and complexity of the measurement model. Attribute- and vector-level agreement rates as well as the root mean square error rates of the model parameters are investigated. In addition, the computer run times for converging are recorded. The result shows that for a majority of the conditions, the accuracy rates of the parameters are quite promising in conjunction with relatively short computation times. Only for the conditions with relatively low sample sizes and high numbers of attributes, the computation time increases with a reduction parameter recovery rate. An application using spatial reasoning data is given. Based on the Bayesian information criterion (BIC), the model fit analysis shows that the DINA (deterministic inputs, noisy, "and" gate) model is preferable to the GDINA with these data.
在学习环境中，了解学习的纵向路径是主要目标之一。用于测量的认知诊断模型（CDM）与掌握程度的转换模型相结合，可能有助于提供有关学生知识概况随时间变化的细粒度信息。一种估计模型参数的有效算法将增强这种组合的实用性。在本研究中，提出了期望最大化（EM）算法，用于估计学生的学习轨迹，测量部分采用广义确定性输入、噪声“与”门（GDINA）及其一些子模型，学习转换采用一阶马尔可夫模型。进行了一项模拟研究，以考察该算法在样本量、属性数量、测试中的时间点数和测量模型复杂度等几个因素下估计学生和模型参数的准确性。研究了属性和向量级别的一致率以及模型参数的均方根误差率。此外，记录了收敛的计算机运行时间。结果表明，在大多数情况下，参数的准确率相当可观，且计算时间相对较短。仅在样本量相对较小且属性数量较多的情况下，计算时间会随着参数恢复率的降低而增加。给出了一个使用空间推理数据的应用示例。基于贝叶斯信息准则（BIC）的模型拟合分析表明，对于这些数据，确定性输入、噪声“与”门（DINA）模型比GDINA模型更优。
